Neutrinos

[00:00:06]One of the most interesting particles in the  Standard Model is the neutrino. They barely ever interact with other particles, making  their detection and subsequent study extremely difficult. Luckily, neutrino physics has come a  long way since Pauli first proposed the idea for the particle in 1930. According to the Standard  Model, the neutrino is a neutral, massless, spin 1/2 fermion with three distinct flavor  states: the electron neutrino, muon neutrino, and tau neutrino. Using this description of  the particle, John Bahcall and other theorists estimated the number of each type of neutrino  that the sun should produce. Then, Ray Davis’ Homestake experiment in the 1960s measured the  solar neutrinos and found approximately 1/3 of the expected flux. This result was replicated in  other experiments, where the number of neutrinos was consistently lower than expectations.  This was known as the Solar Neutrino Problem, and it puzzled physicists for years. Then,  right around the turn of the millennium, two landmark experiments solved the mystery.  The Super-Kamiokande experiment proved that muon neutrinos oscillate, explaining why they weren’t  being seen, and the Sudbury Neutrino Observatory experiment measured the total neutrino flux very  precisely. This had several massive implications.

[00:01:23]First, it solved the solar neutrino problem. The  neutrino flux was at the expected level from the Sun, but the neutrinos were oscillating into  other flavors that could not be detected by the experiments of the time. This gave the false  impression that there were fewer neutrinos in total, while the reality was that the total number  was unchanged as they oscillated between flavor.

[00:01:43]The other realization that came from neutrino  oscillations is that neutrinos must not be massless. They have nonzero mass eigenstates, as  well as flavor eigenstates. To understand this, let’s look at an extremely simplified version  of the theory developed by Pontecorvo, Maki, Nakagawa, and Sakata. Their method  was to construct a matrix that would explain the mixing relationship between  neutrino mass states and flavor states, of which a very simple version could be written  as cosine theta sine theta negative sine theta cosine theta times the vector of mass  states nu 1 and nu 2, is equal to the vector of flavor states nu e and nu mu. For  now, let’s ignore the tau neutrino. Reading off from simple matrix multiplication gives the  relationship that the nu e state is equal to cosine theta times nu 1 plus sine theta times  nu 2. We can do the same for the nu mu state, the muon neutrino. Then add time dependent factors  of e to the negative i times energy times time, use the bra ket notation to project the nu  e state onto the nu mu state, and square the result to find the probability of oscillation from  an electron to a muon neutrino to be P equals sine squared of two theta times sine squared of delta  E times t divided by 2. Since neutrinos are relativistic, their energy is approximately equal  to momentum plus mass squared over 2 times energy, so delta E is approximately delta m squared, aka  the mass difference. If the neutrino is massless, delta m squared is 0 so delta E is 0, and  the sine of 0 is 0, so the probability of oscillation would be 0. Since oscillations happen,  this must mean the neutrinos have nonzero masses.

[00:03:32]Experiments like KATRIN, Project 8, DUNE,  and JUNO are attempting to measure this mass, and KATRIN recently released the tightest upper  bound in the world constraining the mass to less than 0.45 eV. Cosmology claims that the masses  must be smaller than this, so experiments will continue to try to push the upper bound on the  mass as low as possible until the exact values are determined. Additionally, since the delta  m is squared, the state of larger mass is not immediately obvious. There are ongoing experiments  trying to figure out what the order of the three neutrino mass states is, including DUNE and T2K. There is another fascinating part of neutrino physics that could provide some valuable insight  into our universe. Since the neutrino is neutrally charged, there is a possibility that it could be  what is known as a Majorana fermion. This is the other lesser-known type of fermion besides a  Dirac fermion, which obeys the Dirac equations and subsequently has an anti-particle related  to it through negative solutions to the Dirac equation as we discussed earlier. Think about how  an electron has a corresponding anti-particle: the positron. In contrast, Majorana fermions  are their own anti-particle. As you can imagine, a particle being its own anti-particle violates  some symmetries. If neutrinos are Majorana, lepton number is violated. In many models, this  enables leptogenesis, where there are CP violating decays of heavy neutrinos in the early universe.  Importantly, this creates the CP violation that could lead to baryon asymmetry. As a result,  Majorana particles could explain the dominance of matter over anti-matter. Neutrinos could  provide the CP violation we have been looking for that doesn’t exist in the Standard Model  but is needed to explain why we exist at all.

[00:05:22]If neutrinos are Majorana fermions, then  there is a smoking gun that experimental physicists could use to prove this. The  process is called neutrino-less double beta decay. Take one beta decay, which turns a  neutron into a proton and emits an electron and an antineutrino of the electron flavor. If two  happen simultaneously, or “double beta decay”, then two neutrons will turn into two protons and  emit two electrons and two electron antineutrinos.

[00:05:51]This process has been experimentally observed,  but it is uncommon. However, using the fact that neutrinos could be Majorana fermions, Wendell  H. Furry proposed the idea that the two emitted antineutrinos could annihilate with one another,  since they are their own anti-particle. In more complex theoretical language, the two beta  decay vertices would exchange a virtual neutrino. This would result in a process where  two neutrons turn into two protons and emit just two electrons. Hence the name, “neutrino-less  double beta decay”. This interaction has not yet been seen, but experiments like LEGEND, CUPID, and  KamLAND-Zen around the world are searching for it.

[00:06:31]There are a few other important things to mention  when it comes to neutrinos. Rather than just looking at solar neutrinos and neutrinos  produced from sources on Earth or nearby, some experiments like IceCube look for neutrinos  originating far away from astrophysical sources.

[00:06:47]This can help us learn about the structure and  composition of the universe. There is also a Cosmic Neutrino Background, analogous to the  Cosmic Microwave Background, which would give us information about a much earlier universe than  the CMB. An experiment called PTOLEMY is building a demonstrator to prove that an experiment could  look for this. It is extremely hard to detect but would revolutionize cosmology in the same way that  the CMB did. There are also theories about sterile neutrinos, which are hypothetical neutrinos that  don’t feel the weak force. Yet, they mix with the three active flavors and add extra oscillation  frequencies. Certain anomalies have been spotted in reactor and accelerator experiments that  possibly point towards extra sterile neutrino flavors, as well as some theoretical motivations  that let them act as dark matter or CP violating components of the early universe. Searches  for these sterile neutrinos are ongoing at accelerators like Fermilab, and constraints can be  placed on their masses from astrophysical neutrino experiments and cosmological models. We’ve only sketched the landscape, but neutrino experiments now span reactors,  accelerators, underground detectors, and the cosmos, each constraining different pieces  of the puzzle. Despite their weak interactions, neutrinos have become precision tools for  both particle physics and cosmology. With new experiments and revamped versions of old  experiments continuing to start taking data, the possibility of discovering exciting new  physics beyond the Standard Model is growing.