Is Our Particle Set Complete?

Is our set of discovered particles complete?

All of the particles predicted by the Standard Model have been found, and none that haven't been predicted by the Standard Model, have been discovered at this point.  So, the Standard Model's set of discovered particles is complete.

But, is the Standard Model set of particles all that there is?  A variety of different approaches suggest that the answer is yes, or at least, almost yes, with some possible exceptions driven most strongly by data from cosmology.

With some not terribly ambitious assumptions that are well motivated experimentally, it is possible to conclude that the undiscovered fundamental particle spectrum is limited to light, sterile fermions of less than 8 GeV (combined for all undiscovered particles), and to massless, or stable and sub-8 GeV, light bosons that do not interact via any of the three fundamental Standard Model forces.

Counting Standard Model Particles

One way to assess that would be to consider whether there are an equal number of fermion and boson types?

But, it depends upon how you count them.

There are twelve Standard Model particles of spin-1/2 with distinct masses.  There are twelve Standard Model bosons of spin-1 (photons, W+, W-, Z and eight kinds of gluons), plus the Higgs boson (spin-0), which brings the total to thirteen Standard Model bosons.

If this is the correct way to county and  there are an equal number of fermions and bosons, then this "numerology" approach would suggest that since there are twelve fermions and thirteen bosons, that there needs to be one more fermion (perhaps a sterile neutrino singlet to be a warm dark matter candidate) to even the count.  However, if gravitons exist, we might need two fermions to even the count (perhaps a sterile neutrino singlet to address the reactor anomaly data and a spin-3/2 gravitino of 2 keV to be a warm dark matter candidate and counterpart to the graviton in the gravitational sector).

But, does this approach to counting make any sense?  While there are thirteen Standard Model bosons, if you consistently treat particles that differ only in color charge, or that are antiparticles of each other, as one particle, as you do when you say that there are twelve Standard Model fermions, then there are really only five Standard Model bosons.

Then again, if you treat up-type quarks, down-type quarks, charged leptons, and neutrinos, each of which is a set of three particles identical in all respects except mass, then you only have four kinds of fermions instead of five, and the number of kinds of spin-1/2 fermions and the number of kinds of spin-1 bosons is identical (four each), with the spin-0 Higgs boson in an intermediate role (perhaps offset by a spin-3/2 fermion like gravitino dark matter that also doesn't fit the pattern).

Of course, it isn't at all obvious that it is fair, for example, to count the twelve possible kinds of up quarks (left v. right parity, times red-green-blue color, times particle v. antiparticle) just once, while counting gluons which differ only by having eight different kinds of color charge as eight different kinds of particles.  Similarly, why should electron and positron count as one particle, when the W+ boson and the W- boson which are also a particle and antiparticle pair as two particles.

A fuller count would conclude that there are 72 different kinds of quarks, 12 kinds of charged leptons, and six kinds of neutrinos for a total of 90 fermions, compared to 13 bosons, for a total of 103 different kinds of Standard Model particles (treating only particle properties that vary in discrete quantum properties as different).

If there were a graviton and a dark matter particle (a bare minimum in a fully particle based TOE with non-baryonic dark matter), you would need a minimum of 105 different particles to have a complete set.

Many people are very tempted to add right handed neutrinos to the mix which would bring the total to 110 particles (assuming that one of the right handed neutrinos was a dark matter particle, that they come in three generations and have distinct antiparticles, and that these interact only via Higgs boson interactions), and often theorists to add at least one gauge boson to govern interactions in the dark sector bringing the total to 111 particles.

Particles Ruled Out By Electroweak Data.

We have a complete set of particles lighter than the W and Z that can be produced directly in their decays.  Any missing particle would either have to be sterile (i.e. right handed or otherwise not weak force interacting), or if it was a "fertile" particle, would have to be more than 45 GeV in mass.

Higgs boson decay analysis work is likely to bring this cutoff to 63 GeV in a few years (unless there is a new particle with a mass between 45 GeV and 63 GeV that interacts with the Higgs boson, which seems unlikely given how well the preliminary decay data fit a Standard Model Higgs boson).

Possible Patterns Of Interaction

The Standard Model particles have a hierarchical pattern of interactions with four different kinds of bosons, and bosons are the only way that particles interact with each other.

Fermions:
* Left handed quarks couple of gluons, photons, W/Z bosons and Higgs bosons (4)
* Left handed charged leptons couple to photons, W/Z bosons and Higgs bosons (3)
* Neutrinos couple to W/Z bosons and Higgs bosons (2)
* Right handed quarks couple to gluons, photons and Higgs bosons (3)
* Right handed charged leptons couple to photons and Higgs bosons (2)

Bosons:
* Photons do not couple to gluons, photons, W/Z bosons or Higgs bosons (0).
* Gluons couple to gluons, but not to photons, W/Z bosons or Higgs bosons (1).
* W bosons couple to photons and W/Z bosons and Higgs bosons, but not to gluons (3).
* Z bosons couple to W/Z bosons and Higgs bosons, but not to photons and gluons (2).
* Higgs bosons couple to W/Z bosons and Higgs bosons, but not to photons and gluons (2).

Thus, there are 16 possible combinations of interaction patterns with the four kinds of Standard Model bosons, of which 7 are realized in the Standard Model:

* All four (1 possibility) - Left handed quarks.
* Three out of four (4 possibilities) - Left handed charged leptons and W bosons (both interact with photons, W/Z bosons and Higgs boson), and Right handed quarks (gluons, photons and Higgs boson)
* Two out of four (6 possibilities) - Neutrinos, Higgs bosons and Z bosons (each interact with W/Z and Higgs boson), and right handed charged leptons (photons and Higgs boson).
* One out of four (4 possibilities) - Gluons (gluons)
* None of the four (1 possibility) - Photons.

(Note that this analysis assumes that the Standard Model Higgs boson, unlike the weak force gauge boson, interacts with both right parity and left parity particles, which is true so far as I know, even though I don't know enough to be sure that this is the case.  I would welcome comments on this nuance that can confirm or deny the fact from readers who do know.)

Interaction Pattern Gaps:
The 9 combinations of interactions which are not realized in the Standard Model with a description of an example of each kind of hypothetical particle are:

* Three out of four - Left handed electrically neutral quarks (gluons, W/Z bosons and Higgs bosons), and massless left handed quarks (gluons, photons, W/Z bosons)
* Two out of four - Charged gluons (gluons and photons), right handed electrically neutral quarks (gluons and Higgs bosons), massless left handed quarks (gluons, photons, W/Z bosons), and massless W bosons (photons and W/Z bosons).
* One out of four - Right handed neutrinos (Higgs boson only), charged photons (photons only), and massless Z bosons (W/Z only).

Analysis of the Gap Particles:
Of the 9 missing hypothetical particles interaction profiles:
* the apparent rule that particles that interact via W/Z bosons must have mass rules out 4,
* the apparent rule that particles charged particles must have mass rules out 2, and
* the absence of electrically neutral quarks rules out 2 (left and right handed electrically neutral quarks).

The first two rules illustrate the intimate connection between electroweak interactions and the Higgs boson.  It would be interesting to see what kind of experimental data rule out charged gluons and charged photons, however.  Since neither interact via the weak force, it is harder to rule them out with W and Z boson decays, for example, although charged particles are hard to miss (but might be long lived, making colider detectors less suited to seeing them).

Electrically neutral quarks are ruled out by precision electroweak data unless all three generations of them have masses of more than 45 GeV.  Composite neutrons, of course, are collectively electrically neutral, but an electrically neutral quark not ruled out by precision electroweak decays would have to be more than 45 times as heavy.  Electrically neutral quarks would still need to be confined (unless they were almost as heavy as the top quark), so they would form mesons of 91 GeV or more, and baryons of 136 GeV or more (for pure first generation ground states), with composite particles containing some second or third generation electrically neutral quarks being surely unstable, and a ground state of three electrically neutral quarks that might or might not be stable.  Also, they would make possible fractionally charged mesons and baryons which are not observed when bound to Standard Model quarks.  We can be pretty comfortable that these do not exist.

UPDATE 12-16-13: 

The absence of charged gluons and charged photons flows somewhat naturally from their zero rest mass and CPT conservation.  Charge and parity are clearly associated with a direction of time and CP violation is equivalent to T violation.  But, particles with zero rest mass always move at the speed of light at which time is effectively frozen and doesn't pass at all with respect to an observer in the particle itself.  When the particle lacks an internal sense of time direction, it can't have time direction dependent properties like charge and parity.

Conversely, fermions which have either charge and parity, or at least, parity, can't be massless, because a particle must have mass for parity to be well defined in its own reference frame given CPT conservation.  Since W/Z interactions are parity specific (only left handed particles interact via the weak force), only massive fermions can have either weak force interactions or electric charge.

This analysis would likewise explain the lack of CP violation in the electromagnetism and the strong force, both of which are carried by zero rest mass bosons.  However, the QCD suggestion that gluons may dynamically acquire momentum dependent mass in the IR limit within confined systems suggest that there might be strong force CP violation there.

Since only short range massive bosons can carry CP violating forces, "all CP violation is local."

If gravity is carried by a massless graviton, then that element of gravity must also have no CP violation.  But, if the cosmological constant is really dark energy mediated by a massive scalar boson (maybe even the Higgs boson) then there could be an arrow of time in dark energy.

END UPDATE

The ninth possibility, a particle that couples to the Higgs boson, but not photons, gluons and W/Z bosons, is not excluded experimentally (since the lack of interactions makes them so hard to detect), and indeed, is a natural dark matter candidate:
* If it is a spin-1/2 fermion, a "right handed neutrino", or more generically a "sterile neutrino" (as it need not have a correspondence to any of the Standard Model neutrinos).
* If it is a spin-3/2 fermion, a SUSY or non-SUSY gravitino.
* If it is a spin-0 boson, a "sterile Higgs boson", and
* If it is a spin-1 boson, "vector bosonic dark matter".

While there may be "sterile neutrinos" of spin-1/2, I doubt that there are true right handed counterparts to the left handed neutrinos because if there were they should have the same mass of their left handed counterparts, just like all other fermions that differ only in parity.  This is too light to fit any experimental signature driving the need for sterile neutrino-like particles.

Instead, I think that right handed neutrino counterparts to the Standard Model neutrinos do not exist because parity and anti-neutrino/neutrino state would otherwise be degenerate.  I also doubt that neutrinos are really Majorana particles because the whole logic of neutrinos in the Standard Model requires their particle/antiparticle status to be distinct to balance out lepton number conservation.

If there is a "sterile neutrino", I would suspect that it would be a singlet counterpart to the Higgs boson or graviton or both.

Higgs Boson Yukawa Hints

If my analysis above is correct, then there are lots of particles (42 right handed fermions out of 90 fermions in all to be exact) that interact with the Higg boson, but not the W and Z bosons, whose existence can't be ruled out to any extent by precision electroweak decays.

It is very reasonable to think that all fundamental particles with mass have Higgs boson couplings and that their masses are functions of these couplings.

But, there are strong hints from the fundamental particle masses which we have now confirmed appear to be a function of their couplings to the Higgs boson fit a very interesting pattern that profoundly limits the size of a complete set of particles.

The sum of the square of each of the twelve fermion rest masses, and the three boson rest masses (W, Z and Higgs), equals the sum of the square of the Higgs field vacuum expectation value.

This implies that the sum of the suitably equated Yukawa couplings (adjusting the Higgs self-coupling and gauge boson coupling accordingly) for all particles that are known to couple to the Higgs boson are unitary to a precision of about a few parts per thousand of experimental error.

Almost all of the uncertainty in this value comes from the uncertainty in the masses of the top quark and Higgs boson, and there is every reason to believe that the LHC will be able to reduce the Higgs boson mass uncertainty significantly, and the top quark mass somewhat, in the next few years, making this match (if indeed it is a law of nature) even tighter.

If indeed this set of interactions really is unitary (and I sincerely believe that this will be shown to be a law of nature sooner or later), then any and all undiscovered particles that couple to the Higgs boson (as all massive fundamental particles apparently must), can't have more than about 8 GeV of mass combined for all such Higgs boson interacting particles, given the precision of current measurements.

Therefore, it is very reasonable to think that there are no undiscovered massive fundamental particles with masses in excess of about 8 GeV (combined).  The maximum potential mass of any particles that have Higgs boson interactions would have to be small enough that it could not be missed in W and Z boson decays (a 45 GeV cutoff) if it also had any weak force interactions.

We can also say with considerable comfort that existing experimental evidence rules out unknown particles with strong force interactions or electric charge with masses of 8 GeV or less.

Four Standard Model particles weight far more than 8 GeV (the top quark at about 173 GeV, the Higgs boson at about 126 GeV, the Z boson at about 90 GeV, the W boson at about 80 GeV).  Three more Standard Model particles weight between 1 GeV and 8 GeV (the bottom quark at about 4.2 GeV, the tau lepton at about 1.776 GeV, and the charm quark at about 1.3 GeV).  A particle with electric charge or color charge in a similar mass range would have left an unmistakable signature.

Anything resembling a fourth generation Standard Model particle has been ruled out experimentally to the hundreds of GeVs and pretty much all possible SUSY particles (either super-partners or extra Higgs bosons) have been ruled out for masses of less than 95 GeV.  For example, even on December 5, 2011 (two years ago), ATLAS had published the following exclusions:

A limit at 95% confidence level is set excluding a cross-section times branching ratio of 1.1 pb for a top-partner mass of 420 GeV and a neutral particle mass less than 10 GeV. In a model of exotic fourth generation quarks, top-partner masses are excluded up to 420 GeV and neutral particle masses up to 140 GeV.

Less stringently (but less likely to be a law of nature), if one assumed that the squared mass of bosons and the squared mass of fermions were equal, when the bosons are currently greater than the fermions by about 2% of the total, allowing for about 29 GeV to balance the squared mass of the bosons and the squared mass of the fermions.

So, if these assumptions about Higgs Yukawa's being unitary and all massive fundamental particles having Higgs Yukawa's are correct, then any undiscovered massive particles are:

1.  Less than 8 GeV in mass.
2.  Are "sterile" in the sense that they do not interact via the weak force.
3.  Do not have electric charge.
4.  Do not interact via the strong nuclear force.

In other words, any undiscovered massive particles must be in the nature of moderately light sterile neutrinos (or perhaps gauge bosons of some newly discovered short range force), such as a warm dark matter candidate.  The Higgs Yukawa's, of course, themselves, place no boundaries on the universe of possible massless particles.

Supersymmetry is possible under these assumptions only if Standard Model superpartners couple exclusively to non-Standard Model extra Higgs bosons and have no almost no couplings to the Higgs bosons that has been observed at the LHC.  But, as I understand the matter, SUSY's reason for existence includes the desire to make the Higgs boson mass natural and to solve the hierarchy problem, something that a Higgs boson that has no relationship whatsoever to any SUSY particles would not seem to serve well.

This kind of analysis tends to strongly disfavor notions like a heavy sterile see-saw partner to the neutrinos that contribute to their mass.

Cosmology Hints

Cosmology assumptions also strongly disfavor the existence of two new flavors of sterile neutrinos with masses comparable to the three known neutrino flavors, but only mildly disfavor a single flavor of very light sterile neutrinos (with masses on the order of 1 eV or less) of the type suggested by nuclear reactor neutrino stream data discussed below.

In addition, cosmology suggests that we need a nearly collisionless particle significantly heavier than 1 eV to provide dark matter.  Cosmology has also left us with no clear way to understand the source of the asymmetry in the universe between matter and antimatter which might therefore require new physics.

Extensive astronomy research by multiple means has converged on a possible 2 keV mass sterile neutrino as a particularly promising warm dark matter candidate.

Cosmology, particularly in relation to dark matter and dark energy, provides the strongest evidence that the Standard Model is probably not complete.  We need at least one dark matter candidate or force modification (possibly with a new light or massless boson), at a minimum, unless we are truly clever and find some solution to the dark matter and dark energy questions that are currently not being widely discussed.

Also, should we find that there are indeed at least two sterile neutrino types - one of about 1 eV that may oscillate with conventional neutrinos, and a stable one of about 2 keV, the precedents of Standard Model encourage researchers to see if a final third generation light sterile neutrino, possibly itself unstable and possibly playing a role in leptogenesis, also exists adding a new column of leptons to the Standard Model.  A Standard Model extension that does just that and proposes three right handed neutrinos is receiving deserved serious consideration.

On the other hand, if dark matter phenomena turn out to be mostly not a matter of new fundamental dark matter particles, but of modifications to force laws, we may need some new bosons.  For example, it isn't unreasonable to imagine that a tensor-vector-scalar modification of gravity laws would require a tensor graviton (spin-2), a vector graviton (spin-1) and a scalar graviton (spin-0 and possibly identical to the Higgs boson or an inflaton).

Evidence of "inflation" phenomena in the early universe, probably best fit to some sort of slowly shifting scalar field also points to the possible need for an "inflaton" boson which might be coincident with the Higgs boson, but which might also be another spin-0 boson.

One could imagine, perhaps, a family of spin-0 bosons sufficient to make up a two Higgs doublet version of the Standard Model - the Standard Model Higgs boson, a dark energy Higgs boson, an inflaton Higgs boson, and a pair of charged Higgs bosons that demonstrate strong CP violation that help account for baryon asymmetry or baryogenesis or leptogenesis.  Only the first two might be stable enough to be present in the current universe.  Needless to say, any such family of spin-0 bosons would undermine the usefulness of what we know about the Standard Model Higgs boson that seems to sharply limit the undiscovered particle spectrum.  Extra Higgs bosons in the right kinds of theories, could facilitate an evasion of these bounds.  But, it isn't at all obvious that the proposed SUSY extra Higgs bosons have the right properties to achieve these ends.

Of course, it would be even more fantastic if someone could figure out a way in which the humble Standard Model Higgs boson by itself is actually the source of the empirically observed level of dark energy and was also the inflaton, without creating new particles.

The hints from other experimental data can easily accommodate the kinds of particles that the cosmology data (and the reactor data) seem to be hinting at right now.

W and Z Boson Mean Lifetime Hints

No particle has a wider resonance width than the W and Z bosons, which translates into a mean lifetime of about 3*10^-25 seconds.

Generally speaking, resonance width (and its inverse, mean particle lifetime) are strongly correlated with rest mass.  Heavier particles have greater resonance width and shorter mean particle lifetimes.

The heaviest fermion, the top quark, is also by far the shortest lived, with a mean lifetime of just 5*10^-25 seconds, which isn't even long enough, on average, for it to be confined by the strong force into a hadron, unlike all other quarks.  Despite being a strong force interacting particle with QCD color charge, top quarks as such an unstable form of a up-type quark that they simply immediately decay via what is for them the faster acting weak force.

It isn't obvious that it is even conceptually workable to have a fermion whose mean lifetime is less than the mean lifetime of the W boson by which it decays.

If there is some sort of fundamental reason for the link between fermion mass and resonance width, it may be that it is simply impossible for a fermion to have a mass much greater than a top quark as a result.

Thus, weakly interacting particles with masses many times greater than 173 GeV may simply be inconsistent with the laws of physics in some fundamental sense never firmly established or proven so far.  Since SUSY particles must be weakly interacting to play their intended role in electroweak symmetry breaking, it would follow that SUSY particles in the several hundreds of GeV to low TeV mass exclusion ranges that already exist for many parts of the minimum SUSY superpartner spectrum may be simply disallowed.

SUSY has many moving parts, but one non-negotiable element of SUSY is that there must be at least one superpartner for every Standard Model particle.  Every single one of these superpartners must exist at some mass.  And, if some superpartners have been excluded at light masses, then some superpartners must be heavy.  No serious SUSY or string theory advocate of whom I am aware currently claims, for example, that there are no SUSY superpartners with masses of at least 1 TeV, about six times as heavy as a top quark.  The emerging consensus in many SUSY discussions is that if SUSY is correct, that some SUSY superpartners have masses at least on the order of 10 TeV or so, about sixty times the top quark mass.

Given the already tiny difference between the top quark mean lifetime and the W and Z boson mean lifetimes, it is hard to imagine that a 10 TeV sparticle capable of interacting via the weak force that weighs sixty times as much would not have a mean lifetime of less than the W and Z bosons and hence might be ruled out as possible, even if the link between rest mass and mean lifetime is not terribly strict.

So, if no weakly interacting particle can have a mean lifetime of less than the W and Z bosons, and mean lifetime is roughly linked to a particle's rest mass, then it follows that existing experimental evidence effectively rules out SUSY and any other BSM theory with a substantial heavy particle spectrum.

Reactor Anomaly Hints

Some nuclear reactor neutrino data seems to hint at the possibility of a sterile neutrino of approximately 1 eV in mass that oscillates with fertile neutrinos to some extent.  The data aren't strong enough, however, to be conclusive.

LUX Hints

The LUX experiment's recent results the basically rule out the existence of weakly interacting dark matter in the vicinity of the solar system as well modeled densities with particle masses in the range from approximately 5 GeV to 1 TeV again supports the notion that the heavy weakly interacting particle spectrum is complete.

If stable WIMP dark matter was out there, LUX's extraordinary sensitivity should have seen them.

Other Hints

Increasingly long experimental minimum neutrinoless double beta decay frequencies (never convincingly observed), increasingly long minimum mean lifetimes of the proton (never observed to decay), strict lower thresholds on the electron dipole moment of the electron, and the modest amount of any anomalous magnetic moment of the muon (whose current value is within an order of magnitude of the Standard Model's expected value despite being hard to exactly match to the Standard Model), are all very sensitive to features of beyond the Standard Model physics, even at high energies.

Some of these approaches tend to disfavor BSM models including SUSY models with heavy BSM particles in particular, bounding these theories from above, rather than below.

While the limitations on BSM physics from this kind of evidence is not yet definitive, the fact that not even a strong hint of experimental support for major deviations from the Standard Model expectations have been found in any of these contexts tends to favor the conclusion that our set of heavy particles is complete.

Concluding Thoughts

The case that we have found almost all of the particles in the universe with the possible exception of some light sterile fermions and some massless bosons is increasingly a strong one.  All but a handful of the leading BSM physics proposals are disfavored by the analysis and data collected above.

This context supports a minimal approach to BSM theory building, and a need to focus on non-SUSY, non-String theoretic approaches as those approaches appear to me to be clearly doomed to the extent that they are trying to describe reality as opposed to merely serving as toy models upon which ideas that can be later generalized to more realistic Standard Model extensions.