## Wednesday, October 30, 2019

### More Evidence Supports The Younger Dryas Impact Hypothesis

More studies are showing support for the Younger Dryas Impact Hypothesis, which increasingly looks like it had an impact on a global basis. In my view, this is the most plausible explanation.
The Younger Dryas Impact Hypothesis, controversial from the time it was presented in 2007, proposes that an asteroid or comet hit the Earth about 12,800 years ago causing a period of extreme cooling that contributed to extinctions of more than 35 species of megafauna including giant sloths, sabre-tooth cats, mastodons and mammoths. It also coincides with a serious decline in early human populations such as the Clovis culture and is believed to have caused massive wildfires that could have blocked sunlight, causing an "impact winter" near the end of the Pleistocene Epoch. . . .
While the brief return to ice-age conditions during the Younger Dryas period has been well-documented, the reasons for it and the decline of human populations and animals have remained unclear. The impact hypothesis was proposed as a possible trigger for these abrupt climate changes that lasted about 1,400 years.
There is also evidence supporting Greenland as a primary impact location:
[A] team of researchers found unusually high concentrations of platinum and iridium in outwash sediments from a recently discovered crater in Greenland that could have been the impact point. Although the crater hasn't been precisely dated yet, Moore says the possibility is good that it could be the "smoking gun" that scientists have been looking for to confirm a cosmic event. Additionally, data from South America and elsewhere suggests the event may have actually included multiple impacts and airbursts over the entire globe.
The journal reference for the article quoted above is:

Christopher R. Moore, et al., "Sediment Cores from White Pond, South Carolina, contain a Platinum Anomaly, Pyrogenic Carbon Peak, and Coprophilous Spore Decline at 12.8 ka." 9(1) Scientific Reports (2019).. DOI: 10.1038/s41598-019-51552-8

But, multiple other similar anomalies in other locations are also noted:
Moore also was lead author on a previous paper documenting sites in North America where platinum spikes have been found and a co-author on several other papers that document elevated levels of platinum in archaeological sites, including Pilauco, Chile -- the first discovery of evidence in the Southern Hemisphere.
"First, we thought it was a North American event, and then there was evidence in Europe and elsewhere that it was a Northern Hemisphere event. And now with the research in Chile and South Africa, it looks like it was probably a global event," he says.
Several prior posts at this blog have examined this hypothesis in more depth:

* Hiding In Plain Sight (May 3, 2017).

## Sunday, October 27, 2019

### Denmark Was Pretty Warm In 1370 BCE

One of the most famous recovered ancient individuals in Denmark is "Egtved Girl", a 16-18 year old girl, buried in 1370 BCE (in the early Nordic Bronze Age) in an oak coffin which was well preserved because it was in an acidic bog. She was about 5'3" tall. The cause of her death is unknown.

According to a 2019 study cited in Wikipedia (Erik Thomsen and Rasmus Andreasen, "Agricultural lime disturbs natural strontium isotope variations: Implications for provenance and migration studies" 5(3) Science Advances (13 March 2019)):
The Egtved Girl lived about half the year in one area—likely the river valley, in Egtved, and the other half of the year in another place—likely the local plateau, perhaps in the practice of transhumance farming and seasonal pastoral movement within a small area.
What was life like back then?
Settlement in the Scandinavian Bronze Age period consisted mainly of single farmsteads, with no towns or substantial villages known - farmsteads usually consisted of a longhouse plus additional four-post built structures (helms) - longhouses were initially two aisled . . . . Evidence of multiple longhouses at a single site have been found, but they are thought to date to different periods, rather than being of the same date. Settlements were geographically located on higher ground, and tended to be concentrated near the sea. Also associated with settlements were burial mounds and cemeteries, with interments including oak coffins and urn burials; other settlement associations include rock carvings, or bronze hoards in wetland sites.
Both agriculture (including wheat, millet, and barley) and husbandry (keeping of domesticated animals such as cattle, sheep and pigs) were practiced, and fishing and shellfish were also sources of food, as well as deer, elk, and other wild animal hunting. There is evidence that oxen were used as draught animals, domesticated dogs were common, horses were rarer and probably status symbols.
Even though Scandinavians joined the European Bronze Age cultures fairly late through trade, Scandinavian sites present a rich and well-preserved legacy of bronze and gold objects. These valuable metals were all imported, primarily from Central Europe, but they were often crafted locally and the craftsmanship and metallurgy of the Nordic Bronze Age was of a high standard. The archaeological legacy also comprise locally of crafted wool and wooden objects and there are many tumuli and rock carving sites from this period, but no written language existed in the Nordic countries during the Bronze Age. The rock carvings have been dated through comparison with depicted artifacts, for example bronze axes and swords. There are also numerous Nordic Stone Age rock carvings, those of northern Scandinavia mostly portray elk.

Thousands of rock carvings from this period depict ships, and the large stone burial monuments, known as stone ships, suggest that ships and seafaring played an important role in the culture at large. The depicted ships, most likely represents sewn plank built canoes used for warfare, fishing and trade. These ship types may have their origin as far back as the neolithic period and they continue into the Pre-Roman Iron Age, as exemplified by the Hjortspring boat. 3,600-year old bronze axes and other tools made from Cypriot copper have been found in the region. . . .

The Nordic Bronze Age was initially characterized by a warm climate that began with a climate change around 2700 BC. The climate was comparable to that of present-day central Germany and northern France and permitted a relatively dense population and good opportunities for farming; for example, grapes were grown in Scandinavia at this time. A minor change in climate occurred between 850 BC and 760 BC, introducing a wetter, colder climate and a more radical climate change began around 650 BC.
There is no coherent knowledge about the Nordic Bronze Age religion; its pantheon, world view and how it was practised. . . . Many finds indicate a strong sun-worshipping cult in the Nordic Bronze Age and various animals have been associated with the sun's movement across the sky, including horses, birds, snakes and marine creatures (see also Sól). A female or mother goddess is also believed to have been widely worshipped (see Nerthus). Hieros gamos rites [a sexual ritual that plays out a marriage between a god and a goddess, especially when enacted in a symbolic ritual where human participants represent the deities] may have been common and there have been several finds of fertility symbols. A pair of twin gods are believed to have been worshipped, and is reflected in a duality in all things sacred: where sacrificial artifacts have been buried they are often found in pairs. Sacrifices (animals, weapons, jewelery and humans) often had a strong connection to bodies of water. Boglands, ponds, streams or lakes were often used as ceremonial and holy places for sacrifices and many artifacts have been found in such locations. Ritual instruments such as bronze lurs have been uncovered, especially in the region of Denmark and western Sweden. Lur horns are also depicted in several rock carvings and are believed to have been used in ceremonies. Many rock carvings are uncanny in resemblance to those found in the Corded Ware Culture.

A Bronze Age "Lur" similar in concept to a modern sousaphone.
Remnants of the Bronze Age religion and mythology are believed to exist in Germanic mythology and Norse mythology; e.g., Skinfaxi and Hrímfaxi and Nerthus, and it is believed to itself be descended from an older Indo-European proto-religion.
We know this about her burial, together with what might have been a little sibling, or her first child born when she was just old enough to give birth, or a human sacrifice (Danish museum proclamations that an 18 year old woman couldn't possibly have had a 5 year old child are amusing):
Of the girl herself only hair, brain, teeth, nails and a little skin remain. Her teeth reveal that she was 16-18 years old when she died. On her body she wore a short tunic and a knee-length skirt made of cords. A belt plate of bronze decorated with spirals lay on her stomach. She also had a comb made of horn with her in the grave, attached to her belt. Around each arm was a ring of bronze and she had a slender ring in her ear. By her face lay a small box of bark with a bronze awl and the remains of a hair net. At the feet of the Egtved Girl a small bucket of bark had been placed, which once contained a type of beer.
There was also a small bundle of clothing with the cremated bones of a 5-6-year-old child. A few bones from the same child were found in the bark box. The Egtved Girl saw the light of day again when her grave was excavated in 1921 – almost 3500 years later.
The short cord skirt she was buried in, and other clothing and artistic representations of women from that time period, suggest that this was what young adult women wore at the time (but frequently topless and with shorter skirts).

Egtved Girl's actual outfit.

A modern reconstruction of Egtved Girl's outfit.

These outfits were made possible by the fact that Denmark was much warmer then than it is now, although Denmark's climate is on track to return to those temperatures in the not so distant future. As the Old European Culture blog explains:
What was the climate like in Scandinavia at that time if girls could walk around dressed like this? Well much warmer. These girls lived during the so called "Minoan Warm Period" a period of time with much higher average temperatures in the Baltic than they are today. [A] [s]ign of how warm South Baltic was during the time when Egtved girl lived and died is that during that time millet ([a] type of grain) was grown in southern Scandinavia. Today millet is grown in tropical and subtropical regions...

According to this source:
Not much is known about the Minoan warm period beyond what can be gauged from cores from boreholes in the ice sheet. That the climate really was warmer then may be derived from that in the Minoan warm period, which occurred during the bronze age, millet was grown in southern Scandinavia. Today Millet is grown in tropical and subtropical regions, it is an important crop in Asia, Africa and in the southern U.S. The average annual temperature in Mississippi and Alabama is about 10 degrees, which should be compared with today's average annual temperature in Denmark, which is 8 degrees. So maybe the climate in the Minoan warm period, was about 2 degrees warmer than present in southern Scandinavia.

A two degree Celsius difference in average annual temperatures turns out to be a pretty big deal.

About two hundred years later, the climate event of roughly 1177 BCE that triggered Bronze Age collapse, with a cooler and more arid climate that brought down multiple empires, would arrive.

N.B. The coloration and general phenotype of people in Denmark today came into being in Denmark roughly 500 to 1400 years before Egtved Girl lived. The modern phenotype was a product of admixture of the pre-existing Northern European people with migrants from the Pontic-Caspian steppe, roughly speaking, where Ukraine is today.

The pre-existing Northern Europeans had fair hair and light colored eyes but darker, more olive colored skin, while the people of the Pontic-Caspian steppe had fair skin, but darker hair and eye colors. The body and head shape of people in Denmark also changed at about this time as a consequence of this admixture.

## Monday, October 21, 2019

### Estimating Time Depth With Mutation Rates Is Intrinsically Complex

Early estimates of the time depth at which genetic clades emerged were based upon a fixed molecular clock model that turns out to not reflect reality. Mutation does happen at predictable rates, but a workable model is more complex. Not all kinds of genetic mutations take place at the same rate.
Michael E. Goldberg and Kelley Harris, Great ape mutation spectra vary across the phylogeny and the genome due to distinct mutational processes that evolve at different rates (October 15, 2019) doi: https://doi.org/10.1101/805598
Recent studies of hominoid variation have shown that mutation rates and spectra can evolve rapidly, contradicting the fixed molecular clock model. The relative mutation rates of three-base-pair motifs differ significantly among great ape species, suggesting the action of unknown modifiers of DNA replication fidelity. To illuminate the footprints of these hypothetical mutators, we measured mutation spectra of several functional compartments (such as late-replicating regions) that are likely targeted by localized mutational processes. Using genetic diversity from 88 great apes, we find that compartment-specific mutational signatures appear largely conserved between species. These signatures layer with species-specific signatures to create rich mutational portraits: for example, late-replicating regions in gorillas contain an identifiable mixture of a replication timing signature and a gorilla-specific signature. Our results suggest that cis-acting mutational modifiers are highly conserved between species and transacting modifiers are driving rapid mutation spectrum evolution.
The authors also deserve credit for clearly packing the key ideas of their paper into the title.

## Monday, October 14, 2019

### The Exclusion Range For Neutrinoless Double Beta Decay Continues To Expand

Figure 4: The effective Majorana mass mββ as a function of the smallest neutrino mass mMIN. We have used the current best-fit values and the 2σ errors of the oscillation parameters. The Majorana phases α21 and α31, and δ, are varied within their allowed intervals [0, 180º].
"While the grey area on top has been sought for, and excluded by direct searches, experiments will need to reach a sensitivity in the range of 0.01 eV in the effective mass parameter m(ββ) (yellow line) to be able to prove that the mass hierarchy of light neutrinos is normal. That is something that should become possible in the next few years."

The black oval added editorially by me in the figure above is the most likely part of the graph to correspond to reality based upon astronomy data regarding the maximum sum of the neutrino masses of the three neutrino masses, neutrino oscillation data, and other considerations, assuming for sake of argument that neutrinos have Majorana mass rather than Dirac mass (all of the other fundamental fermions of the Standard Model have Dirac mass only). For reference, as I noted in my previous post:
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, [and considering plausibly motivated expectations discussed previously in that post] 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.
Unless neutrinos are Majorana particles (i.e. particles that are their own antiparticles), neutrinoless double beta decay doesn't happen at all, a conclusion that will take experiments somewhat more than 100 times more sensitive than the state of the art experiments done to date. We should be a factor of ten from that threshold in a few years, however.

If neutrinos are Majorana particles, the rate at which neutrinoless double beta decay occurs is a function of the effective Majorana neutrino mass shown on the Y axis, and the absolute mass of the lightest of the three neutrino masses. This is something that our experiments to date wouldn't have been able to see anyway, without regard to the nature of the neutrino mass hierarchy.

## 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 1776.96894(7) MeV, which is consistent with the direct experimental measurement which has an uncertainty of 0.12 MeV, but much, much more precise), and the top quark mass (predicted to be 173,666(125) 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, consistent with the direct measurement at 1.67 sigma, but with a precision better than the plus or minus 400 MeV in the directly measured experimental value) 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 of 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 consistently up to a 1.3 error in the measurements, with the uncertainties in the top quark mass measurement (85.2% of the uncertainty) and the Higgs boson mass measurement (13.6% of the uncertainty) dominating that uncertainty, and uncertainty in bottom quark mass (0.6% of the uncertainty), the charm quark mass (0.5% of the uncertainty) and the W boson mass (0.1% of the uncertainty) accounting for almost of of the remaining uncertainty in the comparison of the experimentally valued masses to the experimentally determined value of the Higgs vev (which is known to a precision of one part per 246 million).

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 (by 2.6 sigma) and the best available estimates of the Higgs boson mass are a bit too high (by 3.3 sigma), both of which would be necessary to make them exactly equal, and since both errors are independent and both have to be correct, the combined deviation of that theoretical prediction is very significant (between 4 sigma and 5 sigma). This almost symmetry between fermions and bosons (in which the squared masses of the bosons accounts for about 51% of the total and the squared masses of the fermions accounts for about 49% of the total), which might be exactly equal at some energy scale greater than pole masses, perhaps the Higg vev energy scale, since boson masses for the most part decline with energy scale faster than fermion masses do, may explain why supersymmetry provides the insights that it does and also why supersymmetry itself is not necessary.

Even if the sum of the square of the fermion masses turn out to not be exactly equal to the sum of the square of the fundamental boson masses, the more general relationship between fundamental fermion pole masses and the Higgs vev that is empirically well established to the limits of current measurement precision, would at least explain the magnitude of the top quark mass as a "filler" after all of the other fundamental fermion masses are accounted for.

This analysis, if theoretically sound, 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. If the Higgs vev really is equally to the square of the fundamental particle masses, the uncertainties in the known fundamental particle masses leave no room for particles with masses over a few GeV that have mostly been ruled out in direct searches, to have been omitted.

* 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)