Musings On Missing Fundamental Particle Possibilities And What Their Absence Might Mean

Disclaimer. This post is made up of more or less numerological speculative conjectures and musings and really has not solid grounding in proven physics or the academic literature. If you are looking for that move along.

How Many Interchangeable Parts Are There?

In the Standard Model of Particle Physics there are 90 kinds of fundamental fermions of spin 1/2 and 13 kinds of fundamental bosons (8 gluons of spin-1, W+, W-, Z and the photon each of spin-1, and one of spin-0, the Higgs boson) for a total of 103 interchangeable parts that differ from each other only in location and momentum, which are continuous parameters related via the uncertainty principle.

A minimal theory of everything must add at least one boson, a graviton of spin-2 bringing the total types of interchangeable parts in the universe to 104.

Vector bosons are also distinguished from each other by helicity (left, right or neutral for a spin-1 particle if massive, but only left or right if massless) which is a discrete although less fundamental trait. I don't think that a spin-0 Higgs boson can have helicity other than zero (another discussion without a really clean answer is here). Considering helicity, there are 28 kinds of bosons (16 gluons, 2 photons, 6 Ws, 3 Zs and 1 Higgs), rather than 13, and the grand total would be 118 without the graviton.

A graviton (if it were massive) could naively have up to five helicity states (since it is spin-2 rather than spin-1), so with the graviton, there would be 123 kinds of interchangable parts that differ from each other only in location and momentum which are continuous parameters related via the uncertainty principle. But, there are arguments that in light of the fact that it is massless (assuming it is massless) and that general relativity is honored, that it should actually only have two states +/- 2 (see also here) or three states, 0 and +/- 2 (in variants from GR), imply a total of 120 or 121 kinds of interchangeable parts with 120 being the most conventional answer.

Otherwise, each of these interchangeable parts is perfectly identical to every other interchangeable part of the same part (subject also to quantum entanglement networks which make some particles distinct from others).

Thus, in the Standard Model extended minimally to include graviton based gravity, any particle can be fully described (except for entanglement links to other particles) by a discrete valued scalar type code with 120-123 possible discrete values, a location vector (in four dimensions) and a momentum vector (in four dimensions). In the Standard Model alone, the vectors are the same but the discrete valued scalar type code would have just 118 possible discrete values. And, everything in the universe is made up of particles (gravitons eliminate a physical medium of space-time that can be warped and have reality apart from gravitons). Put another way, every particle in the universe which makes up everything in the universe can be fully described with nine real numbers in this hypothetical minimal theory of everything (one discrete valued real number and four complex numbers would also get the job done).

Incidentally, the number of particles in the Universe is on the order of 10⁹⁰, so the number of distinct real numbers numbers necessary to fully describe the universe at any given point in time (recognizing that the definition of a given point in time in the universe is definitionally problematic and ignoring quantum entanglement) is about 10⁹¹. It isn't terribly straightforward to quantify exactly how much quantum entanglement complicates this analysis, although it definitely makes it vastly more complex.

Standard Model Fermions

Quarks and Anti-Quarks come in three generations and four possible electromagnetic charges and two possible parities, and for each of the possible types of electromagnetic charges three possible color charges for a total of 72 possibilities. 

Half of them interact via W and Z bosons, gluons and photons:

upLR, upLG, upLB, charmLR, charmLG, charmLB, topLR, topLG, topLB;

antiupRr, antiupRg, antiupRb, anticharmRr, anticharmRg, anticharmRb, antitopRr, antitopRg, antitopRb;

downLR, downLG, downLB, strangeLR, strangeLG, strangeLB, bottomLR, bottomLG, bottomLB;

antidownRr, antidownRb, antidownRb, antistrangeRr, antistrangeRg, anitstrangeRb, antibottomRr, antibottomRg, antibottomRb;

Half of them interact via gluons and photons but not W and Z bosons:

upRR, upRG, upRB, charmRR, charmRG, charmRB, topRR, topRG, topRB;

antiupLr, antiupLg, antiupLb, anticharmLr, anticharmLg, anticharmLb, antitopLr, antitopLg, antitopLb;

downRR, downRG, downRB, strangeRR, strangeRG, strangeRB, bottomRR, bottomRG, bottomRB;

antidownLr, antidownLb, antidownLb, antistrangeLr, antistrangeLg, anitstrangeLb, antibottomLr, antibottomLg, antibottomLb.

Charged Leptons and Anti-Charged Leptons come in three generations and two possible electromagnetic charges and two possible parities for a total of 12 possibilities.

Half of them interact via W and Z bosons and photons:

electronL, muonL, tauL, antielectronR, antimuonR, antitauR;

Half of them interact via photons but not W and Z bosons:

electronR, muonR, tauR, antielectronL, antimuonL, antitauL.

Neutrinos come in three generations and two possible parties for a total 6 possibilities:

They interact via W and Z bosons

neutrinoL, muonneutrinoL, tauneutrinoL;

antineutrinoR, antimuonneutrinoR, antitauneutrinoR.

It is notable that as far as we know, there is no evidence that a left handed neutrino (of any generation) can oscillate with a right handed antineutrino (of any generation). 

But, neutrino oscillation between mass eigenstates is a phenomena not seen in any other kind of Standard Model particle, although there are some similar phenomena.

What's Missing?

There are three Standard Model forces mediated by gluons (strong), W and Z bosons (weak) and photons (electromagnetic), respectively.

* The Standard Model has types of particles that interact via all three of these forces:

36 kinds of fermions interact via gluons, W and Z bosons and photons.

* The Standard Model has types of particles that interact via two of the three possible combinations of two of these forces:

36 kinds of fermions interact via gluons and photons

6 kinds of fermions interact via W and Z bosons and photons

* The Standard Model has types of particles that interact only via each one of these forces:

6 kinds of fermions interact via photons only.

6 kinds of fermions interact via W and Z bosons only

8 kinds of bosons (gluons) interact via gluons only 

* The Standard Model has one type of particle that doesn't interact with gluons or photons or Z bosons, and doesn't interact via the weak force with W bosons.

Like right handed charged leptons, photons only interact with charged particles (i.e. quarks and charged leptons and W bosons) via electromagnetism, but photons don't interact with other photons since they have no color charge or electromagnetic charge or weak force charge (yes, I know that this isn't the proper terminology) themselves.

* The Standard Model doe not have any type of particle that interacts via gluons and W and Z bosons, but not photons. A hypothetical particle of this type would be a "neutral left handed quark" or a "neutral right handed antiquark".

To fit the pattern would have to be a massive fermion with three generations. Neutral left handed quarks would have color charges R, G or B; neutral right handed antiquarks would have color charges r, g or b. 

There would also be neutral right handed quarks and neutral left handed antiquarks that would acquire mass by parity oscillation like charged fermions do with color charges R, G and B and r, g and b respectively. Indeed the difference between color charge and anticolor charge would make the neutral right handed quarks not degenerate with the neutral right handed antiquarks, and would make the neutral left handed antiquarks not degenerate with the neutral left handed quarks.

My only novel (for me) conjecture of the day, is that the non-existence of neutral quarks and neutral anti-quarks is probably one of the biggest hints about deeper string-like or preon-like structure in the Standard Model.

All hadrons have integer electromagnetic charge (baryons must have a charge of zero, +/- 1, or +/- 2; mesons must have a charge of zero, or +/- 1).

All fundamental bosons also have integer electromagnetic charge (zero or +/- 1).

No quarks have integer charge.

Preon Theories?

The most obvious possibility would be that color charged preons are the deep source of electromagnetic charge, in which the color charge would be present but cancelled out, at least in no-zero integer charged fundamental particles.

In this scenario, up-like quarks and antiquarks would contain two color charged preons (with the effective color charge of an up-like quark determined by the color charge type it is missing), down-like quarks and anti-quarks containing one color charged preon, charged leptons containing three color charged preons (one of which color, which would eliminates its need to interact via the strong force which it does only internally). W bosons would likewise have to have three color charged preons (one of each color).

There would be neutrinos containing either no color charged preons or a color charged preon and color charged antipreon, and similarly Z bosons, like neutrinos could either lack color charged preons or have one color charged preon and one color charged antipreon of the same type.

Gluons are already hypothetically a color charged-anticolor charged pair.

Photons could also be a color complete set of preons.

Photons and gluons would lack the "weak force" interaction preon or character (perhaps something parity-like or parity-related), while fundamental fermions including neutrinos, W bosons and Z bosons would all have the "weak force" interaction preon or character. 

It probably makes more sense for neutrinos to have a color charged preon and a color charged antipreon and a weak force core, while Z bosons have a weak force core but no color charged preons. This way, all fermions would have a weak force core and color charged preon combinations.

Worked properly (and the simple naive version I suggested above might not accomplish this) a color charge preon theory could also explain baryon number and lepton number conservation.

* One could also have some sort of knot or string twisting scenario that is functionally equivalent to this preon approach.

Another Observation Regarding Mass and The Weak Force

Every type massive particle in the Standard Model either has weak force interactions via the W and Z boson, or has a parity flipped variant that does. In the case of the quarks, antiquarks, charged fermions, charged antifermions, W boson, Z boson and Higgs boson the source of this mass is an interaction with the Higgs field.

The Standard Model does not resolve the question of the source of the mass of the neutrinos and antineutrinos, but it is notable that they too have weak force interactions via W and Z bosons.

Every type of massless particle in the Standard Model, i.e., the photon and the gluon, does not have weak force interactions. In a minimal theory of everything, the graviton doesn't interact via the weak force either, although gravitons do hypothetically interact with every kind of particle including itself.

Sterile Neutrinos Considered

A hypothetical "sterile neutrino" (i.e. neutrinoR, muonneutrinoR, taunautrinoR, antineutrinoL, antimuonneutrinoL, antitauneutrinoL), per my conjecture would be massless in addition to not interacting via any of the Standard Model forces. Since massless particles can't have distinct generations, a "sterile neutrino" could actually come in only two types: neutrinoR and antineutrinoL.

In a Standard Model with or without gravity, a massless sterile neutrinos are irrelevant and non-existent since they don't interact with anything (although I seem to recall one beyond the Standard Model theory that predicts the existence of massless sterile neutrinos). But, perhaps a massless neutrinoR and antineutrinoL system could be a single Majorana singlet sterile neutrino with Majorana mass not tightly coupled to the fundamental masses of the Standard Model and facilitating a simple dark matter particle. But, this is much less well motivated these days than it used to be because the case for collisionless dark matter of any kind is in such trouble.

But, sterile neutrinos might acquire mass identical to their non-sterile counterparts through oscillations between left and right handed neutrinos, and oscillations between left and right handed antineutrinos, in which case there could be six rather than two versions of them, and they would interact via gravity and hence become dark matter candidates, although then they would be hot dark matter, which again, observational evidence suggests that we don't need.

There is really no experimental motivation, however, that strongly necessitates sterile neutrinos, except that they would make Dirac neutrino mass identical to the other fundamental fermions possible.

The notion of sterile neutrinos that are neither massless nor have masses identical to their non-sterile counterparts of the same generation seems to me to be much less well motivated theoretically, even though right handed neutrinos with masses different than the "fertile" neutrinos of the Standard Model are very popular in beyond the Standard Model physics scenarios.

Gravitinos?

There are fundamental particles with spin-0, spin-1/2, spin-1 and in the hypothetical case of the graviton spin-2. There are no Standard Model fundamental particles with spin-3/2, nor are there any in a minimal theory of everything extension with a spin-2 graviton. 

A spin-3/2 gravitino, as a singlet fermionic dark matter candidate if one needed one (normally found in SUSY theories, but conceivable without SUSY) could theoretically exist and fill this gap. Indeed, it could also conceivably also be a neutral quark with no electromagnetic interactions, or could be a three generation triplet like the other fermions.

Meta

This post brings the posting rate so far this year at this blog to 21 posts per month.