Friday, November 10, 2023

A New Top Quark Pole Mass Analysis And A Few Wild Conjectures Considered

A new paper makes an re-analysis of existing data to determine the top quark pole mass. It comes up with:

which is consistent with, but at the low end of the range of the Particle Data Group's estimate based upon indirect cross-section measurements (bringing these into the same amount of precision as its direct measurements of the top quark mass):

Recent previous coverage at this blog regarding new top quark mass measurements can be found in a February 7, 2023 post, a November 4, 2022 post and a September 1, 2022 post.

Why Care?

Since this new paper produces cross-section based top quark pole mass estimates that closely confirm direct measurements of top quark pole mass measurements with comparable precision, the fact that both measurements are substantially independent of each other makes our confidence in each of  these measurements greater and makes the best fit measurements produced more robust. It also makes combining results from the two methods statistically to produce a single global best fit measurement with a lower combined uncertainty, incorporating all measurement methods, appear more legitimate and appropriate.

In relative terms, the top quark pole mass is already one of the more precisely known physical constants in the Standard Model. It is more precisely determined in relative terms than the other five quark masses, the three neutrino masses, the four CKM matrix parameters, the four PMNS matrix parameters, and the strong force coupling constant. But, it is less precisely determined in relative terms than the three charged lepton masses, the three fundamental boson masses, the electromagnetic and weak force coupling constants, and Newton's constant.

But, because it is the largest mass which is a fundamental constant of the Standard Model, in absolute terms, the magnitude of the uncertainty in the top quark pole mass is huge. At the Particle Data Group cross-section measurement uncertainty, it is about five times the mass of the pion, and more than the masses of eight of the eleven other fundamental fermion masses in the Standard Model. Only the bottom quark mass, the charm quark mass, and the tau lepton mass are greater than the absolute magnitude in the uncertainty alone in the top quark mass from cross-section measurements.

Also, because the top quark mass is so large, precision in this measurement is important for higher loop adjustments to all sorts of calculations in the Standard Model. 

Relevance To Theory Building

Precision in the top quark mass is also critical for assessing global properties of the Standard Model like a proposed LC&P relationship between the Higgs field vacuum expectation value and the fundamental particle masses in the Standard Model:
The global LC&P relationship (i.e. that the sum of the squares of the fundamental SM particle masses is equal to the square of the Higgs vev, which is equivalent to saying that the sum of the SM particle Yukawas is exactly 1), which is about 0.5% less than the predicted value (2 sigma in top quark and Higgs boson mass, implying a theoretically expected top quark mass of 173,360 MeV and a theoretically expected Higgs boson mass of 125,590 MeV if the adjustments were proportioned to the experimental uncertainty in the LC&P relationship given the current global average measurements, in which about 70% of the uncertainty is from the top quark mass uncertainty and about 29% is from the Higgs boson mass uncertainty). . . . 

But, the LC&P relationship does not hold separately for fermions and bosons, which would be analogous in some ways to supersymmetry. This is only an approximate symmetry. The sum of the squares of the SM fundamental boson masses is more than half of the square of the Higgs vev by about 0.5% (3.5 sigma of Higgs boson mass, implying a theoretically expected Higgs boson mass of about 124,650 MeV), while the sum of the squares of the SM fundamental fermion masses is less than half of the square of the Higgs vev by about 1.5% (about 2.8 sigma of top quark mass, implying a theoretically expected top quark mass of about 173,610 MeV). The combined deviation from the LC&P relationship for both fermions and bosons independently is 4.5 sigma, which is a very strong tensions that is nearly conclusively ruled out. One wonders if the slightly bosonic leaning deviation from this symmetry between fundamental fermion masses and fundamental boson masses has some deeper meaning or source.

The result in this new paper, by largely corroborating direct measurements of the top quark mass at similar levels of precision, continues to favor a lower top quark mass than the one favored by LP&C expectations. 

Earlier, lower energy Tevatron measurements of the top quark mass (where the top quark was discovered) supported higher values for the top quark mass than the combined data from either of the Large Hadron Collider (LHC) experiments do and was closely in line with the LP&C expectation. 

But there is no good reason to think that both of the LHC experiments measuring the top quark mass have greatly understated the systemic uncertainties in their measurements (which combine measurements from multiple channels with overlapping but not identical sources of systemic uncertainty). Certainly, the LHC experiments have much larger numbers of top quark events to work with than the two Tevatron experiments measuring the top quark mass did, so the relatively low statistical uncertainties of the LHC measurements of the top quark mass are undeniably something that makes their measurements more precise relative to Tevatron.

Could This Hint At Missing Fundamental Particles?

If I were a phenomenologist prone to proposing new particles, I'd say that this close but not quite right fit to the LP&C hypothesis was a theoretical hint that the Standard Model might be missing one or more fundamental particles, probably fermions (which deviate most strongly from the expected values).

I'll explore some of those possibilities, because readers might find them to be interesting. But, to be clear, I am not prone to proposing new particles, indeed, my inclinations are quite the opposite. I don't actually think that any of these proposals is very well motivated.

In part, this is because I think that dark matter phenomena and dark energy phenomena are very likely to be gravitational issues rather than due to dark matter particles or dark energy bosonic scalar fields, I don't think we need need particles to serve that purpose. Dark matter phenomena would otherwise be the strong motivator for a beyond the Standard Model new fundamental particle. 

I am being lenient in not pressing some of the more involved arguments from the data and theoretical structure of fundamental physics that argue against the existence of many of these proposed beyond the Standard Model fundamental particles. 

This is so, even though the LP&C hypothesis is beautiful, plausible, and quite close to the experimental data, so it would be great to be able to salvage it somehow if the top quark mass and Higgs boson mass end up being close to or lower than their current best fit estimated values.

Beyond The Standard Model Fundamental Fermion Candidates

If the missing fermion were a singlet, LP&C would imply an upper bound on its mass of about 3 GeV. 

This could be a good fit for a singlet sterile neutrino that gets its mass via the Higgs mechanism and then transfers its own mass to the three active neutrinos via a see-saw mechanism. 

It could also be a good fit for a singlet spin-3/2 gravitino in a supersymmetry inspired model in which only the graviton, and not the ordinary Standard Model fermions and bosons have superpartners.

A largely sterile singlet gravitino, and a singlet sterile neutrino, have both been proposed as cold dark matter candidates and at masses under 3 GeV the bounds on their cross-sections of interaction (so that they could have some self-interaction or weak to feeble interaction with ordinary matter since purely sterile dark matter that only interacts via gravity isn't a good fit for the astronomy data) aren't as tightly constrained as heavier WIMP candidates. And, the constraints on a WIMP dark matter particle cross section of interaction from direct dark matter detection experiments gets even weaker fairly rapidly between 3 GeV and 1 GeV, which is what the LP&C conjecture would hint at if either the current best fit value for the top quark mass or the current best fit value for the Higgs boson mass were a bit light.

The LP&C conjecture isn't a useful hint towards (or against) a massive graviton, however, because the experimental bounds on those are on the order of 32 orders of magnitude or more too small to be discernible by that means.

If there were three generations of missing fermions, you'd expect them to have masses about two-thirds higher than the charged lepton masses, with the most massive one still close to 3 GeV, the second generation one at about 176 MeV, and the first generation one at about 0.8 MeV. But these masses could be smaller if the best fit values for the top quark mass and/or Higgs boson mass ended rising somewhat as the uncertainties in those measurements fall.

These masses for a missing fermion triplet might fit a leptoquark model of the kind that has been proposed to explain B meson decay anomalies. The experimental motivation for leptoquarks was stronger before the experimental data supporting violations of the Standard Model principle of charged lepton universality (i.e. that the three charged leptons have precisely the same properties except their masses) evaporated in the face of factors in the data analysis of the seemingly anomalous experimental results from B meson decays. But there are still some lesser and subtle anomalies in B meson decays that didn't go away with this improved data analysis that could motivate similar leptoquark models.

If there were two missing fermions of similar masses (or two missing fermion triplets with their sum of square masses dominated by the third-generation particle of each triplet), this would suggest a missing fundamental particle mass on the order of up to about 2 GeV each.

A model with two missing fermion triplets might make sense if there were two columns of missing leptoquarks, instead of one, just as there are two columns of quarks (up type and down type) and two columns of leptons (charged leptons and neutrinos), in the Standard Model.

Beyond The Standard Model Fundamental Boson Candidates

If the Standard Model fermions are a complete set, and the LP&C conjecture is correct, then we'd be looking for one or more beyond the Standard Model massive fundamental bosons with masses of less than 3 GeV for a singlet, less than about 2 GeV for two similar mass missing bosons, and masses of less than about 1.73 GeV (a tad less than the tau lepton mass) for three similar mass massing bosons.

Probably the most plausible well-explored proposed beyond the Standard Model particle for missing fundamental bosons in this mass range would be an additional electromagnetically neutral Higgs boson in a two Higgs doublet model - either a scalar light Higgs boson "h" (as opposed to a Standard Model heavier scalar Higgs boson "H"), or a pseudoscalar Higgs boson "A", or both. The problem with a two Higgs doublet models, though, is that it fives us four new massive fundamental bosons, even though we only need one to respond to the LP&C hint.

At least one of the two new electromagnetically neutral extra Higgs bosons in a two Higgs doublet model could be short lived and give rise to the neutrino masses, in lieu of existing see-saw models or Majorana mass models for neutrino mass. A mass in the range of perhaps 0.1-3 GeV, more or less, could serve this purpose and we might expect a boson that gives rise to neutrino masses to be significantly smaller than the Standard Model Higgs boson that gives rise to order of magnitude larger quark and charged lepton masses.

Another of these extra Higgs bosons could be stable or be created and destroyed at precisely the same rates, have only weak or feeble interactions with Standard Model particles, and could provide a dark bosonic dark matter candidate, which in  the face of indications that dark matter seems to be more wave-like than particle-like, might be a better fit to the astronomy data than a WIMP.  If the dark matter candidate extra Higgs boson were less massive than the least massive neutrino mass eigenstate (i.e. probably less than 1 meV and perhaps much less), its stability could be explained because it couldn't decay into anything else, since there were no massive particles less massive than it.

The biggest problem with using particles from a two Higgs doublet paradigm to reconcile the shortfall of fundamental particle masses suggested by the LP&C conjecture, however, is that it would imply in a fairly vanilla two Higgs double model, a positively charged and negatively charged Higgs boson (H+ and H-) of identical masses, something which can be pretty definitively ruled out for the masses of up to 1.73 GeV to 2 GeV that the LP&C conjecture could support.

The Particle Data Group notes that charged Higgs bosons have been ruled out for masses of less than 80 GeV (more like 155 GeV if you look at the underlying studies referenced through the year 2015) and for masses between the top quark mass and about 1,103 GeV (looking at studies through 2018). And a number of new results from the LHC since the Particle Data Group values were last updated make that exclusion even stronger. 

There is really no plausible way that particle physicists could have missed an electromagnetically charged fundamental particle (either a fermion or a boson) in the 0.1 GeV (about the same as the muon and strange quark) to 3 GeV (between the tau lepton and charm quark on one hand and the bottom quark on the other) mass range suggested by the LP&C conjecture and current data, even if it was produced very infrequently, in very rare processes that interact at all with any Standard Model particles non-gravitationally. Particle collider particle detectors are exquisitely sensitive to electromagnetically charged particles in that mass range, no matter how short-lived they may be (and stable charged fundamental particles in that mass window would be found, if not in colliders, by other means).

Of course, as a theoretical physicists proposing beyond the Standard Model physics, you can propose any new particles that you like and need not constrain yourself to well-explored proposals like a two Higgs doublet model if you don't want to do so.

Given those constraints, a singlet electromagnetically neutral neutrino mass imparting boson analogous to the Higgs boson for other fundamental Standard Model particles, outside of the two Higgs doublet model, might be a better candidate for a new fundamental boson that fills out the missing fundamental particle mass suggested by the LP&C conjecture. The source of neutrino mass is still an unsolved problem, so that provides at least some motivation for it. 

If this fundamental boson was stable, or produced and destroyed at strictly identical rates, it could also be a dark matter candidate, solving two issues with on BSM particle.

The LP&C conjecture provides no hint for or against a 17 MeV missing fundamental boson, which has been proposed by a single experiment to explain some subtle decay angle issues in nuclear physics, because 17 MeV squared in only about 0.1% of the uncertainty in the sum of the square of the fundamental particle masses, so the existence or non-existence of such a particle would be impossible to determine for the foreseeable future using the LP&C conjecture if it were true. 

Beyond The Standard Model Fundamental Fermion And Boson Set Candidates

Self-interacting dark matter (SIDM) models generally propose one predominant stable, electromagnetically neutral, fermionic dark matter candidate (possibly part of a three generation fermion triplet with more massive but unstable second and third generation counterparts), and one unstable, electromagnetically neutral, bosonic "dark photon" that carries a self-interaction force between dark matter fermions.

Since the mass of an unstable boson is functionally related to the range of the force it carries, which can be estimated from the inferred dynamics of fermionic dark matter particles in SIDM models, we can estimate that the sweet spot in terms of mass for a dark photon that carries the self-interaction force between dark matter fermion particles is about 100 MeV.

If both the dark matter fermion and the dark photon receive their masses via a Standard Model Higgs mechanism, then a dark matter fermion in the 0.1 GeV to 3 GeV range as suggested by the LP&C conjecture with the exact mass ultimately determined masses of the top quark and Higgs boson demand. And, if one had a dark matter fermion triplet, the third-generation unstable dark matter fermion could be at the high end of this mass range, the second-generation unstable dark matter fermion could be in the low hundreds of MeV in mass, and the lightest and stable dark matter fermion could have a mass as small as necessary to fit the astronomy data (e.g. in the keV warm dark matter range, or even in the axion-like very low dark matter particle range).

These four new missing fundamental particles could fit a self-interacting warm dark matter model, fill the LP&C conjecture mass gap, would have no non-Higgs portal interactions with Standard Model particles, and as fairly light, electromagnetically neutral particles with no weak or strong force interactions, that decay to other electromagnetically neutral particles with no weak or strong force interactions, could have escaped detection as a Higgs boson decay channel so far at particle colliders, manifesting merely as missing traverse momentum in Higgs boson decays at levels that can't be ruled out yet.

While neither warm dark matter models, nor self-interacting dark matter models have proven very satisfactory in matching the astronomy data (although each of them do at least marginally better than collisionless cold dark matter models with GeV mass particles do), perhaps combining both of these cold dark matter particle model variants would work better than a model with one rather than both of these features.

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