# AI News, Machine learning used in tracking of COMET (japanese particle physics experiment), part I

## Machine learning used in tracking of COMET (japanese particle physics experiment), part I

Recently I worked together with intern from Imperial College over the tracking system of COMET for two months, and here I'm going to briefly sum our (impressing) results.

For some time these numbers (electronic number, muonic number, tauonic number) were considered to be preserved, but in the late 1960's it was proved, that neutrino oscillations change the leptonic number of system (neutrino can become electronic from muonic, for instance).

Since that time physicists are searching for other processes which change the leptonic number and include charged leptons (electrons, muons, tauons), which could be a key for new physics, however no success in this direction and the results are currently mostly upper limits we can prove for some processes.

When muon hits the aluminum target (in the center), the electron produced travels over helix trajectories of larger radius in magnetic field and hits wires.

## Lepton number

In particle physics, lepton number (historically also called lepton charge[1]) is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction.[2] Lepton number is an additive quantum number, so its sum, not its product, is preserved in interactions.

Mathematically, the lepton number

{\displaystyle L}

is defined by

=

n

&#x2113;

&#x2212;

n

&#x2113;

{\displaystyle L=n_{\ell }-n_{\overline {\ell }}}

,

where

{\displaystyle n_{\ell }}

is the number of leptons and

{\displaystyle n_{\overline {\ell }}}

is the number of antileptons.

Lepton number was introduced in 1953 to explain the absence of reactions such as

{\displaystyle {\bar {\nu }}+n\rightarrow p+e^{-}}

in the Cowan–Reines neutrino experiment, which instead observed

{\displaystyle {\bar {\nu }}+p\rightarrow n+e^{+}}

.[3] This process, inverse beta decay, conserves lepton number, as the incoming antineutrino has lepton number –1, while the outgoing positron (antielectron) also has lepton number –1.

In addition to lepton number, lepton family numbers are defined as Prominent examples of lepton flavor conservation are the muon decays

{\displaystyle \mu ^{-}\to e^{-}+{\overline {\nu }}_{e}+\nu _{\mu }}

{\displaystyle \mu ^{+}\to e^{+}+\nu _{e}+{\overline {\nu }}_{\mu }}

In these, the creation of an electron is accompanied by the creation of an electron antineutrino, and the creation of a positron is accompanied by the creation of an electron neutrino.

Likewise, a decaying negative muon results in the creation of a muon neutrino, while a decaying positive muon results in the creation of a muon antineutrino.

Lepton flavor is only approximately conserved, and is notably not conserved in neutrino oscillation.[4] However, total lepton number is still conserved in the Standard Model.

Numerous searches for physics beyond the Standard Model incorporate searches for lepton number or lepton flavor violation, such as the decays

{\displaystyle \mu ^{-}\to e^{-}+\gamma }

.[5] Experiments such as MEGA and SINDRUM have searched for lepton number violation in muon decays to electrons;

MEG set the current branching limit of order 10−13 and plans to lower to limit to 10−14 after 2016.[6] Some theories beyond the Standard Model, such as supersymmetry, predict branching ratios of order 10−12 to 10−14.[5] The Mu2e experiment, in construction as of 2017, has a planned sensitivity of order 10−17.[7] Because the lepton number conservation law in fact is violated by chiral anomalies, there are problems applying this symmetry universally over all energy scales.

However, the quantum number B − L is commonly conserved in Grand Unified Theory models.

## Electron-Positron Pair Production

Leptons and quarks are the basic building blocks of matter, i.e., they are seen as the 'elementary particles'.

The different varieties of the elementary particles are commonly called 'flavors', and the neutrinos here are considered to have distinctly different flavor.

When the process of nucleosynthesis from the big bang is modeled, the number of types of neutrinos affects the abundance of helium.

## Neutrino

A neutrino (/nuːˈtriːnoʊ/ or /njuːˈtriːnoʊ/) (denoted by the Greek letter ν) is a fermion (an elementary particle with half-integer spin) that interacts only via the weak subatomic force and gravity.[2][3] The mass of the neutrino is much smaller than that of the other known elementary particles.[1] Although only differences of squares of the three mass values are known as of 2016,[4] cosmological observations imply that the sum of the three masses must be less than one millionth that of the electron.[1][5] The neutrino is so named because it is electrically neutral and because its rest mass is so small (-ino) that it was long thought to be zero.

For example, an electron neutrino produced in a beta decay reaction may interact in a distant detector as a muon or tau neutrino.[7][8] For each neutrino, there also exists a corresponding antiparticle, called an antineutrino, which also has half-integer spin and no electric charge.

To conserve total lepton number, in nuclear beta decay, electron neutrinos appear together with only positrons (anti-electrons) or electron-antineutrinos, and electron antineutrinos with electrons or electron neutrinos.[9][10] Neutrinos are created by various radioactive decays, including in beta decay of atomic nuclei or hadrons, nuclear reactions such as those that take place in the core of a star or artificially in nuclear reactors, nuclear bombs or particle accelerators, during a supernova, in the spin-down of a neutron star, or when accelerated particle beams or cosmic rays strike atoms.

In the vicinity of the Earth, about 65&#160;billion (7010650000000000000♠6.5×1010) solar neutrinos per second pass through every square centimeter perpendicular to the direction of the Sun.[11][12] For study, neutrinos can be created artificially with nuclear reactors and particle accelerators.

In contrast to Niels Bohr, who proposed a statistical version of the conservation laws to explain the observed continuous energy spectra in beta decay, Pauli hypothesized an undetected particle that he called a 'neutron', using the same -on ending employed for naming both the proton and the electron.

He considered that the new particle was emitted from the nucleus together with the electron or beta particle in the process of beta decay.[15][nb 2] James Chadwick discovered a much more massive nuclear particle in 1932 and also named it a neutron, leaving two kinds of particles with the same name.

Pauli earlier (in 1930) had used the term 'neutron' for both the neutral particle that conserved energy in beta decay, and a presumed neutral particle in the nucleus, and initially did not consider these two neutral particles as distinct from each other.[15] The word 'neutrino' entered the scientific vocabulary through Enrico Fermi, who used it during a conference in Paris in July 1932 and at the Solvay Conference in October 1933, where Pauli also employed it.

The name (the Italian equivalent of 'little neutral one') was jokingly coined by Edoardo Amaldi during a conversation with Fermi at the Institute of physics of via Panisperna in Rome, in order to distinguish this light neutral particle from Chadwick's neutron.[16] In Fermi's theory of beta decay, Chadwick's large neutral particle could decay to a proton, electron, and the smaller neutral particle (flavored as an electron antineutrino): Fermi's paper, written in 1934, unified Pauli's neutrino with Paul Dirac's positron and Werner Heisenberg's neutron–proton model and gave a solid theoretical basis for future experimental work.

He submitted the paper to an Italian journal, which accepted it, but the general lack of interest in his theory at that early date caused him to switch to experimental physics.[17]:24[18] However, by 1934 there was experimental evidence against Bohr's idea that energy conservation is invalid for beta decay.

The natural explanation of the beta decay spectrum as first measured in 1934 was that only a limited (and conserved) amount of energy was available, and a new particle was sometimes taking a varying fraction of this limited energy, leaving the rest for the beta particle.

McGuire published confirmation that they had detected the neutrino,[20][21] a result that was rewarded almost forty years later with the 1995 Nobel Prize.[22] In this experiment, now known as the Cowan–Reines neutrino experiment, antineutrinos created in a nuclear reactor by beta decay reacted with protons to produce neutrons and positrons: The positron quickly finds an electron, and they annihilate each other.

its existence had already been inferred by both theoretical consistency and experimental data from the Large Electron–Positron Collider.[24] In the 1960s, the now-famous Homestake experiment made the first measurement of the flux of electron neutrinos arriving from the core of the Sun and found a value that was between one third and one half the number predicted by the Standard Solar Model.

This so-called Mikheyev–Smirnov–Wolfenstein effect (MSW effect) is important to understand because many neutrinos emitted by fusion in the Sun pass through the dense matter in the solar core (where essentially all solar fusion takes place) on their way to detectors on Earth.

in association with the corresponding electron, muon, and tau charged leptons, respectively.[6] Although neutrinos were long believed to be massless, it is now known that there are also three discrete neutrino masses, but they don't correspond uniquely to the three flavors.

From cosmological measurements, it has been calculated that the sum of the three neutrino masses must be less than one millionth that of the electron.[1][5] More formally, neutrino flavor eigenstates are not the same as the neutrino mass eigenstates (simply labelled 1, 2, 3).

Recent experimental efforts have established values for the elements of this matrix, and the precision is rapidly improving.[4] The existence of a neutrino mass allows the existence of a tiny neutrino magnetic moment, in which case neutrinos could interact electromagnetically as well;

This oscillation occurs because the three mass state components of the produced flavor travel at slightly different speeds, so that their quantum mechanical wave packets develop relative phase shifts that change how they combine to produce a varying superposition of three flavors.

for example, if total lepton number is zero in the initial state, electron neutrinos appear in the final state together with only positrons (anti-electrons) or electron-antineutrinos, and electron antineutrinos with electrons or electron neutrinos.[9][10] Antineutrinos are produced in nuclear beta decay together with a beta particle, in which, e.g., a neutron decays into a proton, electron, and antineutrino.

Measurements of the Z lifetime have shown that the number of light neutrino flavors that couple to the Z is 3.[6] The correspondence between the six quarks in the Standard Model and the six leptons, among them the three neutrinos, suggests to physicists' intuition that there should be exactly three types of neutrino.

International scientific collaborations install large neutrino detectors near nuclear reactors or in neutrino beams from particle accelerators to better constrain the neutrino masses and the values for the magnitude and rates of oscillations between neutrino flavors.

that is, whether or not the laws of physics treat neutrinos and antineutrinos differently.[4] The KATRIN experiment in Germany will begin to acquire data in 2017 to determine the value of the mass of the electron neutrino, with other approaches to this problem in the planning stages.[1] On 19&#160;July 2013, the results from the T2K experiment presented at the European Physical Society Conference on High Energy Physics in Stockholm, Sweden, confirmed neutrino oscillation theory.[40][41] Despite their tiny masses, neutrinos are so numerous that their gravitational force can influence other matter in the universe.

The three known neutrino flavors are the only established elementary particle candidates for dark matter, specifically hot dark matter, although that possibility appears to be largely ruled out by observations of the cosmic microwave background.

If heavier sterile neutrinos exist, they might serve as warm dark matter, which still seems plausible.[42] Other efforts search for evidence of a sterile neutrino – a fourth neutrino flavor that does not interact with matter like the three known neutrino flavors.[43][44][45][46] The possibility of sterile neutrinos is unaffected by the Z-boson decay measurements described above: If their mass is greater than half the Z-boson's mass, they would not be a decay product.

On the other hand, the currently running MiniBooNE experiment suggested that sterile neutrinos are not required to explain the experimental data,[47] although the latest research into this area is on-going and anomalies in the MiniBooNE data may allow for exotic neutrino types, including sterile neutrinos.[48] A recent re-analysis of reference electron spectra data from the Institut Laue-Langevin[49] has also hinted at a fourth, sterile neutrino.[50] According to an analysis published in 2010, data from the Wilkinson Microwave Anisotropy Probe of the cosmic background radiation is compatible with either three or four types of neutrinos.[51] There are also experiments searching for neutrinoless double-beta decay, which, if it exists, would violate lepton number conservation, and imply a minuscule splitting or difference between the physical masses of what are now conventionally called a “neutrino” and corresponding “antineutrino”, with opposite signs of lepton number.

If this were discovered the two could no longer be mutual antiparticles, and each of the resulting six distinct neutrinos would have no distinct antiparticle partner.[52] Cosmic ray neutrino experiments detect neutrinos from space to study both the nature of neutrinos and the cosmic sources producing them.[53] Before neutrinos were found to oscillate, they were generally assumed to be massless, propagating at the speed of light.

This measurement set an upper bound on the mass of the muon neutrino of 6988801088243500000♠50&#160;MeV at 99% confidence.[54][55] After the detectors for the project were upgraded in 2012, MINOS refined their initial result and found agreement with the speed of light, with the difference in the arrival time of neutrinos and light of −0.0006% (±0.0012%).[56] A

An independent recreation of the experiment in the same laboratory by ICARUS found no discernible difference between the speed of a neutrino and the speed of light.[59] In June&#160;2012, CERN announced that new measurements conducted by all four Gran Sasso experiments (OPERA, ICARUS, Borexino and LVD) found agreement between the speed of light and the speed of neutrinos, finally refuting the initial OPERA claim.[60] The Standard Model of particle physics assumed that neutrinos are massless.

However, the experimentally established phenomenon of neutrino oscillation, which mixes neutrino flavour states with neutrino mass states (analogously to CKM mixing), requires neutrinos to have nonzero masses.[61] Massive neutrinos were originally conceived by Bruno Pontecorvo in the 1950s.

McDonald for their experimental discovery of neutrino oscillations, which demonstrates that neutrinos have mass.[64][65] In 1998, research results at the Super-Kamiokande neutrino detector determined that neutrinos can oscillate from one flavor to another, which requires that they must have a nonzero mass.[66] While this shows that neutrinos have mass, the absolute neutrino mass scale is still not known.

Thus, there exists at least one neutrino mass eigenstate with a mass of at least 6979640870594800000♠0.04&#160;eV.[70] In 2009, lensing data of a galaxy cluster were analyzed to predict a neutrino mass of about 6981240326473050000♠1.5&#160;eV.[71] This surprisingly high value requires that the three neutrino masses be nearly equal, with neutrino oscillations on the order of milli electron-Volts.

On 31 May 2010, OPERA researchers observed the first tau neutrino candidate event in a muon neutrino beam, the first time this transformation in neutrinos had been observed, providing further evidence that they have mass.[74] In July&#160;2010, the 3-D MegaZ DR7 galaxy survey reported that they had measured a limit of the combined mass of the three neutrino varieties to be less than 6980448609416360000♠0.28&#160;eV.[75] A tighter upper bound yet for this sum of masses, 6980368500592010000♠0.23&#160;eV, was reported in March 2013 by the Planck collaboration,[76] whereas a February 2014 result estimates the sum as 0.320 ± 0.081&#160;eV based on discrepancies between the cosmological consequences implied by Planck's detailed measurements of the Cosmic Microwave Background and predictions arising from observing other phenomena, combined with the assumption that neutrinos are responsible for the observed weaker gravitational lensing than would be expected from massless neutrinos.[77] If the neutrino is a Majorana particle, the mass may be calculated by finding the half-life of neutrinoless double-beta decay of certain nuclei.

The characteristic areas for the electroweak interaction are measured in units called nanobarns&#160;(nb) which are 10−33&#160;cm² or 10−37&#160;m², roughly the area of a disc a little more than 0.3&#160;attometer in diameter, or about 1 billionth of the size of a uranium nucleus.

For example, most solar neutrinos have energies on the order of 6986160217648700000♠100&#160;keV–6987160217648700000♠1&#160;MeV, so the fraction of neutrinos with 'wrong' helicity among them cannot exceed 6990100000000000000♠10−10.[82][83] An unexpected series of experimental results for the rate of decay of heavy highly charged radioactive ions circulating in a storage ring has provoked theoretical activity in an effort to find a convincing explanation.

The rates of weak decay of two radioactive species with half lives of about 40 s and 200 s are found to have a significant oscillatory modulation, with a period of about 7 s.[84] The observed phenomenon is known as the GSI anomaly, as the storage ring is a facility at the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt Germany.

The majority of energy in a nuclear reactor is generated by fission (the four main fissile isotopes in nuclear reactors are 235U, 238U, 239Pu and 241Pu), the resultant neutron-rich daughter nuclides rapidly undergo additional beta decays, each converting one neutron to a proton and an electron and releasing an electron antineutrino (n → p + e− + ν e).

The antineutrino energy spectrum depends on the degree to which the fuel is burned (plutonium-239 fission antineutrinos on average have slightly more energy than those from uranium-235 fission), but in general, the detectable antineutrinos from fission have a peak energy between about 3.5 and 6987640870594800000♠4&#160;MeV, with a maximum energy of about 6988160217648700000♠10&#160;MeV.[88] There is no established experimental method to measure the flux of low-energy antineutrinos.

Thus, an average nuclear power plant may generate over 7020100000000000000♠1020 antineutrinos per second above this threshold, but also a much larger number (97%/3% ≈ 30 times this number) below the energy threshold, which cannot be seen with present detector technology.

Each second, about 65 billion (7010650000000000000♠6.5×1010) solar neutrinos pass through every square centimeter on the part of the Earth orthogonal to the direction of the Sun.[12] Since neutrinos are insignificantly absorbed by the mass of the Earth, the surface area on the side of the Earth opposite the Sun receives about the same number of neutrinos as the side facing the Sun.

A second and more important neutrino source is the thermal energy (100&#160;billion&#160;kelvins) of the newly formed neutron core, which is dissipated via the formation of neutrino–antineutrino pairs of all flavors.[95] Colgate and White's theory of supernova neutrino production was confirmed in 1987, when neutrinos from Supernova&#160;1987A were detected.

The water-based detectors Kamiokande II and IMB detected 11 and 8&#160;antineutrinos (lepton number&#160;=&#160;−1) of thermal origin,[95] respectively, while the scintillator-based Baksan detector found 5&#160;neutrinos (lepton number&#160;=&#160;+1) of either thermal or electron-capture origin, in a burst less than 13&#160;seconds long.

For a Type&#160;II supernova, astronomers expect the neutrino flood to be released seconds after the stellar core collapse, while the first electromagnetic signal may emerge hours later, after the explosion shock wave has had time to reach the surface of the star.

The number of neutrinos counted was also consistent with a total neutrino energy of 7046220000000000000♠2.2×1046&#160;joules, which was estimated to be nearly all of the total energy of the supernova.[97] For an average supernova, approximately 10+57 (an octodecillion) neutrinos are released, however the actual number detected at a terrestrial detector

Indeed, the collisions of cosmic rays are supposed to produce charged pions, whose decay give the neutrinos, and also neutral pions, whose decay give gamma rays: the environment of a supernova remnant is transparent to both types of radiation.

The Sudbury Neutrino Observatory is similar, but uses heavy water as the detecting medium, which uses the same effects, but also allows the additional reaction any-flavor neutrino photo-dissociation of deuterium, resulting in a free neutron which is then detected from gamma radiation after chlorine-capture.

MINOS used a solid plastic scintillator coupled to photomultiplier tubes, while Borexino uses a liquid pseudocumene scintillator also watched by photomultiplier tubes and the NOνA detector uses liquid scintillator watched by avalanche photodiodes.

Whereas photons emitted from the solar core may require 40,000 years to diffuse to the outer layers of the Sun, neutrinos generated in stellar fusion reactions at the core cross this distance practically unimpeded at nearly the speed of light.[100][101] Neutrinos are also useful for probing astrophysical sources beyond the Solar System because they are the only known particles that are not significantly attenuated by their travel through the interstellar medium.

The neutrino's significance in probing cosmological phenomena is as great as any other method, and is thus a major focus of study in astrophysical communities.[103] The study of neutrinos is important in particle physics because neutrinos typically have the lowest mass, and hence are examples of the lowest-energy particles theorized in extensions of the Standard Model of particle physics.

Beta particles are electrons or positrons (electrons with positive electric charge, or antielectrons).

Electric charge conservation requires that if an electrically neutral neutron becomes a positively charged proton, an electrically negative particle (in this case, an electron) must also be produced.

Similarly, conservation of lepton number requires that if a neutron (lepton number = 0) decays into a proton (lepton number = 0) and an electron (lepton number = 1), a particle with a lepton number of -1 (in this case an antineutrino) must also be produced.

If it leads to a more stable nucleus, a proton in a nucleus may capture an electron from the atom (electron capture), and change into a neutron and a neutrino.

## Lepton

A lepton is an elementary, half-integer spin (spin ​1⁄2) particle that does not undergo strong interactions.[1] Two main classes of leptons exist: charged leptons (also known as the electron-like leptons), and neutral leptons (better known as neutrinos).

It took until 1947 for the concept of 'leptons' as a family of particle to be proposed.[8] The first neutrino, the electron neutrino, was proposed by Wolfgang Pauli in 1930 to explain certain characteristics of beta decay.[8] It was first observed in the Cowan–Reines neutrino experiment conducted by Clyde Cowan and Frederick Reines in 1956.[8][9] The muon neutrino was discovered in 1962 by Leon M.

The name lepton comes from the Greek λεπτός leptós, 'fine, small, thin' (neuter nominative/accusative singular form: λεπτόν leptón);[14][15] the earliest attested form of the word is the Mycenaean Greek 𐀩𐀡𐀵, re-po-to, written in Linear B syllabic script.[16] Lepton was first used by physicist Léon Rosenfeld in 1948:[17] Following a suggestion of Prof.

When Rosenfeld named them, the only known leptons were electrons and muons, whose masses are indeed small compared to nucleons—the mass of an electron (6999511000000000000♠0.511&#160;MeV/c2)[18] and the mass of a muon (with a value of 7002105700000000000♠105.7&#160;MeV/c2)[19] are fractions of the mass of the 'heavy' proton (7002938300000000000♠938.3&#160;MeV/c2).[20] However, the mass of the tau (discovered in the mid 1970s) (7003177700000000000♠1777&#160;MeV/c2)[21] is nearly twice that of the proton, and about 3,500 times that of the electron.

Thomson and his team of British physicists in 1897.[22][23] Then in 1930 Wolfgang Pauli postulated the electron neutrino to preserve conservation of energy, conservation of momentum, and conservation of angular momentum in beta decay.[24] Pauli theorized that an undetected particle was carrying away the difference between the energy, momentum, and angular momentum of the initial and observed final particles.

Due to its mass, it was initially categorized as a meson rather than a lepton.[25] It later became clear that the muon was much more similar to the electron than to mesons, as muons do not undergo the strong interaction, and thus the muon was reclassified: electrons, muons, and the (electron) neutrino were grouped into a new group of particles—the leptons.

Lederman, Melvin Schwartz, and Jack Steinberger showed that more than one type of neutrino exists by first detecting interactions of the muon neutrino, which earned them the 1988 Nobel Prize, although by then the different flavours of neutrino had already been theorized.[26] The tau was first detected in a series of experiments between 1974 and 1977 by Martin Lewis Perl with his colleagues at the SLAC LBL group.[27] Like the electron and the muon, it too was expected to have an associated neutrino.

The theoretical and measured values for the electron anomalous magnetic dipole moment are within agreement within eight significant figures.[31] In the Standard Model, the left-handed charged lepton and the left-handed neutrino are arranged in doublet (ν eL,

The Higgs mechanism recombines the gauge fields of the weak isospin SU(2) and the weak hypercharge U(1) symmetries to three massive vector bosons (W+, W−, Z0) mediating the weak interaction, and one massless vector boson, the photon, responsible for the electromagnetic interaction.

This is in close agreement with current experimental observations.[32] However, it is known from experiments—most prominently from observed neutrino oscillations[33]—that neutrinos do in fact have some very small mass, probably less than 7000200000000000000♠2&#160;eV/c2.[34] This implies the existence of physics beyond the Standard Model.

The members of each generation's weak isospin doublet are assigned leptonic numbers that are conserved under the Standard Model.[35] Electrons and electron neutrinos have an electronic number of Le&#160;=&#160;1, while muons and muon neutrinos have a muonic number of Lμ&#160;=&#160;1, while tau particles and tau neutrinos have a tauonic number of Lτ&#160;=&#160;1.

The coupling of the leptons to gauge bosons are flavour-independent (i.e., the interactions between leptons and gauge bosons are the same for all leptons).[35] This property is called lepton universality and has been tested in measurements of the tau and muon lifetimes and of Z boson partial decay widths, particularly at the Stanford Linear Collider (SLC) and Large Electron-Positron Collider (LEP) experiments.[36]:241–243[37]:138 The decay rate (Γ) of muons through the process μ− → e− + ν e

On the other hand, electron–muon universality implies[35] This explains why the branching ratios for the electronic mode (17.85%) and muonic (17.36%) mode of tau decay are equal (within error).[21] Universality also accounts for the ratio of muon and tau lifetimes.

The ratio of tau and muon lifetime is thus given by[35] Using the values of the 2008 Review of Particle Physics for the branching ratios of muons[19] and tau[21] yields a lifetime ratio of ~6993129000000000000♠1.29×10−7, comparable to the measured lifetime ratio of ~6993131999999999999♠1.32×10−7.

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