Thursday, March 28, 2013

Cosmic accounting and neutrino mass

What is the universe made of?

A very large part of the mass-energy of the universe according to the six parameter lambda CDM model that predicts the patterns of cosmic microwave background radiation which we observe at about 2.7 degrees Kelvin, is attributable to "dark energy" and "dark matter", and a tiny little bit in principle (which the model disregards) is attributable to ambiant radiation.  The rest is "ordinary" matter of the kind described by the Standard Model of Particle Physics which is the subject of this post.

The best evidence we have available to us suggests that the universe, at a very fine grained level, is almost perfectly electromagnetically neutral.  Since conservation of net charge is maintained in all interactions, this has always been true going back as far as the laws of physics hold.

The best evidence we have available also suggests that protons, neutrons and electrons make up virtually all of the ordinary matter in the universe (i.e. other than dark matter and dark energy), with only an infinitessimal share of it at any one time consisting of mesons, hadrons other than protons and neutrons, muons and taus, all of which are extremely unstable. 

Thus, there is almost exactly one electron for every proton in the universe.

Each proton is made up of two up quarks and one down quark.  It is possible to estimate the number of neutrons relative to the number of protons as well.  About 90% of all known (non-dark matter) atoms are protium (H-1), with proton and electron but no neutron, and over 98% of the remainder is helium-4, with two protons, two neutrons, and two electrons.  In general, for heavier atoms, there are far more protons than neutrons in the naturally occuring isotypes in the proportions in which they appear in nature.  So, the ratio of protons to neutrons is probably between 19-1 and 20-1.

Thus, about 65% of the quarks in the universe are up quarks, about 35% of the quarks in the universe are down quarks, a tiny fraction of a percent of the quarks in the universe at any given moment are strange, charm, bottom or top quarks, and any even smaller fraction of a fraction of a percent of quarks in the universe at any given time are antiquarks.

In the Standard Model, baryon number, which is the number of quarks minus the number of antiquarks, divided by three, is perectly conserved.  Likewise, lepton number which is the number of leptons (i.e. electrons, muons, taus and neutrinos) minus the number of antileptons, is likewise perfectly conserved.

How are neutrinos created?

Neutrinos can be created in two known ways. 

A neutrino-antineutrino pair can be created from the decay of a Z boson.  A Z boson is a heavy electromagnetically neutral weak force boson that couples proportionally to the weak force coupling constant and a particle's weak isospin, to all massive fundamental particles in the Standard Model a bit like a heavy photon.

Far more commonly, neutrinos are created when a W boson decays to a charge lepton and a neutrino or antineutrino.  When the W+ boson decays, it often decays to a positron and electron neutrino, to an antimuon and muon neutrino, or to an antitau and tau neutrino.  In the more common situation, the decay of a W- boson emitted in connection with nuclear beta decay, the W- boson decays to an electron and electron antineutrino, to a muon and a muon antineutrino, or to a tau and a tau antineutrino.

Of course, when a muon or tau are produced, they decay with a high probability to a neutrino and a W+ boson, which in turn decays to another neutrino and a charged antilepton, which in turn annihilates with charged lepton or decays further, often into two antineutrinos and a charged lepton.

The beta decay channel is by far the most common means by which neutrinos are created.  It is fair to assume that there is one antineutrino in existence for every electron (and for each muon and tau) in existence, in addition to an additional antineutrino for every ordinary neutrino in existence that does not have a positron, antimuon or antitau counterpart. 

Thus, the vast majority of neutrinos are actually antineutrinos.  Likewise, the vast majority of antimatter particles in the universe are antineutrinos. 

The mass proportions of ordinary matter in the universe

Protons and neutrons each have masses about 2000 times that of the electron.  So about 99.997% of the non-dark matter in the universe is made up of protons and neutrons (and less than 1% of that is attributable to the rest mass of the quarks in those hadrons - the rest arises dynamically from the strong nuclear force exchange of gluons between them which is mostly localized in the central 1/3rd of a proton or neutron's diameter). 

Almost all of the rest of the non-dark matter in the universe comes from electrons.  Electrons, in turn have masses of about 1,000,000 to 1,000,000,000 times that of the three known kinds of neutrinos and antineutrinos.  Thus, anti-matter makes up something on the order of between one part in two billion and one part in two trillion of the non-dark matter, non-dark energy in the universe by weight, although it is hard to know how many neutrino-antineutrino pairs have been created through sequences of W+ boson decays or Z boson decays and not annihilated each other.  This gross asymmetry of matter and antimatter in the universe is one of the great unsolved questions of physics.

Quarks and charged leptons have a powerful tendency to rapidly decay to the first generation versions of these particles (up quarks, down quarks, and electrons).  But, once you have an antineutrino of a particular type, it oscillates between the three different kinds of antineutrinos and the parameters of those oscillations are just on the brink of being determined.  So, we don't know very accurately what proportions of the different antineutrino types are in the universe.

A few personal conjectures on neutrino mass and matter-antimatter asymmetry

One of the other great unsolved questions in physics is why neutrinos are so much less massive than all of the other Standard Model fermions.

My intuition is that the answer to this question has a deep connection to the matter-antimatter asymmetry in the universe and probably also to the fact that the up quark is stable and the down quark is not unless found neutrons confined in an atomic nuclei.

Since neutrons decay into protons, this decay must be balanced by a negatively charged leptons and in order to conserve lepton number and electromagnetic charge, an electromagnetically neutral antilepton.  If neutrons decayed into protons, it would take a charged antilepton and an electromagnetically neutral lepton to balance the books.

One of the reasons I doubt that neutrinos are their own antiparticles and have Majorana mass is that their essential function in beta decay is to be antileptons that can balance lepton number.  If a neutrino and an antineutrino were the same thing, this wouldn't work.  Their intrinsic antimatter character is critical to the role that antineutrinos play in particle physics.

One way to describe an antiparticle is as an ordinary particle going backward in time.

One way to interpret an annihilation event when a charged particle and charged antiparticle come into contact, and give rise to a photon with energy equal to their combined mass-energy, is that a single particle moving forward in time is knocked backward in time by the incredibly powerful punch of a superenergetic photon.  In this interpretation, the amount of energy necessary to make a particle moving forward in time reverse direction is equal to two times its rest mass time the speed of light squared, plus an adjustment for its momentum.  The energy released in a matter-antimatter annihilation is many orders of magnitude greater than the energy released in a nuclear fusion reaction involving the same mass of reactants.

If you apply the intuition of this interpretation to W- boson decay, you would reason heuristically that a W- boson wants to decay into two particles of roughly equal mass energy.  On one side of the balance is the mass-energy necessary to create an electron.  On the other side of the balance is the mass-energy necessary to create a neutrino and then convert it from a particle into the antiparticle that is necessary to keep the interaction's lepton number balanced.  The feat of creating even a tiny amount of antimatter counterbalances the much easier act of creating of ordinary matter in the form of an electron on the other side of the balance.

The neutrinos then seek a hiearchy of masses between the three generations of neutrinos in a manner similar to that of charged leptons and quarks - but the need to cross the matter-antimatter barrier profoundly suppresses the amount of mass transmitted from charged leptons to antineutrinos via W boson exchange relative to the parallel process for quarks (outlined as a conjecture here).   Effectively, because of this matter-antimatter barrier, neutrinos are only receiving mass contributions from other neutrinos, and charged leptons are receiving contributions only from other charged leptons, unlike up-like quarks which receive contributions from all of the other down-like quarks they can interact with, and down-like quarks which receive contributions from all of the other up-like quarks they can interact with.

I also suspect that the matter-antimatter imbalance in the universe has been with us since not long at all after the Big Bang, probably at the very least by the end of the inflationary era.  Our matter dominanted universe is an arrow of time.  I suspect, but can't prove that there is another universe that exists in the time before the Big Bang, in which causality run in the other direction and what we call antimatter is just as predominant as what we call ordinary matter is in our universe.  Our universe is rushing away from the Big Bang in one direction in time, and the other universe is rushing away from the Big Bang in the other direction in time.  At the "time zero" boundary within the Big Bang, pure energy condenses into matter-antimatter particle pairs with the matter particles ending up on our side of t=0 and the antimatter particles undering up on their side of t=0, because the fundamental essence of matter is that it moves forward in time (as we reckon it) and the fundamental essence of antimatter is that it moves backward in time.

Once you start with a matter dominated universe, annhilation of stray particles of charged antimatter, and ordinary W boson and Z boson decays perpetuate a matter dominated universe with the sole residual exception being about one part per two billion to two trillion of the mass-energy of the universe in the form of antineutrinos.

The questions aren't answered by the Standard Model itself.  They may not even be answerable questions except to the extent that the observed masses of particles and their frequencies coincide, or do not coincide, with a more rigorous version of these heuristic ideas, or to the extent that this kind of thinking also fosters a train of thought that leads to other conclusions that are somehow more rigorously testable.

But, the notion that focusing on the antimatter character of most neutrinos in accounting for their tiny mass, rather than on their lack of electromagnetic charge, may be a useful exercise.

An alternative, although not entirely independent heuristic, could also play a role.  The constant process of alternating between left parity and right parity modes while retaining the same character on the particle-antiparticle dimension, possibly due to the Higgs field, may be an important process in the generation of the rest masses of the fundamental particles.  Since neutrinos can only change between a left parity and right parity mode by simultaneously changing from a particle to an antiparticle mode, which poses a much greater barrier to that transition, their masses are suppressed.

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