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Summer Research Fellowship Programme of India's Science Academies

Neutrino sources and detectors

Nandana Rajeev

Mar Athanasius College, Kothamangalam, Ernakulam, Kerala 686666

Prof. Sanjib Kumar Agarwalla

Associate Professor, Institute of Physics, Bhubaneswar, Odisha 751005

Abstract

Neutrino is the most abundant particle in the Universe after photon. They are the only fermion with very tiny mass and no electric charge. They take part in weak interaction where the mediators are W+, W-, and Z° bosons. In the Standard Model of Particle Physics, there are three flavours of neutrinos. For each neutrino flavour, there is also its charged lepton cousin. There exist both natural as well as artificial neutrino sources. As far as natural sources are concerned, we have neutrinos from the Sun (Solar neutrinos), Earth’s atmosphere (Atmospheric neutrinos), the core of the Earth (Geoneutrinos), neutrinos from Big Bang (Relic neutrinos), and neutrinos from AGN and GRB (High energy cosmic neutrinos). We can produce neutrinos in our laboratories such as reactor antineutrinos from reactor power plants, and accelerator neutrinos from pion and muon decay. Various detection techniques are employed to detect solar, atmospheric and artificial neutrinos. The radiochemical experiment was the first one to count the low energy solar neutrinos. The Super Kamiokande is a large water-based detector surrounded by several photomultiplier tubes which helped to detect the Cherenkov radiation emitted by outgoing charged lepton. The Sudbury Neutrino Observatory (SNO) adopts the same technique but use heavy water (D2O) as the target. There are detectors which employed tons of chlorine (Homes take), and gallium (SAGE, GALLEX, GNO) that periodically checked the excess of argon and germanium, which were produced by the reaction of the neutrino with original substance. There was a long-standing solar and atmospheric neutrino anomaly which observes fewer neutrino events as compared to the theoretical prediction. Later these anomalies were addressed with the help of neutrino oscillation phenomenon which demands that neutrinos should have non-degenerative masses and should mix. During my project period, I am looking forward to having detailed knowledge about various neutrino sources and detection techniques. I will also learn the basics of neutrino oscillation and accomplish the knowledge about the possible neutrino source and detector locations available around the world. I will estimate the distance between various source and detector locations and will study how these baselines can be used to extract valuable information about neutrino oscillation.

Abbreviations

Abbreviations
AGN Active Galactic Nuclei  
GRB Gamma Ray Burst
SNO Sudbury Neutrino Observatory
Super K Super Kamiokande Neutrino Observatory
SAGE Soviet-American Gallium Experiment
GALLEX Gallium Experiment
GNO Gallium Neutrino Observatory
LNGS Laboratorial Nazionali del Gran Sasso
IMB Irvine-Michigan-Brookhaven detector
LEP Large Electron-Positron collider
LSND Liquid Scintillator Neutrino Detector
AMANDA Antarctic Muon And Neutrino Detector Array
DONUT Direct observation of the nu tau, E872
KamLAND Kamioka Liquid Scintillator Antineutrino Detector
BICEP Background Imaging of Cosmic Extragalactic Polarization
PTOLEMY Princeton Tritium Observatory for Light, Early-universe Massive-neutrino Yield.
pp Proton-Proton Chain reaction
pep Proton-electron-Proton Chain reaction
hep 3He–proton fusion
CNO Carbon-Nitrogen-Oxygen cycle
SNEWS Supernova Early Warning System
NESTOR Neutrino Extended Submarine Telescope with Oceanographic Research Project
IceCube IceCube Neutrino Detector
BOREXINO Boron Experiment
Homestake Homestake chlorine experiment
J-PARC Japan Proton Acceleration Research Center
CERN The European Organization ,Nuclear Research
FermiLAB Fermination Accelerator Laboratory
RAL Rutherford Appleton Laboratory
NuMI Neutrinos at the Main Injector
MINERVA Main Injector Experiment for v-A
MINOS Main Injector Neutrino Oscillation Search
MINOS+ Upgraded electronics for MINOS
NOVA NuMI Off-Axis νe Appearance
LHC Large Hadron Collider
ATLAS The Argonne Tandem Linac Accelerator System
CMS Compact Muon solenoid experiment
ALICE Accelerators and Lasers In Combined Experiments
LINAC A medical linear accelerator
MiniBooNE Mini Booster Neutrino Experiment
OPERA Oscillation Project with Emulsion-tracking Apparatus
SNO+ SNO with liquid scintillator
T2K Tokai to Kamioka
NEMO Neutrino Mediterranean Observatory
KM3NOT KM3 Neutrino Telescope
INO Iron Calorimeter Detector @ India-based Neutrino Observatory
DUNE Deep Underground Neutrino Experiment
K2K KEK to kamioka

INTRODUCTION

Appearance of Ghost Particle and Pauli's Proposal

After the discovery of radioactivity by Henry Becquerel in 1896, it was believed that the resulting alpha and gamma particles formed from the corresponding decay have an energy distribution that was different from the initial energy. The concept of beta decay is the emission of an electron at the time and the emitted electron should have particular well-defined energy value to conserve energy under the law of conservation of energy. But the energy of an electron for a particular element is a fixed value. This cause to arise the contradiction. The second problem ascend was followed by the law of conservation of momentum (angular momentum). The decaying radioactive element had an integer spin but the emitted electron had a half-spin.

According to early nuclear physics the nuclei made up of electrons and protons, such that ZAX{}_Z^AXcontaining A number of protons and A-Z number of electrons​ undergo β- decay as;

                                                ZAXZ+1AY+e            (1.1.1)                  \begin{array}{l}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{}_Z^AX\rightarrow{}_{Z+1}^AY+e^-\;\;\;\;\;\;(1.1.1)\;\;\;\;\;\;\;\;\;\\\end{array}

Which shows a violation of universal law of conservation of energy and momentum.

betaenergyspectrum.jpg
    Energy spectrum of β- decay, Expected versus observed.

    This puzzle existed mysterious till 1930, and then Wolf Gang Pauli in his famous letter attempted to solve β-decay energy-momentum refutation, by suggesting a new particle in addition to the electron and proton. Atomic nuclei also contained an extremely small and light neutral particle which was termed as “Neutron” by him. He explained his “Neutron” has half-spin angular momentum and has enough energy to resolve the beta decay problem.

    He assumed

                                                    Z  AXZ+1AY+e    +ϑ                                    (1.1.2)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{}_Z^{\;A}X\rightarrow{}_{Z+1}^AY+e^{\;\;}+\vartheta\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(1.1.2)

    This was the correct process, and the final state contains three bodies. This new formulation also guaranteed that energy of the electron will always be less than the parent-daughter nuclei and the remaining energy is carried out by the neutron (Neutrino). But the new ghost particle was not detected at that time. Later in 1931, Enrico Fermi named it ‘Neutrino’ and it was detected finally in 1956 by Clyde Cowan and Frederick Reines.

    What is a Neutrino?

    Neutrinos are so fundamental particles that mean, alike quark and photons it cannot further break down into smaller fragments. Of all particles with mass, neutrinos are the most abundant in nature. Since they don’t interact with matter, 600 trillions of neutrinos pass through our body harmlessly in one second. That is why they are called “Ghost particle”. But in low energies, they feebly react with matter. Neutrinos are elusive but are impossible to detect. They come in three types, called flavors. There are electron (ʋe), muon (ʋµ), and tau (ʋτ) neutrinos and the existing corresponding antiparticles differ from neutrinos by lepton number and chirality (Neutrinos are left-handed and antineutrinos are right-handed). The strange thing about neutrinos is that they don’t stick on only one flavor, they oscillate and change the flavor. Because when the produced flavor travels through the vacuum, the three mass components of a neutrino travels at different speeds so that their quantum mechanical wave packet produces a phase shift and the superposition occurs. The first experimental discovery of neutrino oscillation by Super-Kamiokande Neutrino Observatory and the Sudbury Neutrino Observatory was recognized with the 2015 Nobel Prize for Physics. Neutrinos almost weigh nothing and travel near the speed of light. But in 1957, when Bruno Pontecorvo explained the solar neutrino problem, with neutrino oscillation, he suggested that neutrinos should have non-zero mass, although we believe that, they have mass 500000 times smaller than the mass of an electron. In most of the particles, mass came from the Higgs field, but neutrino might get their masses from another way.

    History of Neutrino Physics

    Neutrino Physics came to life with the innovation of Radioactivity. Here is the list of some revolutions in this field

    • 1896: Henri Becquerel discovered natural radioactivity.
    • 1897: Discovery of the electron by J J Thomson.
    • 1930: Wolf Gang Pauli postulated the existence of neutral particle, Neutrino to resolve the energy-momentum conservation disputes in β-decay.
    • 1932: Discovery of the neutron by James Chadwick.
    • 1934: Enrico Fermi gave the theory of weak interaction and baptized Pauli’s neutral particle as Neutrino.
    • 1956: Discovery of the neutrino by Clyde Cowan and Frederick Reins using a nuclear reactor.
    • 1962: Discovery of Muon neutrino in Brookhaven National Laboratory.
    • 1968: Launched Homestake experiment detect electron neutrinos produced by the sun.
    • 1978: Discovery of Tau lepton at Stanford Linear Accelerator Center and the existence of it theorized.
    • 1983: Kamiokande becomes operational.
    • 1987: Kamiokande and IMB observed neutrino flux from supernova 1987A.
    • 1989: Kamiokande captured the solar neutrino flux and confirmed the solar neutrino problem by receiving 1/3 of flux over the expected flux of neutrino
    • 1990: IMB confirmed atmospheric neutrino anomaly.
    • 1991: LEP experiment showed that there exist only three light neutrinos.
    • 1994: Neutrino oscillations are seen by the LSND experiment.
    • 1995: Missing solar neutrinos were confirmed by GALLEX on the basics of neutrino oscillation.
    • 1996: AMANDA neutrino telescope observes neutrinos at the Antarctic South Pole.
    • 1998: Revealed the non -zero neutrino mass by Super Kamiokande.
    • 2000: The DONUT collaboration reported Tau type neutrino.
    • 2002: Solution to solar neutrino anomaly by Sudbury neutrino observatory in Canada.
    • 2005: Detection of Geoneutrino by KamLAND.
    • 2012: The most energetic neutrino was observed by IceCUBE experiment.
    • 2015: For detecting atmospheric neutrino oscillation, Takkai Kajitha of the Super Kamiokande experiment and Arthur McDonald of SNO experiment received the 2015 Nobel prize in physics.

    LITERATURE REVIEW

    Natural Neutrino Sources

    The universe is filled with low interacting elementary particle, the neutrino. They contribute about 0.3% of the energy density of the universe, it is more than the contribution of photons. The high energy neutrinos are produced by active galactic nuclei and are considered to be an extragalactic cosmic-ray accelerator and source. The low energy cosmological neutrinos usually relic neutrinos from Big Bang having energy from 0.00001 to 0.0000001 eV still exist around as (330 relic neutrinos per centimeter squared per second).

    energy spectrum of various neutrino sorses - Copy.png
      Energy spectrum of various natural neutrino sources.

      Relic neutrinos

      These are the neutrinos from the Big Bang. They have much to do with the evolution of the universe and cosmology. The evolution of the universe co-operates with cooling and expansion. When the universe was just created, after 0.0000001 seconds, all the fundamental particles were de-coupled and existed in thermal equilibrium.

                                                          γγZ0eeγγ                  (2.1.1)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\gamma\gamma\rightarrow Z^0\rightarrow ee^-\rightarrow\gamma\gamma^-\;\;\;\;\;\;\;\;\;(2.1.1)

      When the temperature started to cool down, then z° bosons and neutrinos de-coupled and developed independently. The rest of the particles like electron, positron, and photon existed still in equilibrium. After 300,000 years the electrons get combined with free-floating nuclei and the transparent universe becomes opaque. When further expansion continued, the temperature started to cool down and the photon acquired the energy of the present day. The Cosmic Microwave Background gives evidence regarding this evolutionary history. WAMP and COBE observed this cosmological background.

      These neutrinos still exist today, with extremely low energy of 0.1 MeV. This makes them difficult to detect because the detectors need to have extremely small threshold energy or otherwise, should be wanted to use cool bodies. About 330 relic neutrinos per centimeter square exist around us. Telescopes such as Plank and BICEP and other experimental techniques such as PTOLEMY are in the mission to calculate the mass of relic neutrinos.

      Geoneutrinos

      Geoneutrinos are produced by the Beta decay of radioactive elements in the core of our earth. Neutrinos were the ultimate messengers. Even if we know the Earth’s crest, knowledge about the Earth’s configuration and uncertainties about Earth’s radioactive content is still a mystery as the floating of celestial bodies on space. When the radioactive elements such as uranium, thorium decay, they produce low energy anti-electron neutrino besides geothermal heat. Geothermal heat is the range of trillion watts responsible for Earth’s magnetic field, the driving force for continental drift, plate tectonics, and convection of Earth mantle.

      In 2005 KamLAND detector detected geoneutrinos with energy greater than 1.8 MeV. The main detection technique, when an antielectron neutrino interacts with a proton in a detector, produces positron and a neutron. The positron undergoes annihilation with electron and produces a flash of light and another flash is produced by the neutron capture. The detector is so sensitive to recognize and to distinguish the flash produced by an anti- electron neutrino.

      The KamLAND data is shown below:

      geo_spectrum.png
        Energy spectrum of geoneutrinos produced by the radioactive decay in the Earth's core

        The black line represents their expected data, colored lines represent geoneutrino flux, and the blue dotted line is their background. The red line represents the geoneutrinos produced from the decay of uranium in the core of the earth, and the green represents the geoneutrino flux from thorium decay. The vertical thick line represents the KamLAND threshold.

        Solar neutrinos

        Most of the neutrinos found in the vicinity of Earth were solar neutrinos. They are produced due to the nuclear fusion process in the core of the sun. Sun generates energy mainly through pp and CNO mechanism. Anti-electron neutrino is produced numerously as this is carried out. About 100 billion neutrinos pass through our thumbnail every second.

        99.8% of the solar output is from the pp chain and only 1.6% is given out by the CNO chain. In the primary reaction of the pp chain, two protons decay into deuterium. 99.7% of the reactions are in this order. In pep chain two protons and an electron decay to deuterium, only 0.23% reactions happened in this modal. The deuterium formed from pp and pep chain fuses with a proton to form heavier helium-3 nuclei and then, Helium-4 nuclei. Helium-3 and Helium-4 together produce Beryllium-7 and gamma-ray. In turn, Beryllium-7 absorbs electron and get transformed into Lithium-7, and accepts a proton and decay to two Helium-4. Beryllium-7 barely reacts with a proton to produce Boron-8, which immediately decays into Helium-4. Only 0.1% of reactions happen in such a manner. The electron neutrino thus produced reach first on earth and eventually heat and light, since neutrino doesn’t interact much.

        600px-Proton_proton_cycle.svg.png
          Solar power generation.

          In the CNO chain, heavier elements like carbon, nitrogen, and oxygen are present as catalysts. It is the main mechanism of energy production in massive stars.

          The main reactions are

                                                            C612+H11N714+γ00            (2.1.2)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;C_6^{12}+H_1^1\rightarrow N_7^{14}+\gamma_0^0\;\;\;\;\;\;(2.1.2)
                                                              N714+H11O815+γ0  0            (2.1.3)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;N_7^{14}+H_1^1\rightarrow O_8^{15}+\gamma_{0\;}^0\;\;\;\;\;\;(2.1.3)
                                                              N713C613+e10+γ00              (2.1.4)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;N_7^{13}\rightarrow C_6^{13}+e_1^0+\gamma_0^0\;\;\;\;\;\;\;(2.1.4)
                                                                C613+H11N714+γ00                (2.1.5)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;C_6^{13}+H_1^1\rightarrow N_7^{14}+\gamma_0^0\;\;\;\;\;\;\;\;(2.1.5)
                                                              O815N715+e01+ϑ00              (2.1.6)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;O_8^{15}\rightarrow N_7^{15}+e_0^1+\vartheta_0^0\;\;\;\;\;\;\;(2.1.6)
                                                                N715+H11C612+He24                  (2.1.7)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;N_7^{15}+H_1^1\rightarrow C_6^{12}+He_2^4\;\;\;\;\;\;\;\;\;(2.1.7)

          Through this mechanism, they only produce two neutrinos with energy ranging from 1.2 to 1.4 Mev. The scientist who looked for these neutrinos in the 1960s found an interesting fact that 2/3 of the expected low energy solar neutrinos were missing. The detection started with Homestake experiment by Ray Davis using a cleaning fluid called perchloroethylene, at an underground gold mine in South Dakota gold mine. They observed 7Be pp neutrinos with 5 MeV energy. Ray Davis’ partner John Bahcall predicted neutrino flux from the sun and later, from various detection experiments, presented a spectrum for solar neutrinos.

          john behcall_1.gif
            Solar neutrino flux diagram

            The figure shows that only gallium experiments detect pp solar neutrinos and the other experiments using chlorine and the famous Super Kamiokande, and Sudbury Neutrino observatory only observed 7Be, 8B, and pep solar neutrinos.

            In 1989 Kamiokande experiment in Japan, a pure water detector observed more solar neutrinos but, still a fraction of neutrinos was missing. SNO using heavy water as a medium and SAGE/GALLEX/GNO, using gallium, also reached on this assumption. This discrepancy in solar flux data is called solar neutrino anomaly and it revealed neutrino flavor oscillation, which was not explained by the standard model of particle physics at early time. Since the neutrino doesn’t interact with matter they reach first on the Earth’s surface. Using this fact the Borexino experiment found that sun-generated the same amount of energy of today as it had produced 100000 years ago.

            Atmospheric neutrinos

            Atmospheric neutrinos are produced above 15 Km from Earth's crust by the collision of the cosmic ray with free-floating nuclei on earth's atmosphere. Cosmic ray mainly consists of high energy proton, heavy nuclei, and other particles from cosmology. When they collide with atmospheric nuclei, they produce hadrons that are unstable and produce muons and in turn produce electron neutrino, electron, and a muon neutrino.

            cosmic-rays-c.jpg
              Atmospheric neutrinos
                                                                          π+μ++ϑμ                  (2.1.8)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\pi^+\rightarrow\mu^++\vartheta_{\mu\;}\;\;\;\;\;\;\;\;(2.1.8)
                                                                    μ+e+ϑe+ϑμ            (2.1.9)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mu^+\rightarrow e+\vartheta_e+\vartheta_\mu^-\;\;\;\;\;\;(2.1.9)
                                                                πμ+ϑμ                  (2.1.10)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\pi^-\rightarrow\mu^-+\vartheta_\mu^-\;\;\;\;\;\;\;\;\;(2.1.10)
                                                                μe+ϑe+ϑμ              (2.1.11)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mu^-\rightarrow e^-+\vartheta_e^-+\vartheta_\mu\;\;\;\;\;\;\;(2.1.11)

              A group of particle physicist from Tata Institute of Fundamental Research (India), Oska, City University (Japan), and Durham University (UK) recorded the first cosmic ray neutrino interaction in an underground laboratory in Kolar Gold Mines, in India, 1965 .The energy of muon neutrino produced varies from 1 GeV to 100 GeV. At moderate energy, we expect to have a ratio .

                                                                  R=(ϑμϑe)DATA(ϑμϑe)SIM                  (2.1.12)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;R=\frac{{\left({\displaystyle\frac{\vartheta_\mu}{\vartheta_e}}\right)}_{DATA}}{{\left({\displaystyle\frac{\vartheta_\mu}{\vartheta_e}}\right)}_{SIM}}\;\;\;\;\;\;\;\;\;(2.1.12)

              R is believed to have the value 2 with 5% uncertainty. Water Cherenkov and tracking calorimeter were the main detecting techniques employed to detect atmospheric neutrino. These atmospheric neutrinos can be detected in every direction. The ratio between the number of muon neutrino and electron neutrino, both from data and observation co-operates with the neutrinos comes down to the detector and the neutrino comes up to the detector by traveling 1300 Km showing a discrepancy, they always give value less than one. This is called atmospheric neutrino anomaly. This is due to the oscillation of neutrino from muon flavor to another.

              In addition to R-value, the Super Kamiokande experiment measured the electron and muon neutrino pathway distribution (zenith angle) and the direction of neutrino. They barely covered 54000 muon neutrino events which were less than the expected. From the plots of zenith angle distribution, it is clear that neutrinos travel more distance like upcoming neutrinos to the detector undergo oscillation and the neutrinos travel down to the detector matches up with expectation.

              atm.gif
                A diagram of an atmospheric neutrino experiment.

                A detector near the surface sees neutrinos that travel about 15 km looking up, while neutrinos arriving at the detector from below can travel up to 13000 Km. This distance is measured by the “zenith angle”; the polar angle as measured from the vertical direction at the detector: cosθzen = 1 is for neutrinos coming directly down, whereas cosθzen = −1 describes upward-going neutrinos.

                The experimental results from Super Kamiokande can give a better explanation to the atmospheric neutrinos produced and about their propagation. In figure 8, the left plots shows electron like events and right shows muon like events. The top and middle are for low energy events and the middle for energy less than 1 GeV, and in bottom figures, the energy is greater than 1 Gev. The red line shows the expectation and the dotted black line represent the Super Kamiokande events.

                a11fig01_1.gif
                  Atmospheric neutrino data from Super Kamiokande experiment.

                  From figure,

                  •  The muon-like sub-GeV events are always less than expected, the reduction in the flux is due to the negative cos θ value, i.e. upcoming events.
                  •  The muon like multi-GeV events matches with the expected rate for cos θ > 0 (downgoing events), where a significant reduction in flux is observed for the upcoming neutrinos.

                  Thus, the main observation is that the upcoming muon neutrinos suffer a decrease in flux since these neutrinos have to travel through much greater distances (∼ 10000 Km as opposed to ∼ 10 Km for down going neutrinos), this indicates that the reduction of neutrinos has a dependence on the distance traveled by them. From the low energy plots, it is clear that half of the muon like interactions are missing. This further indicates flavor oscillation.

                  Supernova neutrinos

                  The last stellar event of a massive star is called a supernova, which produces a huge number of neutrinos of all flavor around the universe. The thermonuclear explosion of a white dwarf or core-collapse of massive star leads to the event. The core process in star for energy generation is hydrogen fusion. When they run out, it leads to their contraction. The star starts to heat up and the helium formed by the burning of hydrogen starts burning and becomes a red giant. After 10,000 years when helium runs out, the CNO cycle begins and the heating up continues with heavier by-products. At low temperature, hydrogen fuses with helium and moves out and form an onion-like structure. In the end, the massive star eventually reaches a stage in which silicon in the core fuses to form iron, and only iron is left behind. Then these stars generate energy mostly in the form of neutrinos, but not as photons. And with time the iron core collapses by high electron degeneracy. Initially, the emission of neutrinos was simultaneous and continuous, but it got ceased when density increased, besides they got imprisoned and were called neutrino sphere. At this stage, shock wave propagates out of the star and interact with neutrino sphere. Periodically the star composed of a core and outer part undergoes an explosion. 99% of the energy is emitted in the form of neutrino, after the collision, the core also produces neutrinos of energy 10-30 MeV.

                  The burning phases of a massive star on its way to a Supernova

                  Fuel

                  T(K)

                  Burning Time

                  Cooling Process

                  H

                  He

                  C

                  Ne

                  O

                  Si

                  0.02

                  0.2

                  0.8

                  1.5

                  2.0

                  3.5

                  10,000,000years

                  50,000 years

                  600 years

                  1 year

                  180 days

                  1 day

                  Photons,Neutrinos

                  Photons,Neutrinos

                  Neutrinos

                  Neutrinos

                  Neutrinos

                  Neutrinos

                  The last supernova event was occurred in 1985 nearby Galaxy, Magellanic cloud, around 150000 light-years apart from our planet. We can observe about 5000 to 8000 events in a supernova but we have only observed 25 on that occurrence.

                  supernova events.png
                    Supernova Neutrinos observed in 23 Februvary 1987.

                    Since supernova is certain, now there exists a network of neutrino experiments called SNEWS. If two detectors observe the large pulse of neutrinos at the same time, it will provide astronomers that information and they can turn their telescope to that particular direction and can collect information. The neutrinos from supernova provide large information about the dark matter and the evolution of the universe.

                    Cosmic neutrinos

                    The neutrinos from the alien sources as well as from another universe can serve as wild knowledge about the atmosphere around there and the information about the undetected stars. This gives importance to Neutrino Astrophysics.

                    Even if we observe high energy neutrinos from the cosmos, the actual source is still a mystery. Some of the detected sources are;

                    1. Black holes, Quasars, Blazers

                    They are active galactic nuclei with ionized matter traveling in the speed of light. When they try to suck in too much matter at once, it can cause jets of particle ejected outward in ultra-realistic speed. They initially produce cosmic rays, then it decays to the neutrino.

                    2. Pulsars

                    They are denser core, leftover after a supernova with a mass of the sun and spins 100 times per second. They produce neutrinos of all flavors.

                    3. Gamma-ray burst

                    It is the most violent energy produced. It will produce neutrino when a cosmic ray proton interacts with the target photons, produced in the prompt gamma-ray emission expected to be created by internal shocks.

                    4. AGN (Active Galactic nucleus)

                    They are believed to be an extragalactic cosmic-ray accelerator and source associated with high energy neutrino and hadronic gamma-ray emission. Roughly 1% of all bright galaxies contain an active core that emits energy with power more than that radiated by the Milky Way. This core is generally concentrated in a region with a size around a solar system. This radiation is thought to come from the gravitational release of energy associated with accelerating super-massive black holes and can be directed in jets with powerful shock accelerations.

                    agn.png
                      Generation of neutrinos from AGN jet.

                      This high energy cosmic neutrinos from various sources detected by ice cube experiment using the neutrino telescope made of tonnes of Antarctic ice. MAGIC and VERITAS were other experiments that look for these peta-electronvolts neutrinos. The Ice cube experiment observed such kinds of neutrinos in September 2017 which had energy 45 times greater than the large hadron collider in the earth. The blazar TXS 0506+056 observed has a high luminosity than a gamma-ray. If we have used the water Cherenkov technique to detect them then a part of the ocean or part of ice cubes in Antarctica must have been the interacting medium. The detecting experiments such as ANASTERS, NESTOR, and Baikal in Russia are under construction using a clean and transparent water body as the medium.

                      Artificial Neutrino Sources

                      We can create neutrinos in our laboratory artificially by the beta decay process. Reactor anti-electron neutrinos are born in a process called beta decay, which happens inside the atomic nucleus. Reactor experiments, much like accelerator experiments that produce muon like neutrinos, can position their detectors at a range of distances from the source to the reactor. Detectors placed at a variety of distances (called short-, middle-, or long-baseline experiments) give neutrinos different opportunities to oscillate and provide valuable information about how neutrinos change over that interval.

                      Reactor neutrinos

                      In 1956 by Cowan and Reins neutrino experiment, Reactor-neutrinos for the first time in history was detected. The experiment exploited a huge flux of anti-neutrinos emitting from the nearby nuclear reactor and a detector consisting of a large amount of water. It is observed that there is the interaction of neutrinos with the proton in water. Mostly the detected neutrinos are anti-electron neutrinos. These neutrinos undergo inverse beta decay and the produced positrons annihilate and produce a flash of light and another flash of light is emitted by neutron capture.

                      Usually, the neutrinos produced by reactors were captured in various detectors at different places (long baseline and short baseline) to study the neutrino oscillation, mixing angle and some parameters. Theta one-three is an observed parameter, it is the mixing angle between two mass states (say mass states one and three) which explains how different mass States are connected together. Bombardment of a particle with radioactive, unstable uranium or plutonium leads to the breakdown of particles into small fragments and subsequently undergo beta decay, most of the energy generated is in the form of neutrinos. But neutrinos won’t undergo radiation themselves. Neutrinos are produced in large numbers and the prediction of the flux is easier in reactors than accelerators. The reactor neutrinos are captured by inverse beta decay.

                                                                        ϑe+pe++n                  (2.2.1)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\vartheta_e+p\rightarrow e^++n\;\;\;\;\;\;\;\;\;(2.2.1)

                      Accelerator neutrinos

                      The efficient way to explore the elusive particle, neutrino, is by producing a neutrino beam. We collectively use proton accelerators to produce them. But only a few places around the world managed to produce neutrino by the accelerator. Japan proton acceleration research center (JPARC), The European organization, Nuclear Research (CERN), Fermination Accelerator Laboratory (FermiLAB), Rutherford Appleton laboratory UK, (RAL) are some accelerators around the world. The proton is accelerated to the speed of light and produces a muon, subsequently a neutrino and an antineutrino. Usually, a bottle of hydrogen is used as the proton. When the accelerated proton smashes with the target, generally beryllium or graphite, create a kaon or short-living pion. Pion has a charge so that the magnetic fields can separate them and focus on a particular charge and can produce neutrino and antineutrino separately. Other by-products formed are absorbed using big blocks of aluminum, concrete or steel.

                      Neutrino_beamline.jpg
                        Neutrino Beam line

                        1. Target

                        The target material has the capacity to withstand the incoming accelerated proton and to produce meson. The target must be long enough to capture the proton interaction and small enough to minimize the meason creation. In NuMI the carbon plates are used as a target.

                        target.jpg
                          Photograph of NuMI target.

                          2. Decay pipe

                          The decay pipe is a tunnel in which the decay of meson happens. The length of the decay pipe is a function of the probability of decay to happen.

                                                                            P=1eLDL0                  (2.2.2)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;P=1-e^\frac{LD}{L_0}\;\;\;\;\;\;\;\;\;(2.2.2)

                          LD is the length of the decay pipe and L0 is the length of the pion decay. Greater the length of the decay pipe greater will be the decay and neutrino flux. The decay pipe can have a length up to 1 Km.

                          3. Energy spectrum

                          The accelerated proton can produce neutrino of energy 10 MeV to 100 MeV. In two body decay the Ev and Qv in lab frame can be related to meson frame.

                          EV=γEV(1+βcos(θ))        (2.2.3)E_V=\gamma E_V^\ast(1+\beta\cos\left(\theta^\ast\right))\;\;\;\;(2.2.3)

                          cos(θ)=  cos(θ)1+βcos(θ)              (2.2.4)\cos\left(\theta\right)=\frac{\;\cos\left(\theta^\ast\right)}{1+\beta\cos\left(\theta\right)}\;\;\;\;\;\;\;(2.2.4)

                          β=PMEM          γ=EMPM                EV=Mm2Mμ22Mμ              (2.2.5)\beta=\frac{P_M}{E_M}\;\;\;\;\;\gamma=\frac{E_M}{P_M}\;\;\;\;\;\;\;\;E_V^\ast=\frac{M_m^2-M_\mu^2}{2M_\mu}\;\;\;\;\;\;\;(2.2.5)

                          The cosθ can have maximum and minimum value ±1

                          For minimum energy

                          EVmin=EMPM  (Mm2Mm22mμ)  (1PmEm)                      =(Mm2Mμ22(Em+Pm))(Mm2Mμ24EM)\begin{array}{l}\begin{array}{l}E_{Vmin}=\frac{E_M}{P_M}\;\left(\frac{M_m^2-M_m^2}{2m\mu}\right)\;\left(1-\frac{P_m}{E_m}\right)\\\;\;\;\;\;\;\;\;\;\;\;=\left(\frac{M_m^2-M_\mu^2}{2\left(E_m+P_m\right)}\right)\sim\left(\frac{M_m^2-M_\mu^2}{4E_M}\right)\\\end{array}\\\\\end{array} (2.2.6)

                          For maximum energy

                          EVmax=EMPM(Mm2Mμ22mμ)(1+PMEM)                      Mm2Mμ2Mm2EM\begin{array}{l}E_{Vmax}=\frac{E_M}{P_M}\left(\frac{M_m^2-M_\mu^2}{2m\mu}\right)\left(1+\frac{P_M}{E_M}\right)\\\;\;\;\;\;\;\;\;\;\;\;\sim\frac{M_m^2-M_\mu^2}{M_m^2}E_M\end{array} (2.2.7)

                          If we consider E=P\left|E\right|=\left|P\right|

                          Then, the lower energy part of the beam must be from pion and the higher energy part must be from Kaon. It is later then proved that, in lab frame the energy of θ angle is merely equal to the energy maximum.

                          EV(θv)EVmax11+γ2θv2                (2.2.8)E_V\left(\theta_v\right)\sim E_{Vmax}\frac1{1+\gamma^2\theta_v^2}\;\;\;\;\;\;\;\;(2.2.8)

                          There can be produced two types of beams based on the magnetic focusing on it.

                          Wide band beams: In wideband beams, they use magnetic horns, usually metal plates magnetized by electricity. Here the diverging meson beam gets transformed into parallel beams using a lens system. In some cases, more than one magnetic horn is needed to focus the beam, but often it is installed behind the horn to recorrect the beam (reflector). The advantage of the wideband beam is the production of a large amount of neutrino flux. But the determination of the energy spectrum of the neutrino is difficult. The energy spectrum obtained here is the combined meson spectrum from the different radius and longitude along the beam axis. To predict a clear neutrino spectrum, the proton collision must be down to the detector.

                           Narrow beam bands: In the narrow beam band, we use a combined magnetic channel focused on a particular beam with specific charge and momentum. Only the selected momentum will be decay in the pipe. So, higher energy beam decay at the bottom of the decay pipe. The energy of the neutrino observed is a function of the radial distance from the neutrino beam axis. There must be two regions in the beam, the lower energy pion beam, and the higher energy kaon beam.

                          The advantage of a narrow beam band is that it can give an accurate clear spectrum of a neutrino with energy as a function of radial distance from the axis with small distractions from the other meson. The disadvantage is that most of the mesons produced must be removed by the magnetic channel so the produced neutrino flux will be very low.

                          3 Off axis beam: To study the neutrino oscillation, we want a monochromatic neutrino beam. If Qv is small, then we can observe only low energy pion beam, with energy ranging from MeV. If we go for off-axis we can observe the beam in another axis.

                          Neutrino-energy-as-a-function-of-the-pion-momentum-for-different-thOAs - Copy.png
                            Neutrino energy as a function of pion momentum at different angles.

                            One of the ways to do this is to go off-axis. That is, to position the experiment, but inclining an angle to the beam axis. We know that the neutrino energy from meson decay as a function of angle is

                            EV(θv)    EVmax11+γ2θv2    0.43Eπ1+γ2θv2                  (2.2.9)E_V(\theta_v)\;\sim\;E_{Vmax}\frac1{1+\gamma^2\theta_v^2}\;\sim\;\frac{0.43E\pi}{1+\gamma^2\theta_v^2}\;\;\;\;\;\;\;\;\;(2.2.9)

                            Where γ=EπMπ on the beam-axis, EV0Eπ.As one moves away from the axis, the neutrino energy spectrum turns over and becomes almost flat as shown in the above figure. If we put a detector at 2 degrees off-axis, the neutrino spectrum becomes monochromatic with an energy of 700 MeV.

                            Some accelerators around the world

                            FermiLAB  

                            NuMI neutrino beamline
                            The high energy proton beam produced here collides with the carbon target, and the produced pions and kaons are focused using magnetic horns. The pion decay into muons and neutrinos in the helium-filled decay volume, the hadron monitors measures the spatial distribution of unaffected mesons and protons, and absorb them by the hadronic absorber. The muon doesn’t get absorbed and continues to the rock, the neutrino which is unaffected by the rock travel beyond it and reaches the far detector at northern Minnesota. MINUS, MINoS+ and ArgoNUAT are the finished operations using NuMI neutrino beamline and NOVA, MINERVA and Lariat are operating still now to solve the mass hierarchy tests of three flavor mixing and supernova neutrinos.

                            Discoveries of J-FermiLAB;

                            • 1964 : Discovery of the existence of Higgs Boson.
                            • 1977 : Discovery of the bottom quark.
                            • 1993 : Observation of origins of high- energy cosmic rays.
                            • 1995 : Discovery of the top-quark .
                            • 1998 : Confirming evidence of dark energy.
                            • 1999 : Observation of direct CP violation in kaon decays.
                            • 2000 : Observation of tau neutrino.
                            • 2000 : Discovery of a quasar at a distance of 27 billion light-years.

                            1. CERN

                            The Large Hadron Collider (LHC) is the world's most powerful particle accelerator. It started operating on 10 September 2008. It contains 28 Km long accelerator ring. Inside the collider tube, they created an ultra-vacuum, and two particles merely at the speed of light in separate pipes are made to approach each other. The pipes are guided inside the accelerator ring and inside the accelerator ring, they maintain a magnetic field with superconducting electromagnets. These particles collide at four positions before the collision, they change the magnetic field around it to the 'squeeze', so that the beam is converged to increase the chance of collision. The four collisions are detected by the corresponding four detectors such as ALTAS, CMS, ALICE, and LHcd.

                            Discoveries of CERN

                            •      1973: The discovery of the neutral current.
                            •    1983: The discovery of W and Z bosons.
                            • 1989: The determination of the number of light neutrino families at the Large Electron-Positron Collider (LEP) .
                            • 1999: The discovery of direct CP violation.​
                            • 2011: Maintaining anti-hydrpgen for over 15 minutes.
                            • 2012: A boson with mass around 125 GeV/c2 consistent with the long-sought Higgs boson.

                            2. J-PARC

                            J-PARC accelerator consists of three accelerators namely LINAC (400MeV), Rapid cycling synchrotron (3 GeV), and main ring synchrotron (30 GeV). Each experiment supplies the high-class proton beam to the material and life science exterminate facility, the hadron experimental facility in each experimental techniques, the secondary particle-like kaons, pions, and muon neutrinos are produced by colliding with gold, mercury, and carbon target.

                            Detectors

                            Since neutrinos are neutral and only undergo weak interaction via virtual w+, w- and z° bosons, and have insignificant mass, it is difficult to detect them by normal detection techniques. We employ detection techniques accordingly with the property of the particle which is to be detected. Since neutrinos don’t show any variation in a magnetic field and don’t undergo any strong interaction, the only technique to detect them was by tracking the trace they left behind after a weak interaction.

                                                                                                                    ϑ+pe++n          \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\vartheta+p\rightarrow e^++n\;\;\;\;\;

                            Here the positron produced undergo annihilation with electron and produce a flash of light and the neutron can be captured. If we reconstruct these tracks, we can understand the presence of electron neutrino and can even recognize that the relation is inverse beta decay, by the analysis of the kinematics of the final state. So, we want to build a low mass detector with extremely fine tracking capability, since the cross-section of the neutrino is very small. Thus, we want to build a detector with high mass, the detector that we want to build up depends on certain factors such as the number of events we want to perform, which kind of interaction should happen, what amount of money and time should be spending, what would be the final state and background. Often it is very difficult to build a detector according to these factors.

                            Usually, detectors are built underground to isolate them from cosmic radiation and other background radiation. Various detection techniques have been used. Super Kamiokande using water as a targeting medium, Sudbury neutrino observatory using heavy water as an interacting medium, MINOS using plastic scintillator, NOVA using an avalanche of photodiodes, Borexino using pseudocmene scintillator. Also, experiments using chlorine, germanium and radiochemical experiments have been used. Using the thermoacoustic effect, ANTARES, ice cube, KM3NOT are collaborators used to detect neutrinos.

                            Radiochemical Technique

                            It is the first experiment to capture low energy solar neutrino. In the radiochemical technique, neutrinos are captured by the weak interaction, say, beta decay process. When a neutrino interacts with a target nuclei, it will produce a daughter nuclei with a new proton number.

                                                                                      ϑ+(A,Z)e+(A,Z+1)                (2.3.1)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\vartheta+\left(A,Z\right)\rightarrow e^-+\left(A,Z+1\right)\;\;\;\;\;\;\;\;(2.3.1)

                            For the detection of the daughter nuclei, very sensible radiochemical interactions are employed, since the neutrino interaction cross-section is very small, say less than 0.00001 cm2. This detection technique is built underground to prevent interaction with cosmic rays, unless, there appears a large amount of proton in the final stage of the detector. Several radiochemical techniques have been running with a different target such as gallium, chlorine, molybdenum, lithium, bromine, and tantalum.

                            Radiochemical neutrino detectors.
                            Neutrino capture on targetThreshold energyComments
                            Chlorine0.814 MeV“Successful”
                            Gallium0.233 MeV“Successful”
                            Iodine789 MeVPrototype only
                            Molybdenum>1.79 MeV“Unsuccessful”
                            Lithium0.862 MeVR&D only
                            Bromine0.470 MeVR&D only
                            Tantalum0.054 MeVR&D only

                            The radiochemical detection method is large and cheap, but we can only collect the neutrino flux produced periodically and not valuable information such as energy, mass, and properties.

                            Homestake

                            Homestake is a neutrino capture experiment using chlorine as targeting medium located in South Dakota gold mine. It was built by Ray Davis in 1965. The detection tank is filled with 615 tons of chlorine with tetrachloroethylene. When a neutrino interacts with chlorine via charged current interaction with a threshold of 814 KeV it produces radioactive argon.

                                                                                    37Cl+ϑe37Ar+e                (2.3.1)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{}^{37}Cl+\vartheta_e\rightarrow{}^{37}Ar+e^-\;\;\;\;\;\;\;\;(2.3.1)

                            Detection utilizes the decay of argon and produces x-ray of 2.8 KeV.

                                                                                    37Ar37Cl+e+ϑe                (2.3.2)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{}^{37}Ar\rightarrow{}^{37}Cl+e^-+\vartheta_e^-\;\;\;\;\;\;\;\;(2.3.2)

                            At the end of detection, the tank should be filled with argon. The fluid is cleaned with helium gas which removes the argon. Then this helium is cooled, and the argon is separated by taking 60 days. The detector takes 2 days to observe the decay of a single argon atom.

                            After several years of running, Homestake captured average solar neutrino flux of 2.56 ± 0.25 SNU, but the standard model of particle physics prediction was 8.1 ± 1.3 SNU. This discrepancy in the measure of solar neutrino flux is called a solar neutrino anomaly. Homestake only captured pep and hep anti-electron solar neutrinos.

                            SAGE/GALLEX/GNO

                            These are three radiochemical detection techniques using gallium as targeting medium which captures the flux of neutrinos by counting the germanium decay, where germanium is formed from the interaction between neutrino and gallium.

                                                                                    71Ga+ϑe71Ge+e              (2.3.3)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{}^{71}Ga+\vartheta_e^-\rightarrow{}^{71}Ge+e^-\;\;\;\;\;\;\;(2.3.3)

                            With threshold 0.233 MeV. Neutrinos were detected by measuring the radioactive decay of germanium to gallium.

                                                                                    71Ge+71Ga+e+ϑe              (2.3.4)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{}^{71}Ge+\rightarrow{}^{71}Ga+e^-+\vartheta_e\;\;\;\;\;\;\;(2.3.4)

                            The detection technique is also nicknamed as Alsace-Larraine (since the cycle is in the model of gallium-germanium-gallium). These three gallium experiments measured pp solar neutrino flux and also found the discrepancy in the observed data and predicted data. The SAGE in Russia, running with 59 tons of gallium measured 70.8 ± 5.0 SNU with the prediction of 129 ± 9 SNU. The GALLEX and GNO running with 30 tons of gallium measured 77.5 ± 85 SNU. A 40 % decrease in the observed neutrino flux was found when compared to prediction. This mismatch phenomenon was called the solar neutrino problem and it revealed neutrino flavor oscillation.

                            Cherenkov Detector

                            Cherenkov detector makes use of the Cherenkov radiation emitted by the passage of a charged particle through a targeting medium, nearly with the speed of light. In Cherenkov detectors, they use clear material like water and ice as medium surrounded by a light-sensitive photomultiplier which produces a characteristic ring for each particle. When a neutrino interacts with nuclei in the medium, they produce charged lepton and making use of this information we can find out the energy, flavor, and properties of the neutrino.

                            In the case of a water Cherenkov detector, the Cherenkov radiation cone is aligned in the direction of the particle and has an opening angle which is the function of the velocity and refractive index of the medium.

                            cosθc=1nβ               β=νc
                            chrenkov radiation.jpg
                              Cherenkov radiation and cherenkov cone.

                              The light sensors produce a circle for each particle in the detector monitor. A fuzzy ring will appear for electromagnetic particles and a rigid ring for muon like particle.

                              t2ksk-events.jpg
                                Rings observed for muon and electron like particle in Super Kamiokande( Right figure shows the nature of muon type particles and left shows the nature of electron like particles).

                                The water medium, Super Kamiokande, and IMB measured around 25 supernova neutrino events from the last explosion. The disadvantage of a Cherenkov detector is that it can’t detect the charged particle below the Cherenkov threshold.

                                Super-Kamiokande

                                Super Kamiokande is a water Cherenkov detector located under mount Keno near Mozumi mine, Japan. The cylindrical stainless-steel detector with 40m height contains 5000 tons of pure water surrounded by 1300 photomultiplier. Super Kamiokande is constructed to capture solar, atmospheric as well as high energy cosmological neutrons. It gives a successful explanation to solar and atmospheric neutrino problem by the evidence of flavor oscillation. When a neutrino interacts with an electron or nuclei in water, they will produce a positron or electron, which produce Cherenkov radiation and the detector detects the particle. The main mode of detection is by elastic scattering ʋe + e-→ ʋe + e- with a threshold of 5 MeV and track the path of incoming neutrino. 0.45 ± 0.02 SNU neutrino flux was detected out from the prediction of 1.0 ±0.25 SNU. Super Kamiokande is best efficient towards charged current interaction and low towards neutral current interaction.

                                super-kamiokande-4[2].jpg
                                  Super-Kamiokande

                                  K2K is an experiment designed to verify neutrino oscillation, mostly atmospheric neutrino oscillation. The neutrinos from J-PARC send to the detector in the off-axis and then oscillation was determined. Later it is upgraded to T2K. This long baseline experiment has measured neutrino oscillation parameters such as theta one-three mixing angle. In T2K, a pure Tau neutrino beam formed from J-PARC is directed to Super-Kamiokande, first, it operates in off-axis so the beam is directed 2.5°. Here the average neutrino energy is 600 MeV. The T2K holds the best measurement in estimating the mixing angle and the mass difference in 23 sectors.

                                  Sudbury neutrino observatory

                                  SNO is a large Cherenkov detector located 2 Km underground in Sudbury Canada. The cylindrical detector having a 12m diameter made of acrylic plastic is filled with 1000 tons of ultra-heavy water. Unless normal water heavy water contains both neutron and proton and being a fragile molecule it only takes 2 MeV to breakdown into proton and neutron. So any neutrino flavor can break down D2O via neutral current interaction. SNO can detect both neutron and neutrino, unlike the other water Cherenkov detectors. The tank is surrounded by ultra-pure ordinary water for shielding. The target medium is viewed by 9700 light sensing photomultipliers.

                                  sno.jpg
                                    Sudbury Neutrino Observatory.

                                    SNO detect neutrino flux through three channels:

                                    1 .Elastic scattering channel [ES]

                                                                                            e+ϑe      e+ϑe                      (2.4.2)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;e^-+\vartheta_e\;\rightarrow\;\;e^-+\vartheta_e\;\;\;\;\;\;\;\;\;\;\;(2.4.2)

                                    The reaction is the same as in Super Kamiokande. Electron neutrino can, however, react via both neutral and charged current interaction. But Muon neutrino and Tau neutrino only interact via neutral current interactions. Elastic scattering channel gives a combination of Muon, Tau and electron type neutrino flux.

                                                                                          ϕ(ϑe)+ϕ1.5(ϑμ)+ϕ(ϑτ)                  (2.4.3)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\phi\left(\vartheta_e\right)+\phi1.5\left(\vartheta_\mu\right)+\phi\left(\vartheta_\tau\right)\;\;\;\;\;\;\;\;\;(2.4.3)

                                    2. Charged current channel [CC]

                                                                                            ϑe+dp+p+e                (2.4.4)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\vartheta_e+d\rightarrow p+p+e\;\;\;\;\;\;\;\;(2.4.4)

                                    Only electron neutrino undergoes charged current interaction. This channel is to check whether the solar neutrino flux obtained in SNO was correct compared to the other solar neutrino experiments

                                    3. Neutral current channel [NC]

                                                                                            ϑ+dn+p+ϑ                  (2.4.5)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\vartheta+d\rightarrow n+p+\vartheta\;\;\;\;\;\;\;\;\;(2.4.5)

                                    This reaction will give the flux of ϕ(ϑe)+ϕ(ϑµ)+ϕ(ϑτ). The neutrino produced is detected via a 6.3 MeV gamma-ray produced by the auxiliary reaction.

                                                                                              n+dH3+γ                  (2.4.6)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;n+d\rightarrow H^3+\gamma\;\;\;\;\;\;\;\;\;(2.4.6)

                                     From the following three steps , SNO was able to calculate the individual flux of each neutrino flavor in the unit

                                                                                            ϕCC=φ(ϑe)+φ1.5(ϑμ)+φ(ϑτ)=1.76±0.01              (2.4.7)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\phi_{CC}=\varphi\left(\vartheta_e\right)+\varphi1.5\left(\vartheta_\mu\right)+\varphi\left(\vartheta_\tau\right)=1.76\pm0.01\;\;\;\;\;\;\;(2.4.7)
                                                                                            ϕES=φ(ϑe)=2.39±0.26                                          (2.4.8)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\phi_{ES}=\varphi\left(\vartheta_e\right)=2.39\pm0.26\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(2.4.8)
                                                                                            ϕES=φ(ϑe)+φ(ϑμ)+φ(ϑτ)=5.09±0.63                (2.4.8)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\phi_{ES}=\varphi\left(\vartheta_e\right)+\varphi\left(\vartheta_\mu\right)+\varphi\left(\vartheta_\tau\right)=5.09\pm0.63\;\;\;\;\;\;\;\;(2.4.8)

                                    The observed electron neutrino flux was 2/3 times smaller than the muon neutrino and tau neutrino. From this, it is evident that ϑeϑμor ϑτ and the solar neutrino problem is solved.

                                    MiniBooNE

                                    MiniBooNE contains a spherical tank carrying 800 tons of mineral oil with scintillator doping, surrounded by 1280 photomultiplier located around 500 m away. From the cherenkov radiation, the low energy muon and proton which is invisible in water can be detected. The main goal of the experiment is to obtain ϑeϑμ​of oscillation . It started collecting data from 2013 in FermiLAB.

                                    miniboone.png
                                      MiniBooNE detector

                                      By boosting the muon beam, they looked for the electron neutrino appearance. The pion produced in the accelerator immediately decay to form muon neutrino of 0.1 GeV energy about 99.7% pure form and only 0.3% of muon decay to an electron neutrino. The appearance of electron neutrino was observed by its charged current interaction with oil. In 2012, at low energy, excess amount of electron and electron antineutrino were observed. The only way to explain the data is a sterile neutrino concept with CP violation, but this was all beyond the standard model of particle physics.

                                      miniboone graph.png
                                        Anti-electron neutrino and neutrino data from MiniBooNE.

                                        Excess of electron neutrino and anti-electron neutrino events were observed in MiniBooNE experiment. The dots show data. The colored histogram shows the expected background from some different sources. Both neutrino and anti-neutrino data showed the excess of events at low energy.

                                        ANTARES

                                        ANTARES is a neutrino telescope situated in the Mediterranean Sea in 2.5 m depth. It accommodates 350m long, 12 separate vertical strings of photomultiplier each containing 70 optical modules and placed 70 m apart from each other. ANTARES started collecting data from 2008. When atmospheric muon neutrino interacts with seawater, they produce high energy muon and it produces Cherenkov radiation in the medium which is captured by photomultipliers. Thus the neutrino is identified. The goal of ANTARES is that they found magnetic monopole and now, they are searching for dark matter, in the form of neutrino annihilation.

                                        AMANDA

                                        AMANDA detects the neutrino that has energy greater than 50 GeV using photomultiplier tube string buried 1 .5 to 2 Km inside Antarctic ice, in the South Pole. It contains a 3-D array of detectors. When a high energy neutrino interacts with hydrogen or oxygen molecule in water in ice, muon or hadronic shower is produced, which radiates Cherenkov radiation in the medium. The AMANDA detector can observe the path and direction of the neutrino by recording the arrival time of the individual photon with a resolution approximation of 2 degrees. The data collected by AMANDA gives important clues about dark matter. In 2005, after 9 years of successful running, AMANDA upgraded to iceCube neutrino observatory.

                                        IceCube neutrino observatory

                                        The IceCube experiment was supervised by the University of Wisconsin Madison. It is the upgraded version of AMANDA and it also contains spherical optical sensors (DOMs) with each photomultiplier tube. In IceCube experiment, it contains an array of series of Cherenkov detectors with two detectors above each ice cube string. The glacis ice cube acts as a cosmic ray shower detector. The deep core called the low energy region of an ice cube, which is extended to observe low energy neutrinos, say below 100 GeV. When the ice cube detector captures high energy neutrino flux, they count the signals and sent them to satellite to collect further information regarding those neutrino fluxes. IceCube is very sensitive to neutrinos having energy from 1011GeV to 1012GeV. Say most sensitive to muon due to high penetration.

                                        Scintillation Technique

                                        Scintillator detector makes use of the scintillation, the property of luminescence when excited by ionizing radiation. They are primarily constructed to detect anti-electron neutrino emitted by detectors in the range of energy 2 to 3 MeV. Scintillation light is isotopic and has very small threshold energy, so it can detect low energy neutrinos compared to the Cherenkov detector which has high threshold energies. Inorganic crystal, organic plastics and organic liquids (often toxic) can be used as scintillation material.

                                        They employ the same detection technique as a Cherenkov detector. The scintillator is enclosed in a large tank surrounded by photosensors to capture scintillation light. Since the light is isotopic it cannot reconstruct the particle direction and path.

                                        In 1956, an experiment by Frederic Reins and Clyde Cowan used two water targets in which one containing CdCl2. When the particle strikes on water, it undergoes inverse beta decay with protons of water and produces positron and neutrons. Positron undergoes annihilation and the emitted photons are captured, the cadmium in CdCl2 absorbs neutrinos resulting in the emission of gamma-ray and it is captured some microseconds, after the capturing of annihilated photons.

                                        KamLAND and Borexino were other experiments that made use of scintillation radiation to collect data regarding neutrino oscillation and energy spectrum.

                                        KamLAND

                                        KamLAND is a liquid scintillator detector build in Kamioka mine 10 Km away from Super Kamiokande. It build to look for the electron anti-neutrino produced by the reactors around Japan within a 150 Km distance. Since the threshold of KamLAND is very low, it can be used to detect low energy solar neutrinos more precisely than SNO and Super Kamiokande, but the detector must be always extremely pure and clean from background radioactive radiations. KamLAND contains a stainless-steel container having 18 m diameter filled with 1000 tons of scintillator liquid in a nylon weather balloon, the inner lining contains 1879 photomultiplier tubes. Non-scintillating highly purified oil around the balloon provides buoyancy for the balloon and acts as a buffer and keep the balloon always away from the photomultiplier and provide shielding from external radiation. A 3.2 kiloton cylindrical water container vessel acts as a muon counter which in turn protects from cosmic radioactivity from the surrounded rock.

                                        kamland.jpg
                                          KamLAND detector

                                          KamLAND is built to study the neutrino oscillation and oscillation parameters. When the neutrino strike with the target material, it undergoes inverse beta decay and produce positron and a neutr0n.

                                                                                                                  ϑe+pe++n                    (2.5.1)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\vartheta_e+p\rightarrow e^++n\;\;\;\;\;\;\;\;\;\;(2.5.1)

                                          The positron undergoes annihilation and produces a flash of light. The positron provides the data about the incident energy of the neutrino. The neutron is captured by hydrogen and produces 2.2 MeV gamma-ray which is captured within 10 to 100 microseconds, later the annihilated photon is captured.

                                                                                                                  p+ne++ϑe                    (2.5.2)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;p+n\rightarrow e^++\vartheta_e\;\;\;\;\;\;\;\;\;\;(2.5.2)

                                          KamLAND can also detect solar neutrino using an elastic scattering of neutrino and electron.

                                                                                                              ϑe+eϑe+e                (2.5.3)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\vartheta_e+e^-\rightarrow\vartheta_e+e^-\;\;\;\;\;\;\;\;(2.5.3)

                                          This reaction will not produce any neutron so only a single flash of light is emitted by the annihilation of the electron which must be also mimicked by the background radiation so that the output may contain far less signal purity and more background issues from the material in the detector which can also undergo radioactive decay

                                          Borexino

                                          Borexino is a scintillating detection technique built to study the solar neutrino flux. It observed pp, 7Be, pep neutrino fluxes from the sun and compared with the energy spectrum of the sun to confirm the data. It is a sphere-shaped stainless steel tank that holds a signal detector in it and also has an external water tank for shielding. It follows the same mechanism as KamLAND. It captures neutrino by the elastic scattering of a neutrino with an electron in water. The experiment started collecting data from 2007. Borexino is a member of the supernova early warning system, which searches for a rare process and has the potential to search for unknown particles.

                                          Radio Detector

                                          Radio detector looks for the Cherenkov radiation emitted by the high energy cosmological neutrino using an antenna. Usually, the antenna is a balloon-borne device that flies in the atmosphere and detects the Askaryan radiation emitted by ultra-high energy neutrinos.

                                          Radio ice Cherenkov experiment is a radio detecting technique to detect the high energy neutrino source and to find out the neutrino nucleon cross-section. The detector is buried 100 to 350 m inside the Antarctic ice and the antenna is about 140 to 120 m deep inside the ice. The detector detects the Cherenkov radiation in the radio regime of the electromagnetic spectrum from the interaction of high energy neutrino with an Antarctic ice cap. Antarctic impulse transient antenna employed for the detection is also sensitive to gamma-ray burst too. The energy spectrum of ultra-high energy neutrino ranges from 50 PeV to 1 EeV.

                                          Tracking and Hybrid Detector

                                          They are built to detect the track of high energy neutrinos. They consist of alternating layers of passive (absorbing material) and active (detecting materials) layers. The passive layer, made of dense and magnetized steel which performs the detection of mass and momentum of incoming particles, where, the active layer performs the actual detection by tracking the path of the incoming particle. The experiment Nova suggested that, by eliminating the absorbing material and bringing very active material made of scintillator or plastic scintillator, photomultiplier and by using various ionization chamber we can detect the incoming particle with moderate accuracy. The particle which undergoes neutral current interaction identified via hadronic content and the particle which undergo charged current interaction identified via charged lepton track. Consider if the particle is muon which is produced by charged current interaction, it is then detected by tracing the large penetrating track left behind. The length and curvature produced by the particle in the magnetic field provide energy and charge information. If the produced particle is electron then it will produce an electromagnetic shower in the detector or if it is a Tau particle it will immediately decay into a pion and charged lepton, which cannot be observed by these kinds of the detector.

                                          In the case of the NuTeV detector, the active layer contains spark champers, scintillating bars, resistive plate champers and any technology that will generate a signal. Particle energy is determined here based on the range of the particle, magnetic tracking and shower calorimetry. In NuTeV the target iron plates are interspaced between the scintillators and drift chamber to identify the mass of the host particle in the first part of the detector and the momentum from the second part which contains a magnetic channel (magnetic channel bends a charged particle).

                                          India-based neutrino observatory (INO)

                                          The discovery of neutrino, as well as neutrino oscillation, is just a primary step. There are still several questions to be answered. There exist several detectors all over the world to detect them. A few years ago, an idea shaped to build up India-based Neutrino Observatory (INO).

                                          • The ICAL detector

                                          The detector called iron calorimeter detector has 30000 resistive plates which are arranged in a stack of 150 layers, there the iron plates are interspaced between them. The dimensions of one module of the detector are 16m×16m×14.5m and the entire detector has a dimension of 48m×16m×14.5m. The detector is built 1300m deep inside the Bodi hills near Theni, Tamil Nadu to isolate it from other background radiations. The detector looks forward to collecting clear and accurate information about the mixing parameters. About 3.6 million channels are used to collect signals from resistive plates to computers. The current-carrying coil through the detector produces a magnetic field to bend the host particle, and the entire detector is magnetized. The massive detector weighing 50 kilotons is the world's largest electromagnet. When the project came to action, it will observe the sky through neutrinos.

                                          Schematic-diagram-of-RPC-detector-and-three-towers-of-ICAL-detector-are-shown-1-9.png
                                            A diagram of ICAL detector

                                            Coherent Recoil Detector

                                            At very low energies, a neutrino can scatter from the entire nucleus of an atom rather than the nucleon. Such a process is called coherent neutral current neutrino-nucleus elastic scattering. A detector that uses this phenomenon for detection doesn't bother about the flavor of neutrino. Most of the detectors in these kinds must be small in size compared to other detecting techniques.

                                            Telescopes

                                            On detecting neutrino flux and their oscillation telescopes play a major role.

                                            Under water

                                            •   Baikal deep under water neutrino telescope
                                            •   ANTARES
                                            • AMANDA
                                            • KM3NeT
                                            • NESTOR Project

                                            Under ice

                                            •   AMANDA
                                            •   IceCube

                                            Underground Neutrino Observations

                                            • Gran Sasso National Laboratory
                                            • Soudan mine, home of Soudan 2, MINUS, and CDMS​
                                            •   Kamioka Obseratory, Japan

                                            Early Anomalies in Neutrino Physics

                                            The Solar Neutrino Anomaly

                                            Sun is the main source of energy for Earth. The solar neutrino problem concerned a large discrepancy between the fluxes of solar neutrinos as predicted from the Sun's luminosity and measured directly. The discrepancy was first observed in the mid-1960s and finally resolved around 2002. Early attempts to explain the discrepancy proposed that the models of the Sun were wrong. The solar neutrino problem was resolved with an improved understanding of the properties of neutrinos. According to the Standard Model of particle physics, there are three flavors of neutrinos: electron neutrinos, muon neutrinos, and tau neutrinos. Electron neutrinos are the ones produced in the Sun and the ones detected by the above-mentioned experiments, in particular, the chlorine-detector Homestake Mine experiments. Figure 23 shows the observed solar neutrino flux from different experiment and their standard model prediction.

                                            theoryvsexp.gif
                                              The state of the solar neutrino problem before SNO. Each group of bars represents a different type of experiment: Chlorine on the left, water in the middle and Gallium on the right. The blue bars in each cluster represent the measurements of individual experiments, in SNUs. The middle bar shows the Standard Solar Model prediction. In all cases, the measurements are less than predicted.

                                              The Sudbury Neutrino Observatory (SNO) started collecting data. That experiment aimed at the 8B solar neutrinos, which at around 10 MeV are not much affected by oscillation in both the Sun and the Earth. From SNO data it has been clear that the produced electrotype neutrino on sun changes its flavor to muon type or tau type. And thus the phenomenon of neutrino flavor oscillation revealed.

                                              Atmospheric Neutrino Anomaly

                                              They are produced as decay products in hadronic showers resulting from collisions of cosmic rays with nuclei in the atmospheric electron-neutrinos and muon-neutrinos are produced mainly by the decay chain of charged pions to muons to an electron. But when we observe these muon type atmospheric neutrino, there arose a discrepancy between the observed data and standard model prediction. Super Kamiokande is an efficient detector that looked for high energy neutrinos and studies the proton decay, Solar and Atmospheric Neutrino Anomalies and the Supernova neutrinos. It gave observations in Sub-GeV range (visible energy < 1.33 GeV) and Multi GeV range (visible energy > 1.33 GeV). In sub GeV range half of the muon neutrinos were missing on the overall range of zenith angles. In multi GeV range, there is a UP-DOWN ASYMMETRY for muon neutrinos and also the double ratio found to be less than one. Since the 𝜈𝑒 data remains unaltered, it was assumed that many 𝜈𝜇 have oscillated to 𝜈𝜏. The data from Super-K and Kamiokande were analyzed by assuming flavor oscillation of 𝜈𝜇→ 𝜈𝜏, and the results overlapped, and hence FLAVOR BASED NEUTRINO OSCILLATION was accepted as the cause of atmospheric neutrino anomaly in 1998. The SOUDAN -2 which can detect the direction of incoming neutrinos also confirmed the deficit of upward - going 𝜈𝜇. And MACRO – large underground detector gave consistent results with Super-K.

                                              Neutrino Oscillation

                                              We know that neutrinos are produced in the weak interaction. By definition, these particles are always associated with a charged lepton. Neutrinos are also classified in terms of “mass”, neutrino1 (ϑ1), neutrino 2 (ϑ2) and neutrino 3 (ϑ3), have a mass of: m1, m2, and m3, respectively (see figure 24). The classifications in terms of flavor and mass, are mixed with each other. (See figure 24).The Flavor Eigen states and mass Eigen states cannot be determined at the same time.

                                              waves.jpg
                                                Neutrinos are mixing between flavor Eigen state and mass Eigen state and Neutrinos in terms of both flavor and mass

                                                We can understand neutrino oscillation in accordance with its particle and wave nature. Therefore, ν1, ν2, and ν3, each with different mass Eigen states, travel through space as waves that have a different frequency. (See figure 25) The flavor of a neutrino is determined as a superposition of the mass Eigen states. One type of flavor oscillates because of the phase of the wave changes. This phenomenon is called neutrino oscillation. It occurs when neutrinos have mass and non-zero mixing.

                                                waves.jpg
                                                  Type of  the flavour oscillation when neutrinos travel through space.

                                                  In terms of quantum mechanics, we can explain neutrino oscillation as follows;

                                                  If the system is in one of its stationary states | Ψi˃ and it will remain in that state. The time evolution of the wave function, if the state is prepared after time t is | Ψi (t) ˃= e-Et | Ψi (0) ˃ which is not one of the Eigen states of the system then the probability to find the system in this state will oscillate in time with the frequency. Suppose a neutrino produced with a flavor, say, να (α= e, μ, τ) and we know that each flavor state is a mixture of three mass Eigen states with slightly different masses. As mass Eigen states evolve quantum mechanically then the probability of finding a neutrino created in a given flavor state (να) to be in the same state (or any other flavor state νβ) oscillates with time.

                                                  Two Flavour Oscillation in Vaccum

                                                  Let as consider two neutrino flavor states say ׀ϑα˃ and ׀ϑβ˃ connected two mass Eigen states ׀ϑ1˃ and ׀ϑ2˃ via a unitary matrix U.

                                                  [ϑαϑβ]  =[Uα1Uα2Uβ1Uβ2][ϑ1ϑ2]\begin{bmatrix}\vartheta_\alpha\\\vartheta_\beta\end{bmatrix}\;=\begin{bmatrix}U_{\alpha1}&U_{\alpha2}\\U_{\beta1}&U_{\beta2}\end{bmatrix}\begin{bmatrix}\vartheta_1\\\vartheta_2\end{bmatrix}

                                                   for the parameterization of given 2 × 2 unitary matrix, we need only one mixing angle, say, we can write a general 2 × 2 mixing matrix having the parameter ’θ’ as

                                                  [ϑα1ϑα2ϑβ1ϑβ2]=[cos(θ)sin(θ)sin(θ)cos(θ)]\begin{bmatrix}\vartheta_{\alpha1}&\vartheta_{\alpha2}\\\vartheta_{\beta1}&\vartheta_{\beta2}\end{bmatrix}=\begin{bmatrix}\cos\left(\theta\right)&\sin\left(\theta\right)\\-\sin\left(\theta\right)&\cos\left(\theta\right)\end{bmatrix}

                                                  We can write

                                                                                                          ϑα=cos(θ)ϑ1+sin(θ)ϑ2                                                  (2.12.1)                                                        ϑβ=sin(θ)ϑ1+cos(θ)ϑ2                                          (2.12.2)\begin{array}{l}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\vartheta_\alpha=\cos\left(\theta\right)\vartheta_1+\sin\left(\theta\right)\vartheta_2\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(2.12.1)\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\vartheta_\beta=-\sin\left(\theta\right)\vartheta_1+\cos\left(\theta\right)\vartheta_2\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(2.12.2)\end{array}

                                                  Since mass Eigen states is an Eigenstate of free particle Hamitonian with Eigenvalue Ek and each mass Eigen state have its mass(Mk)

                                                  Then

                                                                                                              HVk>=EkVk>                                (2.12.3)                                                          Ek=P2+MK2                                          (2.12.4)\begin{array}{l}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;H\left|V_k>=E_k\right|V_k>\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(2.12.3)\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;E_k=\sqrt{P^2+M_{{}_K}^2}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(2.12.4)\end{array}

                                                  | Vk > is a quantum mechanical state it can evolve with time.

                                                                                        Vk>=eEktVk(0)>                      (2.12.3)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left|V_k>=e^{-Ekt}\right.\left|V_k(0)>\;\;\;\;\;\;\;\;\;\;\;(2.12.3)\right.

                                                  we can write ϑ1 and ϑ2 as

                                                                                                    ϑ1(t)>=eE1ktϑ1(0)>            (2.12.6)                                                  ϑ2(t)>=eE2ktϑ2(0)>            (2.12.7)\begin{array}{l}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left|\vartheta_1(t)>=e^{-E1kt}\left|\vartheta_1\right.(0)>\;\;\;\;\;\;(2.12.6)\right.\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left|\vartheta_2(t)>=e^{-E2kt}\left|\vartheta_2\right.(0)>\;\;\;\;\;\;(2.12.7)\right.\\\end{array}

                                                  where e-E1ktand e-E2kt are phase factors

                                                  At t= 0

                                                  ϑα=0 ,ϑβ=1 and equations (2.12.1) and (2.12.2) becomes

                                                                                          cos(θ)ϑ1(0)>+sin(θ)ϑ2(0)>=1              (2.12.8)                                        sin(θ)ϑ1(0)>+cos(θ)ϑ2(0)>=1              (2.12.9)\begin{array}{l}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\cos\left(\theta\right)\left|\vartheta_1(0)>+\sin\left(\theta\right)\right.\left|\vartheta_2(0)>=1\;\;\;\;\;\;\;(2.12.8)\right.\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\sin\left(\theta\right)\left|\vartheta_1(0)>+\cos\left(\theta\right)\right.\left|\vartheta_2(0)>=1\;\;\;\;\;\;\;(2.12.9)\right.\\\\\end{array}

                                                  (2.12.8)*sinθ+(2.12.9)*cos​​θ gives

                                                                                                    sin2θ+cos2θ(  ϑ2(0)>)=sinθ                                                  ϑ2(0)>=sinθ                                                                (2.12.10)\begin{array}{l}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\sin^2\theta+\cos^2\theta(\;\left|\vartheta_2(\right.0)>)=\sin\theta\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left|\vartheta_2(0)>=\sin\theta\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(2.12.10)\right.\end{array}

                                                  (2.12.8)*cosθ+(2.12.9)*sinθ

                                                                                          sin2θ+cos2θ(  ϑ1(0)>)=cosθ                                            ϑ1(0)>=cosθ                                                        (2.12.11)    \begin{array}{l}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\sin^2\theta+\cos^2\theta(\;\left|\vartheta_1(0)>)=\cos\theta\right.\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left|\vartheta_1(0)>=\cos\theta\right.\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(2.12.11)\\\;\;\end{array}

                                                  At time t=t,

                                                                              ϑ1(t)>=eE1kt  ϑ1(0)>                            ϑ2(t)>=eE2kt  ϑ2(0)>                            ϑα(t)>=cosθ  ϑ1(t)>+sin  ϑ2(t)>                            cos2θeE1kt  +sin2θeE2kt                                (2.12.12)                            ϑβ(t)>=sinθ  ϑ1(t)>+cos  ϑ2(t)>                          sinθeE1kt  cosθ+sinθcosθeE2kt        (2.12.13)\begin{array}{l}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left|\vartheta_1(t)>=e^{-E1kt\;}\left|\vartheta_1(0)>\right.\right.\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left|\vartheta_2(t)>=e^{-E2kt\;}\left|\vartheta_2(0)>\right.\right.\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left|\vartheta_\alpha(t)>=\cos\theta\;\left|\vartheta_1(t)\right.\right.>+\sin\;\left|\vartheta_2(t)>\right.\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\cos^2\theta e^{-E1kt\;}+\sin^2\theta e^{-E2kt\;}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(2.12.12)\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left|\vartheta_\beta(t)>=-\sin\theta\;\left|\vartheta_1(t)\right.\right.>+\cos\;\left|\vartheta_2(t)>\right.\\\;\;\;\;\;\;\;\;\;\;\;\;\;\sin\theta e^{-E1kt\;}\cos\theta+\sin\theta\cos\theta e^{-E2kt\;}\;\;\;(2.12.13)\end{array}

                                                  Probability ϑαϑβ

                                                                                    P(ϑαϑβ)  =<ϑβ(t)  ϑα  (t)>2                                                                    =ϑβ(t)2                                                                    =sin2θsin2θ(m2L4E)            in  natural  units                                                                    =sin2θsin2θ(1.27m2  LE)                      (2.12.14)\begin{array}{l}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;P_{(\vartheta_\alpha\rightarrow\vartheta_\beta)\;}=\left|<\vartheta_\beta(t)\;\left|\vartheta_{\alpha\;}(t)\left.>\right|^2\right.\right.\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\left|\vartheta_\beta(t\left.)\right|\right.^2\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\sin^2\theta\sin^2\theta\left(\frac{\triangle m^2L}{4E}\right)\;\;\;\;\;\;in\;natural\;units\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\sin^2\theta\sin^2\theta\left(1.27\triangle m^2\;\frac LE\right)\;\;\;\;\;\;\;\;\;\;\;(2.12.14)\end{array}

                                                  The survival probability can be obtained as:

                                                                                                        P(ϑαϑα)=1sin22θsin2(1.27m2LE)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;P_{\left(\vartheta_\alpha\rightarrow\vartheta_\alpha\right)}=1-\sin^22\theta\sin^2(1.27\triangle m^2\frac LE)

                                                  Parameters

                                                  • Mixing angle(θ) : θ is called mixing angle. It defines how different flavour states are from the mass states. If θ=0, the flavour states are identical to the mass states. If θ is π\4 then the oscillations are said to be maximal and at some point along the path between source and detector.
                                                  •   The mass squared difference, ∆ m2: If there are 2 flavours there will be 2 mass states. This parameter is the difference in squared masses of each of these states. For neutrino oscillations to occur, at least one of the mass states must be non-zero.
                                                  •   L/E : This is the parameter that, we experimentalists control. L is the distance between the source and the detector, and E is the energy of the neutrino. We can not change the value of θ and ∆ m2 but we can change the value of L and E. The argument of sine function is taken a maximum value at each (2n+1) π/2 angle, the oscillation becomes maximum for the following condition:

                                                  1.27m2LE=(2n+1) π/2 where n=0,1,2.......

                                                   For first oscillation maxima n=0

                                                  LE=π2.54m2\frac LE=\frac\pi{2.54\triangle m^2}

                                                  METHODOLOGY

                                                  By reading the lecture notes of Amul Dighe and intellectual peoples of neutrino physics and by the help of professor Sanjib Kumar Agarwalla I get to introduce into neutrino physics. Introduction to the elementary particle by David Griffith and neutrino physics by Kai Zuber served me more about the properties and its quantum mechanical behavior. I derived equation for the propagation of neutrinos in a vaccum and coded a program in SciLAB to plot the probability of appearance and disappearance transition of a neutrino with varying energy for different baselines. And also coded a program in MATLAB to calculate the shortest distance between various artificial neutron sources and detectors so that I can study more about various baselines and neutrino oscillations.

                                                  RESULTS AND DISCUSSION

                                                  Shortest Distance between Source and Detector

                                                  There are two types of neutrino detectors based on the distance travelled by the neutrino from the source to a detector (baseline). If the neutrino wants to travel a long distance to the detector to get detected it is called a long-baseline detector or far detector or if the detector is built near the point of production of a neutrino it is then called near detector or short baseline detector. Both the detectors will allow the scientist to study about neutrino beam before and after oscillation. Based on that there are two kinds of experiments.

                                                  • Disappearance Experiment

                                                  It looks for the disappearance of one flavor to another. Here the ratio between the neutrino spectrum in source and detector shows the oscillation pattern.

                                                  images.jpg
                                                    Ratio of neutrino energy spectra before and after oscillation

                                                    2. Appearance experiment

                                                    The figure shows the ratio of far detector neutrino and near detector neutrino flux. The dip shows the neutrino oscillating and it gives a measurement of the sin2θ position of it in the x-axis and gives relevance of ∆m2complicated.

                                                    Looks for the new flavor. But it is difficult to distinguish the new neutrino flavor from the background radiation which mimics the same mechanism in the detector.

                                                    Here is the table which provides the shortest distance between different artificial sources and detectors. By this, we can find a different short baseline and long-baseline detectors.so we can look for the appearance and disappearance of neutrino flavor. And also can assign the distance travelled by the neutrino through core,crest,and mantle on its propagation from source to detector.

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                                                      Distance between FermiLAB and various detectors
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                                                        Distances from CERN to different sources
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                                                          Distances from J-PARC to different sources
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                                                            Distances from Rutherford Appleton Laboratory,UK to different sources.

                                                            Probability Plots

                                                            Now we know the probability equations for neutrino oscillation. Here we are going to use some neutrino oscillation parameters and going to plot the trasition probability for disapperance channel.

                                                            plot 1

                                                            L=295 Km, Mixing angle θ = 45º For energy range E = 0.1 GeV to1.2 GeV

                                                            Δm2=2.4×103eV2,  2.5×103eV2,2.6×103eV2      \Delta m^2=2.4\times10^{-3}eV^2,\;2.5\times10^{-3}eV^2,2.6\times10^{-3}eV^2\;\;\;
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                                                              Disappearance probability

                                                              Transition probability curve for appearance channel

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                                                                Appearance channel

                                                                Plot 2

                                                                L=295 Km, Mixing angle θ = 45º For energy range E = 0.1 GeV to1.2 GeV

                                                                Δm2=2.4×103eV2\Delta m^2=2.4\times10^{-3}eV^2

                                                                1 Transition probability for disappearance probability

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                                                                  Disappearance channel

                                                                  2 Transition probability curve for appearance channel

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                                                                    Appearance channel

                                                                    CONCLUSION AND RECOMMENDATION

                                                                    The missing energy in β-decay was a serious problem in the earlier 20th century, which was solved by Pauli by proposing a chargeless fermion, later known by "neutrino". In this project report, we discussed how Pauli’s proposed hypothesis helped to solve the energy-momentum violation in β-decay. During the project, I acquired detailed knowledge about various neutrino sources and detection techniques. I also learned the basics of neutrino oscillation and accomplished the knowledge about the possible neutrino source and detector locations available around the world and estimated the distance between various source and detector locations and studied how these baselines can be used to extract valuable information about neutrino oscillation parameters.

                                                                    After the detection of neutrino, the solar and atmospheric neutrino anomalies were observed, which was another big problem at that time. The neutrino oscillation phenomenon has solved these anomalies. We learned about how neutrino flavors are mixed and derived oscillation probabilities expressions for two flavor oscillation in a vacuum and plotted these results to interpret the neutrino oscillation phenomenon.

                                                                    Now I wanted pursue my studies on the topics 3 flavor neutrino oscillation in a vacuum, Matter effects on neutrino oscillations, The CP violation in the neutrino sector, Masses of the mass Eigen states.

                                                                    REFERENCES

                                                                    •      T. Kajita, E. Kearns, M.Shiozawa. 2016. Establishing atmospheric neutrino oscillations with Super Kamiokande. : Science Direct, 2016.

                                                                    •      G Rajasekaran, THE STORY OF THE NEUTRINO, [arXiv:1606.08715v1]

                                                                    •      E. Kh. Akhmedov, Neutrino physics, [arXiv:hep-ph/0001264v2]

                                                                    •      D P Roy, Eighty Years Of Neutrino Physics, [arXiv:0809.1767[hep-ph]

                                                                    •      Sanjib Kumar Agarwalla, Yee Kao, and Tatsu Takeuchi, Analytical Approximation of the Neutrino Oscillation Matter Effects at large θ13, [arXiv:1302.6773v3]

                                                                    •      S. K. Agarwalla, SOME ASPECTS OF NEUTRINO MIXING AND OSCILLATIONS, PhD,Thesis [arXiv:0908:4267v2]

                                                                    BIBLIOGRAPHY

                                                                    • David Griffiths,INTRODUCTION TO ELEMENTARY PARTICLES
                                                                    • Kai Zuber,NEUTRINO PHYSICS

                                                                    ACKNOWLEDGEMENTS

                                                                    I would like to thank Science Academies’ (Indian Academy of Sciences, Indian National Science Academy, and The National Academy of Sciences, India )for providing me this wondrous opportunity to work on the topic “Neutrino Sources and Detectors ” in summer 2019 at Institute of Physics, Bhubaneswar.

                                                                    I would like to extend my sincere and heartfelt gratitude to my project guide Dr. Sanjib Kumar Agarwalla, who has helped me in this endeavor and has always been very cooperative, and without his help, guidance, and encouragement, the project couldn’t have been what it evolved to be.

                                                                    I extend my heartfelt thanks to my teachers Dr. Deepa S and Prof. Saritha Nair for their invaluable suggestions and constant guidance.

                                                                    Mere acknowledgment may not redeem the debt I owe to my dear friend Joseph Kureethadom, At last, but not least, gratitude to my family and my dear teammates Md Ful Hossain Sk, Masoom Singh, Soumya Chembra, Sujith Sahoo and Nimmy Sara Alex who has been my constant source of encouragement and support throughout this project within a limited time frame.

                                                                    Citations

                                                                    • https://www-boone.fnal.gov/
                                                                    • https://en.wikipedia.org/wiki/Neutrino_oscillation
                                                                    • www.hyper-k.org/en/neutrino.html
                                                                    • https://www.ias.ac.in/article/fulltext/reso/021/10/0911-0924

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