## Sunday, October 13, 2019

### Some Standard Model Fundamental Constant Conjectures And Related Conjectures

Background

The Standard Model has many parameters that must be determined experimentally, although there is not a unique way to describe these constants as some constants are functions of other constants. For example, one could choose to make either the Higgs vev or the weak force dimensionless coupling constant part of your fundamental list of constants and derived the others from that. Similarly, you define either the dimensionless Higgs boson coupling constants called Yukawas, or the pole masses of the fundamental fermions and bosons, as the more fundamental quantity.

One way to summarize the list of experimentally measured constants in the Standard Model is that there are 12 fundamental fermion masses, 3 fundamental boson masses, 4 CKM matrix parameters (which govern the probability that quarks transform into different kinds of quarks), 4 PMNS matrix parameters (that govern the probability that neutrinos oscillate to different neutrino masses), and three standard model force coupling constants (for the electromagnetic, weak force and strong force), for a total of 23 experimentally measured parameters, plus some additional more general physical constants determined experimentally, including, at a minimum, Planck's constant and the speed of light in a vacuum, for a total of 25. This list, however, is somewhat redundant. One of the fundamental boson masses (either the W or the Z boson) can be derived from the other of the electroweak boson masses and the electromagnetic and weak force coupling constants, bringing the list to 24.

Some of the most solid relationships conjectured below can eliminate one parameter each from the CKM matrix and PMNS matrix (the theta13 angle in each of them), the tau lepton mass (predicted by Koide's rule to be 1776.969 MeV), and the top quark mass (predicted to be 173,666 MeV based upon the relationship of the sum of the square of the fundamental particle masses given their measured values to the square of the Higgs vev) from the list, in theory reducing the number of truly independent experimentally measured parameters to 20. Less solid relationships, if developed further and validated, could further reduce this list substantially.

Gravity as explained through general relativity, has two more experimentally measured constants: the gravitational coupling constant a.k.a. Newton's constant "G", although it can be defined in one of several dimensionless ways, and the cosmological constant a.k.a. lambda (which is the most common, but also disputed explanation for phenomena attributed to "dark energy" that are not well understood at a fundamental level). This would bring the total number of fundamental constants of physics to 27.

Some dark matter and/or modified gravity theories that seek to explain dark matter and/or dark energy phenomena, dispense with the cosmological constant and/or add one or more experimentally measured fundamental constants to explain dark matter and/or dark energy phenomena (and sometimes one more additional fermion and/or boson types as well).

Why these parameters take the values that they do is an open question that is mostly unanswerable at this time. But, almost everybody involved in this branch of physics intuitively and personally believes that these relationship are not just random and have some cause based upon some deeper theory that is not currently known to us.

Some conjectures.

* The CP violation parameters in the CKM matrix and PMNS matrix are an effect that is actually independent o the other three parameters in each matrix. It also is worth noting that the CP violation phase could be the same in the CKM matrix and PMNS matrix given the great uncertainty involved in the PMNS matrix value. In the CKM matrix, the CP violating phase is δ13 = 1.20 ± 0.08 radians (i.e. 68.8º plus or minus 4.6º). In the PMNS matrix, the mean measurement for the CP violating phase is 246º subject to very large error bars that make the central number measurement not very meaningful. The two values could also be complementary and actually add up to 360º.

One possibility that seems plausible is that the CP violation in both cases arises through W boson interactions (and possible a parallel fundamental boson currently unknown related to neutrino oscillation), which take place only with left parity matter and not with right parity matter. It further seems plausible to me that CP violation is maximal at tree level in the relevant interactions, and that deviations from maximal CP violation in W boson interactions arise from higher order loops.

* I strongly suspect for symmetry reasons and because massless particles do not experience the passage of time in the way that massive particles do, that any force mediated by a massless boson (i.e. electromagnetism mediated by photons, the strong force mediated by gluons with zero rest mass, and quantum gravity mediated by massive gravitons) are necessarily not CP violating as a result.

Similarly, particles that do not have electromagnetic charge and also decay in a matter-antimatter preserving fashion, like the massive Z boson and the Higgs boson, can likewise not violate CP on symmetry grounds (although Z bosons only interact with left parity particles which may be more subtly CP violating in a sense).

* I suspect that CPT is perfectly conserved in a final theory, as is conservation of mass-energy. I suspect that the non-conservation of energy in general relativity with a cosmological constant will be ultimately explained in some other way that conserves mass-energy in a final quantum gravity theory. I suspect that the matter-antimatter asymmetry largely results from matter going mostly forward in time following the Big Bang, while antimatter goes mostly backward in time following the Big Bang in a mirror universe where the second law of thermodynamics runs in the opposite direction.

* I suspect that all dark matter and dark energy phenomena will ultimately be explained as quantum gravity effects, and that dark matter particles (other than massless gravitons) will be ruled out. I suspect that the only BSM particles, other than massless gravitons, that have not yet been discovered, are limited to a possible neutrino oscillation boson, possible right handed neutrinos and left handed antineutrinos with the same mass as their parity partners and no Standard Model interactions, and some set of particles (less numerous than the current set of Standard Model particles) that give rise to the Standard Model particles (with the caveats noted above, if necessary) and no other particles whatsoever, such as fundamental string-theory like strings or some kind of preon.

* I suspect that baryon number and lepton number are conserved in all processes except sphaleron processes (if those actually even exist, and in which case B-L is still conserved), and possibly in the graviton equivalent to photo-production of particles. Hence, neutrinoless double beta decay does not occur, and neither do proton decay, or at the tree level, flavor changing neutral current processes.

* The conventional explanation of neutrino oscillation which is sufficient as a phenomenological theory is that there is a mismatch between three electroweak neutrino flavors and three mass eigenstates causing them to oscillate. But, the possibility that neutrino oscillation is actually mediated by a new fundamental boson analogous to the W boson, or that it involves a combined virtual W+ and W- boson loop, are possibilities that have not been ruled out to my satisfaction so far that could provide a first principles explanation of some of the associated physical constants that are measured experimentally.

* I seriously doubt that neutrinos are Majorana particles that are their own anti-particles, even though they lack electromagnetic charge and appear to come only in left handed neutrinos and right handed anti-neutrinos which would be inconsistent with the conventional Higgs mass generation mechanism. I likewise find a seesaw mechanism to be highly implausible. I do think it is plausible that there exist right handed neutrinos with the same mass as their left handed counterparts that don't interact with any of the three Standard Model forces and instead merely interact with their left handed counterparts, and left handed antineutrinos that are analogous, that make it possible for neutrinos to have a standard Higgs mechanism Dirac mass just like all of the other fundamental fermions in the Standard Model. I strongly suspect that there are no "sterile neutrinos" and that the "reactor anomaly" that suggested that they might exist with a mass on the order of 1 eV is actually just a fluke or an experimental design problem.

* In both the CKM matrix and the PMNS matrix, ignoring CP violation, the probability of a first to second generation transition times the probability of a second to third generation transition, is equal to the probability of a first to third generation transition. Thus, these are actually matrixes with at most three independent parameters (including CP violation), not four. It is possible that these two remaining generation transition parameters can even be reduced to two experimentally measured parameters or even just one for both matrixes, but simply reducing them from three to two for each matrix would represent scientific progress. If the same one or two parameters can be used to explain generation transitions in bot the CKM matrix and the PMNS matrix, this would probably be due to a concept known as "quark-lepton complementarity" since the sum of the CKM and PMNS matrix mixing angles for theta12 are fairly close to a combined 45º (which is the maximal mixing angle), as are the the sum of the CKM and PMNS matrix mixing angles for theta23.

In the case of the PMNS matrix, applying this formula with angles in radians, this implies a mixing angle from the first to third generation of 7.994º, while the measured value is 8.54º plus or minus 0.15º. Given the uncertainties in theta12 which is 33.62º plus or minus about 0.77º and theta 23 which is 42.8º plus or minus about +1.9º/-2.9º, this results are consistent at two sigma.

In the case of the CKM matrix, this implies a first to third generation mixing angle of 0.172º compared to the measured value of 0.201º plus or minus 0.011º which is also consistent at two sigma due to the uncertainty in this value combined with the uncertainty in the other two measured values that enter into the calculation.

Doing a global fit of the CKM and PMNS parameters with these constraints would be interesting and informative.

This relationship also suggests that the probability of a fermion generation change in logically prior in a deeper theory to the masses of the particles at particular generations.

* It is plausible to me that there may be some functional relationship between the Cabibbo Angle (of the CKM matrix a.k.a. lambda in the Wolfenstein parameterization) and Weinberg Angle (which pertains to the relative masses of the W boson and the Z boson as a result of fundamental relationships between electroweak theory quantities), as they are numerically quite similar and both involve the weak force, although they are not similar enough to each other to have values consistent with each other given current measurement precision.

This observation and the fact that all fundamental particles that interact via the weak force have a rest mass, while all fundamental particles that do not have rest mass do not interact via the weak force, makes wonder if the W boson plays a more central role in generating the fundamental particle rest masses (including the neutrino masses) and the Higgs boson is less important in this process than commonly assumed, with the W boson dynamically balancing the fundamental fermion masses.

* The overall mass scale of the Standard Model fermions is probably a function of the Higgs vacuum expectation value (which is itself intimately related at a functional level to the weak force coupling constant) since the sum of the square of the fundamental fermion pole masses is equal to the square of the Higgs vev.

This also explains why the Higgs boson has the mass that it does (to fill the gap not filled by the other fundamental particles of the Standard Model). From this perspective, the Higgs boson mass is very "natural". The "hierarchy problem" related to the Higgs boson mass is simply a function of an unnatural way to think about the means by which the Higgs boson mass arises.

If this is the explanation of the overall mass scale of the rest masses of the Standard Model fundamental particles, it appears that the fundamental fermion masses account for slightly less than half of the total, while the fundamental boson masses (which are known more precisely) account for slightly more than half of the total (something that wouldn't change if there was a massless graviton).

The best available estimates of the top quark mass are a bit too low and the best available estimates of the Higgs boson mass are a bit to high to make them exactly equal are increasingly difficult to fit within two sigma error bars. The predominant barrier to showing this definitively one way or the other are the uncertainties in the top quark mass measurement and the Higgs boson mass measurement (with uncertainty in the W boson mass being the next most pertinent). This almost symmetry between fermions and bosons is why supersymmetry provides the insights that it does and also why supersymmetry itself is not necessary.

If the sum of the square of the fermion masses turn out to be exactly equal to the sum of the square of the fundamental boson masses, either evaluated at pole mass or at some other notable momentum transfer scale such as one related to the Higgs vev energy scale, this would also explain the magnitude of the top quark mass as a "filler" after all of the other fundamental fermion masses are accounted for.

This analysis is also one of the more fruitful arguments to rule out the existence of new heavy fundamental particles types, particularly as top quark, Higgs boson and W boson mass measurements grow more precise.

* The rank order of the mixing angles of theta12 and theta23 in the CKM and PMNS matrixes has a relationship to the magnitude of the mass ratios of the starting and ending points involved in those transitions (adjusting in some appropriate matter, such as a geometric mean, for the fact that the CKM matrix involves two sets of mass differences per generation and not just one). Likewise, by some appropriate measure, bigger differences in mixing angles correspond to bigger differences in mass ratios of the starting and ending points involved in those transitions. Note that this description very carefully avoids stating a particular functional relationship, which is unknown.

This implies that the ratio of third generation to second generation quark partners in W boson transitions is higher than the ratio of second generation to first generation quark partners in W boson transitions since the mixing angles are 2.38% and 13.04% respectively. The respective geometric means in those case are about 275 and 100 respectively, and the ratio of the mixing angles is about 5.5.

The neutrino mixing angle for the third generation to the second is about 42.8% (assuming a first quadrant value), and the neutrino mixing angle for the second generation to the first is about 33.62% , and the ratio of the mixing angles is about 0.79. So, the ratio of the third generation neutrino mass to the second generation neutrino mass (which is about 5.6 or less), should be smaller than the ratio of the second generation neutrino mass to the first generation neutrino mass.

If the pattern of the CKM matrix were to hold, one would expect the ratio of the second heaviest neutrino mass to the lightest neutrino mass to be about 9.

Assuming the increasingly experimentally favored normal hierarchy, and given that the mass difference between the heaviest neutrino mass and the middle neutrino mass is about 49.4 meV and the difference between the middle neutrino mass and the lightest neutrino mass is about 8.7 meV, one would expect the lightest neutrino mass to be a little less than 1 meV, but probably not much lower than 0.5 meV.

This implies absolute neutrino masses of about 0.9 meV, 9.6 meV, and 59 meV, with a sum of the three neutrino masses equal to about 69.5 meV plus or minus about half an meV. This is very close to the minimum mass possible for the sum of the three neutrino mass eigenstates, given what we know already.

* The difference between the electron mass and the lowest neutrino mass is due fundamentally in some manner (possibly due to their respective self-couplings) to the ratio of the electromagnetic force coupling constant to the weak force coupling constant which is of approximately the same order of magnitude. Likewise the electron and up quark masses may be a function of their self-couplings, although the mechanism by which higher generation fermions acquire their masses and why they have only three generations, is still somewhat mysterious even if we can come up for a mathematical formula that accurately determines the fundamental fermion masses.

* Lepton universality is probably only an approximate rather than an absolute symmetry that holds only because the ratio of the mass of each charged lepton to the mass of each charged lepton less the corresponding neutrino mass is so close to 1 for all three of the charged leptons. Violations of lepton universality in excess of this magnitude is probably due to experimental and/or theoretical error.

* The fact that Koide's Rule holds for the charged leptons to the limits of experimental accuracy, is probably for fundamental reasons similar to those for lepton universality and the fact that there are only three charged leptons.

* The ratio of the quark masses appears to be, at first order, the product of something very close to Koide's rule, but adjusting for the possibility that there could be transitions other than the most common one implicated by Koide's rule implemented directly, by making an adjustment of an order of magnitude equal to the mass difference of the omitted transition time the probability of the omitted transition taking place under Koide's rule.

* I think that it is plausible that the Standard Model formulation of the fundamental equations and axioms of quantum chromodynamics a.k.a. QCD a.k.a. the modern explanation of the strong force that holds protons, neutrons and other hadrons together, is incomplete and missing a rule or two, or a key axiom or two. For example, I would not be surprised if a missing axiom established that free standing glueballs were impossible for some reason.

### Key Contribution To Two CKM Matrix Parameters Now 57% More Precisely Measured.

In the Standard Model, the CKM matrix which expresses the probability with which quarks are transformed into different kinds of quark via W boson interactions is described which four parameters which in the Wolfenstein parameterization are called λ, A, ρ¯, and η¯. It is often described in approximated form as follows (in which the "i" is the imaginary number) and the O() term refers to "additional contributions with a combined magnitude on the order of the fourth power of lambda":

The absolute value of the square of each entry is the probability that an up-like quark will transform into a particular down-like quark (and the complex conjugate of the matrix shown above is the probability that a particular down-like quark will transform into a particular up-like quark).

The value of the Wolfenstein parameters and the uncertainties in those measurements as of a 2017 article summarizing the current global averages is as follows:

λ = 0.2251 +0.0004 −0.0004,
A = 0.831 +0.021 −0.031,
ρ¯ = 0.155 +0.008 −0.008,
η¯ = 0.340 +0.010 −0.010.

The global fits discussed in a June 5, 2018 review from the Particle Data Group linked above comes up with slightly different values, the first of which quoted below is based upon frequentists statistics and the second of which is based upon Bayesian statistics (which I would tend to favor in these circumstances).

The last of these parameters is the sole source of CP violation in the Standard Model and is one of the more difficult to measure. One way to measure it is to determine the angles that going into the "unitary triangle" shown below (which is over constrained because all three can be determined independently but they must add up to 180º) as it is defined for this purpose, which defines both of the last two parameters of the four Wolfenstein parameterization parameters of the CKM matrix.

A new paper improves the precision with which ρ¯, and η¯ are known.

As the introduction of the paper cited below explains:
Cabibbo-Kobayashi-Maskawa (CKM) matrix, is the central goal of heavy flavor physics program. Specifically, using B decays to determine the three angles α, β and γ of the usual non-squashed unitarity triangle of the CKM matrix respectively and thus to test the closure of the unitarity triangle is a very straightforward and promising way to accomplish this goal. Any discrepancies would suggest possible new sources of CP violation beyond the standard model. In principle, α, β and γ can be determined via measurements of CP violating asymmetry in neutral B decays to CP eigenstates.
The hardest to measure of the three angles in the unitary triangle is gamma. The introduction to the new article cited below continues by explained that:
[I]t is well known that the angle β can be determined in a reliable way with the help of the mixing induced CP violation of a single ”gold-plated” mode B0 → J/ψKS.
Likewise, for α, it can be extracted using neutral B decay, B0 → π +π −, using the isospin symmetry analysis to separate the strong phase difference of tree and penguin contributions by other B → ππ decays.
Theoretically, similar with the measurement of β and α, a straightforward way to obtain of γ might be to use CKM-suppressed B0 s decay, B0 → ρKS, or a analysis for the decays B0 s → D0φ, D¯ 0φ and D0 1φ. However, the observed mixing-induced CP asymmetries are expected to be strongly diluted by the large Bs − B¯ s mixing, so that to determine γ in this way is considerably more involved than β and α.
The third angle γ is currently the least known. It usually depends on strong phase difference of different B decays, which is difficult to calculate reliably. One of the theoretically cleanest way of determining γ is to utilize the interference between the b → cus¯ and b → ucs¯ decay amplitudes with the intermediate states D0 and D¯0 mesons subsequently decay to common final states rather than to use B− → D0KS and B− → D¯0KS decays directly, due to the large uncertainties of the two amplitudes ratio rB and strong phase difference between them.
But, it turns out that using their approach they were able to make great improvements with respect to the status quo in measuring gamma. Before this paper, the latest combination of γ measurements by the LHCb collaboration yielded:

(74.0 +5.0 −5.8 )º.

But, the latest result for CKM angle γ from the paper below is

(69.8 ± 2.1 ± 0.9)º

which implies a combined error of the new result of

(69.8 ± 2.3)º.

The relative error in this hard to measure physical constant is now 3%. Thus, the new paper provide a margin of error that is 57% smaller than the previous margin of error, in addition to dragging down the mean value of the physical constant by about 0.72 sigma (i.e. standard deviations of margin of error in the old value). The new value is consistent with the old world average value at the 0.67 sigma level.

Comparing the margins of error in the previous world average for gamma and the margins of error in the global average value of ρ¯, and η¯, it looks to me like the error margin in these actual CKM parameters will probably be reduced by roughly a third to half of the improvement in the precision of gamma. Thus, the margins of error for ρ¯, and η¯ are likely to decline by about 15%-30% each, with the global fit estimate of ρ¯ going up slightly and the global fit estimate of η¯ going down slightly. Thus, my back of napkin non-rigorous estimate is that the new global averages and margins of errors for the affected Wolfenstein parameters of the CKM matrix after considering this paper might be roughly on the order of:

ρ¯ = 0.158 +0.006 −0.006,

η¯ = 0.336 +0.008 −0.008.

This isn't a huge improvement in the ultimate bottom line parameter measurements. But, every improvement in the CKM matrix parameters improves the accuracy of every single electroweak calculation going forward, and also improves our ability to distinguish experimentally between background noise in experimental results and beyond the Standard Model signals. If signals are not seen, the exclusions of beyond the Standard Model physics are stronger as a result, and if signals are seen the power of the experiments to see them is greater,  all other things being equal.

The paper is:

# Extraction of the CKM phase γ  from charmless two-body B meson decays

Utilizing all the experimental measured charmless
BPP

PV

decay modes, where P(V)
denotes a light pseudoscalar (vector) meson, we extract the CKM angle
γ
by global fit. All the unknown hadronic parameters are fitted with
γ
together from experimental data, so as to make the approach least model dependent. The different contributions for various decay modes are classified by topological weak Feynman diagram amplitudes, which are to be determined by the global fit. To improve the precision of this approach, we consider flavor SU(3) breaking effects of topological diagram amplitudes among different decay modes by including the form factors and decay constants. The fitted result for CKM angle
γ
is $(69.8 \pm 2.1 \pm 0.9) ^{\degree}$. It is consistent with the current world average with a better precision.
 Comments: 15 pages, including 2 figures Subjects: High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Experiment (hep-ex) Cite as: arXiv:1910.03160 [hep-ph] (or arXiv:1910.03160v1 [hep-ph] for this version)

## Tuesday, October 8, 2019

### The Last Woolly Mammoths

A relict population of woolly mammoths survived on an isolated island long after they had gone extinct everywhere else.
The last woolly mammoths lived on Wrangel Island in the Arctic Ocean; they died out 4,000 years ago within a very short time. An international research team from the Universities of Helsinki and Tübingen and the Russian Academy of Sciences has now reconstructed the scenario that could have led to the mammoths' extinction. The researchers believe a combination of isolated habitat and extreme weather events, and even the spread of prehistoric man may have sealed the ancient giants' fate.
From Science Daily

### Ruins Of Major Early Bronze Age City Found In Israel

Ruins of a city more than a dozen times larger than Jericho in the early Bronze Age (ca. 3000 BCE) have been found in Israel. It had trade networks that reached at least as far South as Egypt and also to the North.  It was build on the ruins of a Neolithic settlement two thousand years older than that.

### Minimum Mass Bound Established For Thermal Dark Matter

The most popular category of dark matter particle theories are thermal dark matter theories. A new analysis sets rigorous minimum mass limits on dark matter particles in such theories that most importantly place a bound too high to be consistent with warm dark matter theories that are among the most promising thermal dark matter theories.

# Refined Bounds on MeV-scale Thermal Dark Sectors from BBN and the CMB

New light states thermally coupled to the Standard Model plasma alter the expansion history of the Universe and impact the synthesis of the primordial light elements. In this work, we carry out an exhaustive and precise analysis of the implications of MeV-scale BSM particles in Big Bang Nucleosynthesis (BBN) and for Cosmic Microwave Background (CMB) observations. We find that, BBN observations set a lower bound on the thermal dark matter mass of mχ>0.4MeV at 2σ. This bound is independent of the spin and number of internal degrees of freedom of the particle, of the annihilation being s-wave or p-wave, and of the annihilation final state. Furthermore, we show that current BBN plus CMB observations constrain purely electrophilic and neutrinophilic BSM species to have a mass, mχ>3.7MeV at 2σ. We explore the reach of future BBN measurements and show that upcoming CMB missions should improve the bounds on light BSM thermal states to mχ>(1015)MeV. Finally, we demonstrate that very light BSM species thermally coupled to the SM plasma are highly disfavoured by current cosmological observations.
 Comments: 28 pages, 10 figures, 6 tables Subjects: High Energy Physics - Phenomenology (hep-ph); Cosmology and Nongalactic Astrophysics (astro-ph.CO) Report number: KCL-2019-75 Cite as: arXiv:1910.01649 [hep-ph] (or arXiv:1910.01649v1 [hep-ph] for this version)