Solar Neutrino Problem

Why should we even care about neutrinos coming from the sun in the first place? In the 1960’s, the processes governing the interior of the sun were not well understood. There was a strong suspicion that the suns main energy source was the fusion of Hydrogen into Helium, but there was no direct evidence for this hypothesis. This is because the photons produced in fusion processes have a mean free path of about ​10^(-10) times the radius of the sun [1]. That is to say, it takes thousands of years for the light produced inside the core of the sun to escape and be detected at Earth. Photons then are not a good experimental observable to use if we want to understand the interior of the sun.

Additionally, these fusion processes also produce neutrinos, which are essentially non-interacting. Their non-interactive properties on one hand means that they can escape the interior of the sun unimpeded. Neutrinos thus give us a direct probe into the core of the sun without the wait that photons require. On the other hand though, these same non-interactive properties mean that detecting them is extremely difficult.

The undertaking to understand and measure these neutrinos was headed by John Bahcall, who headed the theoretical development, and Ray Davis Jr, who headed the experimental development.

In 1963, John Bahcall gave the first prediction of the neutrino flux coming from the sun [1]. Five years later in 1968, Ray Davis provided the first measurement of the solar neutrino flux [2]. They found that the predicted value was about 2.5 times higher than the measured value. This discrepancy is what became known as the solar neutrino problem.

This plot shows the discrepancy between the measured (blue) and predicted (not blue) amounts of electron neutrinos from various experiments. Blue corresponds to experimental measurements. The other colors correspond to the predicted amount of neutrinos from various sources. This figure was first presented in a 2004 paper by Bahcall [3].

Broadly speaking, there were three causes for this discrepancy:

  1. The prediction was incorrect. This was Bahcalls domain. At lowest order, this could involve some combination of two things. First, incorrect modeling of the sun resulting in inaccurate neutrino fluxes. Second, inaccurate calculation of the observable signal resulting from the neutrino interactions with the detector. Bahcall and his collaborators spent 20 years refining this work and much more but the discrepancy persisted.
  2. The experimental measurement was incorrect. During those same 20 years, until the late 1980’s, Ray Davis’ experiment was the only active neutrino experiment [4]. He continued to improve the experimental sensitivity, but the discrepancy still persisted.
  3. New Physics. In 1968, B. Pontecorv and V. Gribov formulated Neutrino oscillations as we know it today. They proposed that Neutrino flavor eigenstates are linear combinations of mass eigenstates [5]. At a very hand-wavy level, this ansatz sounds reasonable because a neutrino of one flavor at production can change its identity while it propagates from the Sun to the Earth. This is because it is the mass eigenstates that have well-defined time-evolution in quantum mechanics.

It turns out that Pontecorv and Gribov had found the resolution to the Solar Neutrino problem. It would take an additional 30 years for experimental verification of neutrino oscillations by Super-K in 1998 [6], and Sundbury Neutrino Observatory (SNO) in 1999 [7].


References:

[1] – Solar Neutrinos I: Theoretical This paper lays out the motivation for why we should care about solar neutrinos at all.

[2] – Search for Neutrinos from the Sun The first announcement of the measurement of the solar neutrino flux.

[3] – Solar Models and Solar Neutrinos This is a summary of the Solar Neutrino Problem as presented by Bahcall in 2004.

[4] – The Evolution of Neutrino Astronomy A recounting of their journey in neutrino oscillations written by Bahcall and Davis.

[5] – Neutrino Astronomy and Lepton Charge This is the paper that laid down the mathematical groundwork for neutrino oscillations.

[6] – Evidence for Oscillation of Atmospheric Neutrinos The Super-K collaboration reporting their findings in support of neutrino flavor oscillations.

[7] – The Sudbury Neutrino Observatory The SNO collaboration announcing that they had strong experimental evidence for neutrino oscillations.

Additional References

[A] – Formalism of Neturino Osciallations: An Introduction. An accessible introduction to neutrino oscillations, this is useful for anyone who wants a primer on this topic.

[B] – Neutrino Masses, Mixing, and Oscillations. This is the Particle Data Group (PDG) treatment of neutrino mixing and oscillation.

[C] – Solving the mystery of the missing neutrinos. Writen by John Bahcall, this is a comprehensive discussion of the “missing neutrino” or “solar neutrino” problem.

Discovering the Top Quark

This post is about the discovery of the most massive quark in the Standard Model, the Top quark. Below is a “discovery plot” [1] from the Collider Detector at Fermilab collaboration (CDF). Here is the original paper.

This plot confirms the existence of the Top quark. Let’s understand how.

For each proton collision that passes certain selection conditions, the horizontal axis shows the best estimate of the Top quark mass. These selection conditions encode the particle “fingerprint” of the Top quark. Out of all possible proton collisions events, we only want to look at ones that perhaps came from Top quark decays. This subgroup of events can inform us of a best guess at the mass of the Top quark. This is what is being plotted on the x axis.

On the vertical axis are the number of these events.

The dashed distribution is the number of these events originating from the Top quark if the Top quark exists and decays this way. This could very well not be the case.

The dotted distribution is the background for these events, events that did not come from Top quark decays.

The solid distribution is the measured data.

To claim a discovery, the background (dotted) plus the signal (dashed) should equal the measured data (solid). We can run simulations for different top quark masses to give us distributions of the signal until we find one that matches the data. The inset at the top right is showing that a Top quark of mass of 175GeV best reproduces the measured data.

Taking a step back from the technicalities, the Top quark is special because it is the heaviest of all the fundamental particles. In the Standard Model, particles acquire their mass by interacting with the Higgs. Particles with more mass interact more with the Higgs. The Top mass being so heavy is an indicator that any new physics involving the Higgs may be linked to the Top quark.


References / Further Reading

[1] – Observation of Top Quark Production in pp Collisions with the Collider Detector at Fermilab – This is the “discovery paper” announcing experimental evidence of the Top.

[2] – Observation of tt(bar)H Production – Who is to say that the Top and the Higgs even have significant interactions to lowest order? The CMS collaboration finds evidence that they do in fact interact at “tree-level.”

[2] – The Perfect Couple: Higgs and top quark spotted together – This article further describes the interconnection between the Higgs and the Top.

Discovering the Tau

This plot [1] is the first experimental evidence for the particle that would eventually be named the tau.

On the horizontal axis is the energy of the experiment. This particular experiment collided electron and positron beams. On the vertical axis is the cross section of a specific event resulting from the electron and positron beams colliding. The cross section is like a probability for a given event to occur. When two particles collide, many many things can happen, each with their own probability. The cross section for an event encodes the probability for that particular event to occur. Events with larger probability have larger cross sections and vice versa.

The collaboration found one event could not be explained by the Standard Model at the time. The event in question looks like:

This event is peculiar because the final state contains both an electron and a muon with opposite charges. In 1975, when this paper was published, there was no way to obtain this final state, from any known particles or interactions.

In order to explain this anomaly, particle physicists proposed the following explanations:

  1. Pair production of a heavy lepton. With some insight from the future, we will call this heavy lepton the “tau.”

  2. Pair production of charged Bosons. These charged bosons actually end up being the bosons that mediate the weak nuclear force.

The production of tau’s and these bosons are not equally likely though. Depending on the initial energy of the beams, we are more likely to produce one than the other. It turns out that at the energies of this experiment (a few GeV), it is much more likely to produce taus than to produce the bosons. We would say that the taus have a larger cross section than the bosons. From the plot, we can read off that the production of taus, their cross section, is largest at around 5 GeV of energy. Finally, since these taus are the result of pair production, they are produced in pairs. This bump at 5 GeV is the energy at which it is most likely to produce a pair of taus. This plot then predicts the tau to have a mass of about 2.5 GeV.

References

[1] – Evidence for Anomalous Lepton Production in e+−e− Annihilation. This is the original paper that announced the anomaly that would become the Tau.

[2] – The Discovery of the Tau Lepton. This is a comprehensive story of the discovery of the Tau, written by Martin Perl who would go on to win the 1995 Nobel prize in Physics for its discovery.

[3] – Lepton Review. Hyperphysics provides an accessible review of the Leptonic sector of the Standard Model.