Particle physics – Beyond the standard model

Neutrino physics

Dr Teppei Katori

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Dr Katori is a senior lecturer at Queen Mary University of London. He obtained his PhD from Indiana University, Bloomington, USA and after doing a postdoc at MIT he came to the UK for his current position.

He has a wide interest in physics, from nuclear physics and particle physics to theoretical and experimental astrophysics. He was awarded the 2012 IUPAPC11 young scientist prize and the 2013 American Physical Society Henry Primoakoff award on his work on neutrino physics.

https://www.qmul.ac.uk/spa/people/academics/profiles/tkatori.html

https://pprc.qmul.ac.uk/~katori/

https://twitter.com/teppeikatori?lang=en

My notes from the lecture (if they don’t make sense then it is entirely my fault)

The standard model included 3 types of neutrinos: electron neutrino (ne), muon neutrino (nm) and Tau neutrino (nt). They are special because they only interact with the weak force (W or Z)

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W bosons mediate the weak force when particles with charge are involved, and Z bosons mediate the weak force when neutral particles are involved.

https://atlas.physicsmasterclasses.org/en/wpath_lhcphysics2.htm

The W particle is heavy (80.4 GeV/c2) and decays almost immediately after its production. In one third of the W-decays, a lepton and a neutrino are produced. In these cases, the leptons can be an electron, a muon, or a tau with equal probability. Before the tau can be detected in the detector, it decays as well.

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The muon emits a W- boson and converts into a muon-neutrino; the W boson decays into an electron and an electron-antineutrino. Charge and lepton number are conserved

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https://arxiv.org/pdf/physics/0103091.pdf

By emitting an electrically charged W boson, the weak force changes the flavour of a quark, which causes a proton to change into a neutron, or vice versa.

http://www.phys.spbu.ru/content/File/Library/studentlectures/schlippe/pp05-02.pdf

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Neutrino – quark collisions can take place only via IVB (intermediate vector boson) exchange; if a W boson is exchanged, the reaction is called a charged current (CC) process.

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Neutrino – quark scattering can go via Z boson exchange; this is called neutral current (NC) process

https://en.wikipedia.org/wiki/Vector_boson

https://atlas.physicsmasterclasses.org/en/zpath_lhcphysics2.htm

Since Z is neutral the sum of the charges of its decay products must be 0. This is because in nature charge is conserved.

In 10% of the Z-decays, charged lepton-antilepton pairs are produced. The three possible charged lepton pair types are electron-positron, muon-antimuon, and tau-antitau pairs. Each pair is approximately equally probable. This gives 3 decay possibilities.

The Z boson decays in 20% of the cases into a neutrino-antineutrino pair. Our detector is not capable of detecting neutrinos since they almost don’t interact with anything (no electric charge). The neutrinos are therefore invisible to us and the only way we can “see” them is when we measure that there is some energy or transverse momentum missing after the collision (since we know that both transverse momentum and energy should be conserved in the collision). The neutrino decays gives another 3 possibilities.

Neutrinos are called ghost particles as they do not really interact with things. It is extremely hard to stop them

How to stop particles

In school we use the following diagram to illustrate the penetrating power of each of the types of nuclear radiation

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https://www.anythingradioactive.com/rough%20guide%20to%20radioactivity

In reality a few cm of air can also stop alpha radiation but the lead needs to be very thick to stop most gamma radiation getting through.

However to stop neutrinos getting to us you would need a piece of lead as thick as the distance between the Sun and Pluto surrounding Earth and then you would probably only stop one.

There are neutrinos everywhere.

https://en.wikipedia.org/wiki/Solar_neutrino

Electron neutrinos are produced in the Sun as a product of nuclear fusion. Solar neutrinos constitute by far the largest flux of neutrinos from natural sources observed on Earth, as compared with e.g. atmospheric neutrinos or the diffuse supernova neutrino background.

About 60 billion electron neutrinos reach us from the Sun but there is only a 25% chance of a neutrino hitting you in your lifetime.

https://en.wikipedia.org/wiki/Bubble_chamber

A bubble chamber is a vessel filled with a superheated transparent liquid (most often liquid hydrogen) used to detect electrically charged particles moving through it. It was invented in 1952 by Donald A. Glaser, for which he was awarded the 1960 Nobel Prize in Physics.

https://en.wikipedia.org/wiki/Donald_A._Glaser

Because neutrinos are neutral you can only identify them by the products of their interaction with other particles.

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This photograph of tracks in the Gargamelle bubble chamber provided the first confirmation of the weak neutral-current interaction. A neutrino, which leaves no track, enters from the top and knocks on an electron, giving it enough energy to create the small downward “shower” of curling tracks. The Gargamelle collaboration announced the discovery of the weak neutral current in July 1973 (Image: Gargamelle/CERN)

https://home.cern/news/news/experiments/seeing-invisible-event-displays-particle-physics

https://videos.cern.ch/record/1069969

https://en.wikipedia.org/wiki/Gargamelle

Gargamelle was a heavy liquid bubble chamber detector in operation at CERN between 1970 and 1979. It was designed to detect neutrinos and antineutrinos, which were produced with a beam from the Proton Synchrotron (PS) between 1970 and 1976, before the detector was moved to the Super Proton Synchrotron (SPS). In 1979 an irreparable crack was discovered in the bubble chamber, and the detector was decommissioned. It is currently part of the microcosm exhibition at CERN, open to the public.

https://en.wikipedia.org/wiki/Introduction_to_eigenstates

An eigenstate is the measured state of some object possessing quantifiable characteristics such as position, momentum, etc. The state being measured and described must be observable (i.e. something such as position or momentum that can be experimentally measured either directly or indirectly), and must have a definite value, called an eigenvalue.

https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)

In quantum mechanics, a Hamiltonian is an operator corresponding to the sum of the kinetic energies plus the potential energies for all the particles in the system (this addition is the total energy of the system in most of the cases under analysis). It is usually denoted by H. Its spectrum is the set of possible outcomes when one measures the total energy of a system. Because of its close relation to the time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.

Neutrinos are produced via the weak interaction:

ne and nμ are eigenstates of the Hamiltonian for the weak interaction – in weak processes they will be stationary states

However, in “free space” (i.e., when they are produced in the sun and travel to the earth) their energy is described by the Hamiltonian for their relativistic energy

Eigenstates for this Hamiltonian are NOT the same – IF these two neutrinos don’t have the same mass – these two Hamiltonians won’t commute!

Weak interaction eigenstates are not Hamiltonian?

Neutrino oscillations

https://en.wikipedia.org/wiki/Neutrino_oscillation

Neutrino oscillation is a quantum mechanical phenomenon whereby a neutrino created with a specific lepton family number (“lepton flavour”: electron, muon, or tau) can later be measured to have a different lepton family number. The probability of measuring a particular flavour for a neutrino varies between 3 known states, as it propagates through space.

First predicted by Bruno Pontecorvo in 1957, neutrino oscillation has since been observed by a multitude of experiments in several different contexts. Notably, the existence of neutrino oscillation resolved the long-standing solar neutrino problem.

Neutrino oscillation is of great theoretical and experimental interest, as the precise properties of the process can shed light on several properties of the neutrino. In particular, it implies that the neutrino has a non-zero mass, which requires a modification to the Standard Model of particle physics. The experimental discovery of neutrino oscillation, and thus neutrino mass, by the Super-Kamiokande Observatory and the Sudbury Neutrino Observatories was recognized with the 2015 Nobel Prize for Physics.

https://en.wikipedia.org/wiki/Bruno_Pontecorvo

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Bruno Pontecorvo (22 August 1913 – 24 September 1993) was an Italian nuclear physicist, an early assistant of Enrico Fermi and the author of numerous studies in high energy physics, especially on neutrinos.

Neutrino oscillation arises from mixing between the flavour and mass eigenstates of neutrinos. That is, the three neutrino states that interact with the charged leptons in weak interactions are each a different superposition of the three (propagating) neutrino states of definite mass. Neutrinos are emitted and absorbed in weak processes in their flavour eigenstates but travel as mass eigenstates.

As a neutrino superposition propagates through space, the quantum mechanical phases of the three mass states advance at slightly different rates, due to the slight differences in their respective neutrino masses. This results in a changing superposition mixture of mass eigenstates as the neutrino travels; but a different mixture of mass eigenstates corresponds to a different mixture of flavour states. So a neutrino born as, say, an electron neutrino will be some mixture of electron, mu, and tau neutrino after traveling some distance. Since the quantum mechanical phase advances in a periodic fashion, after some distance the state will nearly return to the original mixture, and the neutrino will be again mostly electron neutrino. The electron flavour content of the neutrino will then continue to oscillate – as long as the quantum mechanical state maintains coherent. Since mass differences between neutrino flavours are small in comparison with long coherence lengths for neutrino oscillations, this microscopic quantum effect becomes observable over macroscopic distances.

Light interference can be used to explain the process.

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https://en.wikipedia.org/wiki/Superposition_principle

Waves are usually described by variations in some parameter through space and time such as the height of the wave, the amplitude.

In any system with waves, the waveform at a given time is a function of the sources. In other words, when two or more waves meet the resultant amplitude is the sum of the individual amplitudes.

https://en.wikipedia.org/wiki/Quantum_superposition

Quantum superposition is a fundamental principle of quantum mechanics. It states that, much like waves in classical physics, any two (or more) quantum states can be added together (“superposed”) and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states. Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution.

https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation

If two neutrino Hamiltonian eigenstates v1 and v2 have different phase rotations then quantum interference occurs.

If v1 and v2 have different masses they will have different velocities and there will be a different phase rotation.

Neutrinos exhibit the properties of a particle as well as a wave. Therefore, neutrino1, neutrino2 and neutrino3, each with different mass eigenstates, travel through space as waves that have a different frequency. The flavour of a neutrino is determined as a superposition of the mass eigenstates. The type of the flavour oscillates, because the phase of the wave changes.

Eigenstates with different masses propagate with different frequencies. The heavier ones oscillate faster compared to the lighter ones. Since the mass eigenstates are combinations of flavour eigenstates, this difference in frequencies causes interference between the corresponding flavour components of each mass eigenstate. Constructive interference causes it to be possible to observe a neutrino created with a given flavour to change its flavour during its propagation.

https://en.wikipedia.org/wiki/Neutrino_oscillation#Propagation_and_interference

The basic physics behind neutrino oscillation can be found in any system of coupled harmonic oscillators. A simple example is a system of two pendulums connected by a weak spring (a spring with a small spring constant). The first pendulum is set in motion by the experimenter while the second begins at rest. Over time, the second pendulum begins to swing under the influence of the spring, while the first pendulum’s amplitude decreases as it loses energy to the second. Eventually all of the system’s energy is transferred to the second pendulum and the first is at rest. The process then reverses. The energy oscillates between the two pendulums repeatedly until it is lost to friction.

The behaviour of this system can be understood by looking at its normal modes of oscillation. If the two pendulums are identical then one normal mode consists of both pendulums swinging in the same direction with a constant distance between them, while the other consists of the pendulums swinging in opposite (mirror image) directions. These normal modes have (slightly) different frequencies because the second involves the (weak) spring while the first does not. The initial state of the two-pendulum system is a combination of both normal modes. Over time, these normal modes drift out of phase, and this is seen as a transfer of motion from the first pendulum to the second.

The description of the system in terms of the two pendulums is analogous to the flavour basis of neutrinos. These are the parameters that are most easily produced and detected (in the case of neutrinos, by weak interactions involving the W boson). The description in terms of normal modes is analogous to the mass basis of neutrinos. These modes do not interact with each other when the system is free of outside influence.

When the pendulums are not identical the analysis is slightly more complicated. In the small-angle approximation, the potential energy of a single pendulum system is mgx2/2L, where g is the standard gravity, L is the length of the pendulum, m is the mass of the pendulum, and x is the horizontal displacement of the pendulum.

Increasing the number of neutrinos complicates matters. Complex phases need to be introduced in addition to the rotation angles, which are associated with CP violation but do not influence the observable effects of neutrino oscillation.

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The blue curve shows the probability of the original neutrino retaining its identity. The red curve shows the probability of conversion to the other neutrino.

The probability of measuring a particular flavour for a neutrino varies between 3 known states, as it propagates through space.

http://www.hyper-k.org/en/neutrino.html

Neutrino mixing is expressed in terms of three mixing angles: θ12, θ23 and θ13, and the parameter of CP violation. Neutrino oscillation experiments have previously measured three mixing angles and their squared mass differences: m12-m22, m22-m32.

The amplitude of the neutrino “wave” is dictated by the mixing angles and its period by the neutrino mass.

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The type of the flavour oscillates when neutrinos travel through space.

https://www.nobelprize.org/prizes/physics/2015/summary/

The Nobel Prize in Physics 2015 was awarded jointly to Takaaki Kajita and Arthur B. McDonald “for the discovery of neutrino oscillations, which shows that neutrinos have mass.”

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https://www.nobelprize.org/uploads/2018/06/advanced-physicsprize2015-1.pdf

https://www.symmetrymagazine.org/article/nobel-prize-awarded-for-discovery-of-neutrino-oscillations

Neutrinos come in three types: electron, muon and tau. In the 1960s, scientists on an experiment studying neutrinos from the sun found that they were detecting only a third the number of particles they expected to see. This was called the “solar neutrino problem.”

Physicists speculated that the problem lay in their calculations or in the experiment. But Kajita’s and McDonald’s experiments showed that the solar neutrino problem was caused by the extraordinary nature of neutrinos.

Kajita led a team on the Super-Kamiokande experiment near Tokyo, which started operation in 1996. McDonald led a team at Sudbury Neutrino Observatory in Ontario, which began in 1999.

Both experiments used large detectors located underground to catch passing neutrinos. Super-Kamiokande studied muon neutrinos produced by cosmic rays interacting with Earth’s atmosphere. SNO studied electron neutrinos produced by the sun.

Because neutrinos can travel straight through the planet, Super-Kamiokande studied the particles as they approached from above in space and also below through the ground. The neutrinos should have arrived from all directions at the same rate; the only difference between them was the distance they had to travel before they reached the detector.

But scientists found that they detected more muon neutrinos coming from above than from below. They hypothesized that the neutrinos traveling all the way through the Earth had had more time to oscillate, or change to another type of neutrino.

At SNO, scientists used a detector that could identify electron neutrinos from the sun but also take an overall tally of neutrino interactions from all three types of neutrinos.

They saw the solar neutrino problem repeated; they were capturing just a third of the electron neutrinos they expected to see. But their count of all three types of neutrinos together matched their expectations. They concluded that electron neutrinos must have changed into muon and tau neutrinos as they travelled.

Super-Kamiokande and SNO solved the solar neutrino problem. But they also gave scientists another surprising insight into the particles: Because only particles with mass can oscillate, neutrinos must have mass.

https://breakthroughprize.org/Laureates/1/P1/Y2016

The 2016 Breakthrough Prize in Fundamental Physics was awarded to five experiments investigating neutrino oscillation.

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Neutrino physics is the home of discovery physics

Neutrino masses

Neutrino masses are not predicted by the standard model

The seesaw mechanism relates extremely small neutrino masses with the grand unification theory (GUT)

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https://en.wikipedia.org/wiki/Seesaw_mechanism

In the theory of grand unification of particle physics, and, in particular, in theories of neutrino masses and neutrino oscillation, the seesaw mechanism is a generic model used to understand the relative sizes of observed neutrino masses, of the order of eV, compared to those of quarks and charged leptons, which are millions of times heavier.

There are several types of models, each extending the Standard Model. The simplest version, type 1, extends the Standard Model by assuming two or more additional right-handed neutrino fields inert under the electroweak interactions, and the existence of a very large mass scale. This allows the mass scale to be identifiable with the postulated scale of grand unification.

The most popular conjectured solution currently is the seesaw mechanism, where right-handed neutrinos with very large Majorana masses are added. If the right-handed neutrinos are very heavy, they induce a very small mass for the left-handed neutrinos, which is proportional to the inverse of the heavy mass.

If it is assumed that the neutrinos interact with the Higgs field with approximately the same strengths as the charged fermions do, the heavy mass should be close to the GUT scale. Because the Standard Model has only one fundamental mass scale, all particle masses must arise in relation to this scale.

There are other varieties of seesaw and there is currently great interest in the so-called low-scale seesaw schemes, such as the inverse seesaw mechanism.

The addition of right-handed neutrinos has the effect of adding new mass scales, unrelated to the mass scale of the Standard Model, hence the observation of heavy right-handed neutrinos would reveal physics beyond the Standard Model. Right-handed neutrinos would help to explain the origin of matter through a mechanism known as leptogenesis.

https://en.wikipedia.org/wiki/Leptogenesis_(physics)

In physical cosmology, leptogenesis is the generic term for hypothetical physical processes that produced an asymmetry between leptons and antileptons in the very early universe, resulting in the present-day dominance of leptons over antileptons.

M(neutrino) = (standard model)2/(Grand unification)

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The masses of the quarks and leptons of the standard model. The heaviest standard model particle is the top quark; the lightest non-neutrino is the electron, which is measured to have a mass of 511 keV/c². The neutrinos themselves are at least 4 million times lighter than the electron: a bigger difference than exists between all the other particles. All the way at the other end of the scale, the Planck scale hovers at a very high 1019 GeV. We do not know of any particles heavier than the top quark. (HITOSHI MURAYAMA OF HITOSHI.BERKELEY.EDU)

https://medium.com/starts-with-a-bang/why-supersymmetry-may-be-the-greatest-failed-prediction-in-particle-physics-history-e4e7d3879a00

Neutrino standard model (vSM): The standard model + 3 active massive neutrino is established

Unknown parameters of vSM: Precise value of the mixing angle q23; Order of the neutrino masses (is it the normal order m1 < m2 < m3 or inverted order m1 > m2 > m3); Are the neutrinos Dirac or Majorana; Does the Dirac CP phase apply; Does the Majorana CP phase apply; What is the absolute neutrino mass

Beyond vSm (BSM): 4th neutrino search (sterile neutrino search)

https://arxiv.org/pdf/1906.01739.pdf;

Dark matter search with neutrinos (IceCube etc); Space-time tests with neutrinos

https://www.sciencedaily.com/releases/2018/07/180716151607.htm

A new study demonstrates that Einstein is right again. The most thorough test yet finds no Lorentz violation in high-energy neutrinos.

Undetected neutrinos:

Big bang neutrino background; Diffuse supernovae neutrino background; Solar CNO cycle neutrinos; Solar atmospheric neutrinos; GZK neutrinos

https://en.wikipedia.org/wiki/Greisen%E2%80%93Zatsepin%E2%80%93Kuzmin_limit

Dirac or Majorana

https://en.wikipedia.org/wiki/Sterile_neutrino

Sterile neutrinos (or inert neutrinos) are hypothetical particles (neutral leptons – neutrinos) that interact only via gravity and do not interact via any of the fundamental interactions of the Standard Model. The term sterile neutrino is used to distinguish them from the known active neutrinos in the Standard Model, which are charged under the weak interaction.

Sterile neutrinos allow the introduction of a Dirac mass term as usual. This can yield the observed neutrino mass, but it requires that the strength of the Yukawa coupling be much weaker for the electron neutrino than the electron, without explanation.

https://en.wikipedia.org/wiki/Dirac_equation

https://en.wikipedia.org/wiki/Yukawa_interaction

Unlike for the left-handed neutrino, a Majorana mass term can be added for a sterile neutrino without violating local symmetries (weak isospin and weak hypercharge) since it has no weak charge. However, this would still violate total lepton number.

https://en.wikipedia.org/wiki/Majorana_fermion

A Majorana fermion (also referred to as a Majorana particle, is a fermion that is its own antiparticle. They were hypothesized by Ettore Majorana in 1937. The term is sometimes used in opposition to a Dirac fermion, which describes fermions that are not their own antiparticles. Only neutrinos in the standard model can be Majorana.

https://en.wikipedia.org/wiki/Majorana_equation

https://en.wikipedia.org/wiki/Lepton_number

It is possible to include both Dirac and Majorana terms: this is done in the seesaw mechanism. In addition to satisfying the Majorana equation, if the neutrino were also its own antiparticle, then it would be the first Majorana fermion. In that case, it could annihilate with another neutrino, allowing neutrinoless double beta decay. The other case is that it is a Dirac fermion, which is not its own antiparticle.

https://en.wikipedia.org/wiki/Double_beta_decay#Neutrinoless_double_beta_decay

Look for Majorana nature of neutrinos with neutrinoless double beta decay. Only seen with a few elements such as 82Se, 76Ge, 100Mo and 130Te

If the neutrino is a Majorana particle (i.e., the antineutrino and the neutrino are actually the same particle), and at least one type of neutrino has non-zero mass (which has been established by the neutrino oscillation experiments), then it is possible for neutrinoless double beta decay to occur. Neutrinoless double beta decay is a lepton number violating process. In the simplest theoretical treatment, known as light neutrino exchange, a nucleon absorbs the neutrino emitted by another nucleon. The exchanged neutrinos are virtual particles.

With only two electrons in the final state, the electrons’ total kinetic energy would be approximately the binding energy difference of the initial and final nuclei, with the nuclear recoil accounting for the rest. Because of momentum conservation, electrons are generally emitted back-to-back.

Observing neutrinoless double beta decay, in addition to confirming the Majorana neutrino nature, can give information on the absolute neutrino mass scale and Majorana phases in the PMNS matrix, subject to interpretation through theoretical models of the nucleus, which determine the nuclear matrix elements, and models of the decay.

The observation of neutrinoless double beta decay would require that at least one neutrino is a Majorana particle, irrespective of whether the process is engendered by neutrino exchange.

As of 2017, the strongest limits on neutrinoless double beta decay have come from GERDA in 76Ge, CUORE in 130Te, and EXO-200 and KamLAND-Zen in 136Xe. The expected half-life is 1027 years.

mbb is the effective Majorana mass of the electron neutrino and is extracted from the measured half-life.

https://en.wikipedia.org/wiki/CP_violation (charge-parity symmetry violation)

In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge conjugation symmetry) and P-symmetry (parity symmetry). CP-symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle (C symmetry) while its spatial coordinates are inverted (“mirror” or P symmetry).

It plays an important role both in the attempts of cosmology to explain the dominance of matter over antimatter in the present Universe, and in the study of weak interactions in particle physics.

CP violation with leptons

https://physics.stackexchange.com/questions/429461/why-is-it-so-important-to-measure-cp-violation-in-the-lepton-sector

If CP violation is measured in the lepton sector, there are theories which explain the baryon asymmetry observed in the present universe as mathematically connected with generation of the lepton asymmetry, and these models would become mainstream:

The Standard Model is extended by adding right-handed neutrinos, permitting implementation of the see-saw mechanism and providing the neutrinos with mass. At the same time, the extended model is able to spontaneously generate leptons from the decays of right-handed neutrinos. Finally, the sphalerons are able to convert the spontaneously generated lepton asymmetry into the observed baryonic asymmetry. Due to its popularity, this entire process is sometimes referred to simply as leptogenesis.

https://arxiv.org/pdf/1610.03074.pdf

Neutrino oscillations – depends on CP violation (dirac CP phase)

https://iopscience.iop.org/article/10.1088/1126-6708/2004/10/058/pdf

The effect of neutrino oscillations could be down to a new force. Consequences of a new force mediated by a light scalar particle for neutrino oscillation experiments are considered in the above paper. Such a force could give rise to neutrino masses and mixings whose matter dependence for earth densities is much more significant than the MSW effect.

https://en.wikipedia.org/wiki/Mikheyev%E2%80%93Smirnov%E2%80%93Wolfenstein_effect

The Mikheyev–Smirnov–Wolfenstein effect (often referred to as matter effect) is a particle physics process which can act to modify neutrino oscillations in matter.

https://en.wikipedia.org/wiki/T2K_experiment

T2K (Tokai to Kamioka, Japan) is a particle physics experiment that is a collaboration between several countries, including Japan, Canada, France, Germany, Italy, South Korea, Poland, Russia, Spain, Switzerland, the United States, and the United Kingdom. It is the second generation follow up to the K2K experiment, a similar long baseline neutrino oscillation experiment.

The J-PARC facility produces an intense off-axis beam of muon neutrinos. The beam is directed towards the Super-Kamiokande detector, which is 295 km away. The main goal of T2K is to measure the oscillation of nμ to ne and to measure the value of mixing angle q13, one of the parameters of the Pontecorvo–Maki–Nakagawa–Sakata matrix.

On June 15, 2011, the T2K collaboration announced the observation of six electron neutrino-like events compared to an expected background of 1.5, a significance of 2.5 standard deviations.

On July 19, 2013, at the European Physical Society meeting in Stockholm, the international T2K collaboration announced a definitive observation of muon neutrino to electron neutrino transformation.

On August 4, 2017, Mark Hartz revealed at a KEK seminar that the latest data from T2K hinted at CP violation, rejecting the hypothesis that neutrinos and antineutrinos oscillate with the same probability at the 95% confidence (2σ) level.

50 billion neutrinos from J-PARC pass through the detector per second.

https://youtu.be/u-UH3EwIEIs

https://warwick.ac.uk/fac/sci/physics/staff/academic/boyd/warwick_week/neutrino_physics/neutrino_lec_1.pdf

https://naturalsciences.ch/service/news/92546-t2k-presents-hint-of-cp-violation-by-neutrinos

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https://t2k-experiment.org/

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Components of the ND280 near detector

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A very large cylinder of ultra-pure water. Most of the neutrinos pass through without interacting but, due to the high energies of the neutrinos and the intensity of the beam, some do interact with the water.

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Super K can distinguish muons (which produce a sharp ring) from electrons (which produce a more diffuse ring).

http://www-sk.icrr.u-tokyo.ac.jp/realtimemonitor/

The apparatus was refurbished in 2018

http://www.hyperk.org/

Hyper-Kamiokande (HK) is to be the next generation of large-scale water Cherenkov detectors. It is planned to be an order of magnitude bigger than its predecessor, Super-Kamiokande (SK), with the optimal design consisting of two half megaton tanks equiped with ultra high sensitivity photosensors. The Hyper-Kamiokande detector is both a “microscope,” used to observe elementary particles, and also a “telescope” for observing the Sun and supernovas, using neutrinos.

https://youtu.be/JFOE3D2z7LM

It is the aim of Hyper-Kamiokande to elucidate the Grand Unified Theory and the history of the evolution of the Universe through an investigation of proton decay and CP violation (the difference between neutrinos and antineutrinos), together with the observation of neutrinos from supernova explosions.

Hyper-Kamiokande is part of an international research project aiming to start experimentation in the second half of 2020s (set up finished in 2025 and experimental work expected to start in 2026).

https://en.wikipedia.org/wiki/Hyper-Kamiokande

Neutrino interaction physics and nuclear physics

https://www.kth.se/social/upload/518bfe1af276540308a329e3/neutrino_physics_applications.pdf

Nuclear-structure calculations are important for many applications in neutrino physics and nuclear astrophysics

Neutrino-nucleus scattering can be used to probe properties of the neutrino. However, accurate knowledge about the nuclear structure of the relevant target are needed.

Neutrinos are the key particle for astro-nuclear physics, particle physics and cosmology. Nuclear physics is helping to pin down its properties and sources.

https://www.scitecheuropa.eu/neutrinos/90321/

https://www.researchgate.net/publication/45871193_Neutrino_Interactions_Importance_to_Nuclear_Physics/link/0fcfd50a41c82c4e08000000/download

https://iopscience.iop.org/article/10.1088/1742-6596/1056/1/012060/pdf

https://iopscience.iop.org/article/10.1088/1742-6596/888/1/012013/pdf

Discovery of nucleon correlation in neutrino scattering

Given enough energy, the neutrino can actually begin to resolve the internal structure of the target: the neutrino can scatter off an individual quark inside the nucleon: DIS (deep inelastic scattering) and it manifests in the creation of a hadronic shower.

Sterile neutrino search – MiniBooNe

https://en.wikipedia.org/wiki/MiniBooNE

MiniBooNE is an experiment at Fermilab designed to observe neutrino oscillations (BooNE is an acronym for the Booster Neutrino Experiment). A neutrino beam consisting primarily of muon neutrinos is directed at a detector filled with 800 tons of mineral oil (ultrarefined methylene compounds) and lined with 1,280 photomultiplier tubes. An excess of electron neutrino events in the detector would support the neutrino oscillation interpretation of the LSND (Liquid Scintillator Neutrino Detector) result.

MiniBooNE started collecting data in 2002.

https://www-boone.fnal.gov/

https://physics.aps.org/articles/v11/122

Confirming previous controversial results, the MiniBooNE experiment detects a signal that is incompatible with neutrino oscillations involving just the three known flavours of neutrinos.

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Scheme of the MiniBooNE experiment at Fermilab. A high-intensity beam of accelerated protons is focused onto a target, producing pions that decay predominantly into muons and muon neutrinos. The resulting neutrino beam is characterized by the MiniBooNE detector.

MiniBooNE found significantly more electron-neutrino-like events than expected from neutrino oscillations or known backgrounds.

What could explain this excess? Immediately after the Liquid Scintillator Neutrino Detector (LSND) observations, theorists put forward the idea that the electron neutrino excess could be due to a fourth, sterile neutrino (particles that only interact through gravity and aren’t foreseen in the standard model).

Unfortunately, other experiments have made serious dents in the sterile neutrino theory.

https://sbn.fnal.gov/

The international Short-Baseline Neutrino Program at Fermilab will measure properties of neutrinos, specifically how the flavour of a neutrino changes as it moves through space and matter.

High energy neutrino astronomy

https://arxiv.org/pdf/1102.3591.pdf

This is a unique tool to test BSM phyiscs. Neutrinos are direct messengers from supernova.

Detection of HE neutrinos from SN remnants will prove that these objects are sources of galactic cosmic rays (CR) and the Standard Model of Galactic Cosmic Ray origin will be confirmed. Jet models of Gamma Ray Bursts (GRBs) and Active Galactic Nuclei (AGN) can be proved. Detection of cosmogenic neutrinos can clarify the origin of Ultra High Energy Cosmic Rays (UHECR) and determine the model of transition from galactic to extragalactic CRs.

Registration of HE neutrinos from the centre of the Sun or Earth indicate the annihilation of Dark Matter (DM) particles there.

Mirror matter can be discovered with help of oscillation mirror neutrinos into visible ones.

IceCube detector

https://icecube.wisc.edu/

https://en.wikipedia.org/wiki/IceCube_Neutrino_Observatory

The IceCube Neutrino Observatory (or simply IceCube) is a neutrino observatory constructed at the Amundsen–Scott South Pole Station in Antarctica. Its thousands of sensors are located under the Antarctic ice, distributed over a cubic kilometre.

Similar to its predecessor, the Antarctic Muon And Neutrino Detector Array (AMANDA), IceCube consists of spherical optical sensors called Digital Optical Modules (DOMs), each with a photomultiplier tube (PMT) and a single-board data acquisition computer which sends digital data to the counting house on the surface above the array. IceCube was completed on 18 December 2010.

DOMs are deployed on strings of 60 modules each at depths between 1,450 to 2,450 meters into holes melted in the ice using a hot water drill. IceCube is designed to look for point sources of neutrinos in the TeV range to explore the highest-energy astrophysical processes.

image

In November 2013 it was announced that IceCube had detected 28 neutrinos that likely originated outside the Solar System.

https://indico.cern.ch/event/743975/contributions/3129652/attachments/1714473/2765331/Simulation_in_IceCube_2018a.pdf

https://youtu.be/wfVM6To7XfE

http://cdnsecakmi.kaltura.com/s/p/537811/sp/53781100/serveFlavor/entryId/0_2os69wkq/v/2/flavorId/0_x90corfm/forceproxy/true/name/a.mp4?aeauth=1563750366_fa85cfda0d3a71b878f63cb0fd957ad1

https://www.youtube.com/watch?v=iv-Rz3-s4BM

Quantum gravity search with astrophysical neutrinos

Might help us finally come up with a “Theory of everything”

https://en.wikipedia.org/wiki/Quantum_gravity

Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics, and where quantum effects cannot be ignored, such as near compact astrophysical objects where the effects of gravity are strong.

The current understanding of gravity is based on Albert Einstein’s general theory of relativity, which is formulated within the framework of classical physics. On the other hand, the other three fundamental forces of physics are described within the framework of quantum mechanics and quantum field theory, radically different formalisms for describing physical phenomena. It is sometimes argued that a quantum mechanical description of gravity is necessary on the grounds that one cannot consistently couple a classical system to a quantum one.

https://en.wikipedia.org/wiki/Albert_Einstein

One of the difficulties of formulating a quantum gravity theory is that quantum gravitational effects only appear at length scales near the Planck scale, around 10−35 meter, a scale far smaller, and equivalently far larger in energy, than those currently accessible by high energy particle accelerators. Therefore physicists lack experimental data which could distinguish between the competing theories which have been proposed and thus thought experiment approaches are suggested as a testing tool for these theories.

http://rxiv.org/pdf/1711.0295v2.pdf

It has long been known that Supernovas produce an intense flux of neutrinos. What is not known is what causes the Supernova to eject a significant amount of mass into the surrounding galactic area. If gravity and neutrinos are correlated, then it becomes quite clear what causes the explosion. If a temporary high flux of neutrinos corresponds with an increased temporary gravity field, this could possibly cause the star to contract with high pressure during this quick burning only to have the gravity return to prior levels. The outer mass would then shoot off like a spring as the pressure stabilizes.

Accelerated expansion without dark matter? This model may help find answers to the accelerated expansion of the Universe. If space-time is consumed during neutrino formation in dense systems, and if neutrino pairs are absorbed in photon pair production and other energy-mass conversions in intergalactic regions, space-time would form. As the space increases, more area for these reactions would allow more reactions to occur resulting in an outward acceleration.

The space between galaxies where large amounts of cosmic waves and neutrinos converge would be a prime area for matter formation. This would then result in neutrinos being used in the process and space-time being formed. Over greater distances, this may also produce gravitational lensing, especially between where galaxies more closely converge. This is because there would be a higher amount of cross sectional radiation and neutrinos density from the nearby galaxies. Recent analysis of galaxy ellipticities has found this gravitational lensing.

https://phys.org/news/2005-09-ancient-neutrinos-theory-quantum-loop.html

https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model

https://en.wikipedia.org/wiki/TXS_0506%2B056

TXS 0506+056 is a very high energy blazar (a type of active galactic nuclei) – a quasar with a relativistic jet pointing directly towards Earth – of BL Lac-type. With a redshift of 0.3365 ± 0.0010, it is about 1.75 gigaparsecs (5.7 billion light-years) from Earth. Its approximate location on the sky is off the left shoulder of the constellation Orion. Discovered as a radio source in 1983, the blazar has since been observed across the entire electromagnetic spectrum.

https://en.wikipedia.org/wiki/Active_galactic_nucleus

An active galactic nucleus (AGN) is a compact region at the centre of a galaxy that has a much higher than normal luminosity over at least some portion of the electromagnetic spectrum with characteristics indicating that the luminosity is not produced by stars.

TXS 0506+056 is the first known source of high energy astrophysical neutrinos, identified following the IceCube-170922A neutrino event in an early example of multi-messenger astronomy. The only astronomical sources previously observed by neutrino detectors were the Sun and supernova 1987A, which were detected decades earlier at much lower neutrino energies.

Both signals of neutrinos and photons are detected coincidently. It is a third celestial neutrino source (after the Sun and a supernova such as 1987A)

https://en.wikipedia.org/wiki/SN_1987A

SN 1987A was a peculiar type II supernova in the Large Magellanic Cloud, a dwarf galaxy satellite of the Milky Way. It occurred approximately 51.4 kiloparsecs (168,000 light-years) from Earth and was the closest observed supernova since Kepler’s Supernova, visible from earth in 1604. 1987A’s light reached Earth on February 23, 1987, and as the first supernova discovered that year, was labelled “1987A”. Its brightness peaked in May, with an apparent magnitude of about 3.

Approximately two to three hours before the visible light from SN 1987A reached Earth, a burst of neutrinos was observed at three neutrino observatories. This was likely due to neutrino emission, which occurs simultaneously with core collapse, but before visible light was emitted.

https://www.youtube.com/watch?v=je_3bLbiGKQ

Fuzzy quantum gravity space-time may slow down neutrinos

From the distance of TXS 0506+056 (1.3Gpc), energy of astrophysical neutrinos (>200 TeV), and time delay (~10days), scale of quantum fluctuation of space-time is limited to <10-16GeV-1

https://en.wikipedia.org/wiki/Quantum_foam

Quantum foam or spacetime foam is the fluctuation of spacetime on very small scales due to quantum mechanics. The idea was devised by John Wheeler in 1955.

https://en.wikipedia.org/wiki/John_Archibald_Wheeler

In a quantum theory of gravity, spacetime would consist of many small, ever-changing regions in which space and time are not definite, but fluctuate in a foam-like manner.

Wheeler suggested that the Heisenberg uncertainty principle might imply that over sufficiently small distances and sufficiently brief intervals of time, the “very geometry of spacetime fluctuates”. These fluctuations could be large enough to cause significant departures from the smooth spacetime seen at macroscopic scales, giving spacetime a “foamy” character.

https://en.wikipedia.org/wiki/Lorentz_covariance

In relativistic physics, Lorentz symmetry, named after Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also been described as “the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space”

https://en.wikipedia.org/wiki/Hendrik_Lorentz

Lorentz-violating neutrino oscillation refers to the quantum phenomenon of neutrino oscillations described in a framework that allows the breakdown of Lorentz invariance. Today, neutrino oscillation or change of one type of neutrino into another is an experimentally verified fact; however, the details of the underlying theory responsible for these processes remain an open issue and an active field of study. The conventional model of neutrino oscillations assumes that neutrinos are massive, which provides a successful description of a wide variety of experiments; however, there are a few oscillation signals that cannot be accommodated within this model, which motivates the study of other descriptions. In a theory with Lorentz violation, neutrinos can oscillate with and without masses and many other novel effects described below appear. The generalization of the theory by incorporating Lorentz violation has shown to provide alternative scenarios to explain all the established experimental data through the construction of global models.

image

More statistics are needed to study quantum gravity

Conclusions

The current standard model includes three types of active neutrinos

Small neutrino masses –> related to high energy scale physics (GUT)?

Majorana neutrinos –> lepton number violation process?

Dirac CP phase –> matter-antimatter asymmetry of the universe?

Neutrino oscillations (interferometer) can be used to look for new physics to go beyond the standard model. Their long propagation and high energy are useful to look for new physics.

There are many ongoing experiments and future planned experiments

https://icecube.wisc.edu/science/beyond

An in-depth exploration of the neutrino universe requires a next-generation IceCube detector. Named IceCube-Gen2 and based upon the robust design of the current detector, the goal for the new observatory is to deliver statistically significant samples of very high energy astrophysical neutrinos, in the PeV to EeV range, and yield hundreds of neutrinos across all flavours at energies above 100 TeV. This will enable detailed spectral studies, significant point source detections, and new discoveries.

https://indico.cern.ch/event/615891/contributions/2650198/attachments/1507727/2349837/gen2_43.pdf

Postscript:

I have a physics degree but its emphasis was experimental. I avoided the advanced quantum mechanics module because I knew my maths wasn’t good enough.

In researching this topic I found a lot of maths which I did not understand so it may be that I have not interpreted the information correctly. For that I apologise.

Wikipedia was an invaluable source of information

Helen

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