The Not Quite Boson-Fermion Mass Symmetry Considered

Background

The sum of the square of each of the fundamental boson masses, plus the sum of the square of each of the fundamental fermion masses, equals to the square of the Higgs vacuum expectation value to a precision of 0.012% (easily within the experimental measurement error of the source masses), four significant digits if:

* one assumes that the mass of the Higgs boson is actually one half of the W boson mass and the Z boson mass (91.1876 GeV), and
* one also uses global fit values for the W boson mass (80.376 GeV/c^2) and the top quark mass (173.2 GeV/c^2) rather than taking individual best estimates of these masses without considering global fit considerations, and
* one calculates the Higgs vacuum expectation value of 242.29 GeV that these best fit values imply (together with the canonical value of the electromagnetic force coupling constant and its beta function governing its running).

The Higgs boson mass if this relationship is correct is 125.97 GeV (well within experimental bounds and accurate to five significant digits).  The four significant digit accuracy of the Higgs vev to the sum of the fundamental particle masses squared is as accurate as the least accurately known of the inputs that have a significant impact on the total (the top quark mass).

In my view, this is quite compelling evidence that both the 2H=2W+Z and Higgs vev squared equals sum of fundamental particle rest mass squared relationships are true and fundamental rather than mere coincidences (which isn't to say that I have all of the details of the mechanism that illustrates how these fundamental relationships arise).  We are moving into an era where these relationships can be evaluated with precision.

The Not Quite Boson-Fermion Mass Symmetry

If these relationships are true, then the sum of the square of the three boson masses (W, Z, and Higgs) is about 2.1% greater than the sum of the square of the masses of the twelve fermions (six quarks, three charged leptons and three neutrinos, but dominated by the top quark mass which accounts for 99.94% of the total).

If the first two relationships that almost precisely match the best possible estimates of the Standard Model parameters are true, it cannot be true that the sum of the squares of the boson masses and the sum of the square of the fermion masses are equal.  Or at any rate, it can't be true for rest masses and the coupling constant strength at the energy level ordinarily used by physicists.

This is a frustrating thing.  If the two were equal, we would have this profound boson-fermion mass symmetry - hinting that the boson-fermion symmetries of SUSY might be present in the plain old Standard Model, although more subtly.  If the two were wildly different, we wouldn't even think to look at the relationship of the two quantities.  But, they are instead close, but not quite close enough to possibly be the same.

It might be that there is a profound boson-fermion mass symmetry, but that it only manifests under the right conditions or from the right perspective.  For example, there might be some energy scale at which the boson masses and fermion masses and coupling constants run at which 2H=2W+Z and the sum of squares relationship to Higgs vev, and the boson-fermion mass symmetry all hold simultaneously, and below which the boson-fermion mass symmetry is broken.  Perhaps above this threshold, there is even a subtle shift in the running of the electroweak coupling constants that causes the three Standard Model coupling constants to converge at a single point.

One could also imagine this approximate symmetry corresponding to one or more other approximate symmetries in physics, which perhaps together produce an exact symmetry.

For example, perhaps the magnitude of boson-fermion mass asymmetry in the Standard Model exactly corresponds to the aggregate amount of CP violation found in the Standard Model when measured appropriately, or to some appropriate function of the Weinberg angle that governs electroweak unification, or to the amount by which quark-lepton complementarity does not quite perfectly hold in the CKM and PMNS matrixes.

Or, perhaps boson-fermion mass asymmetry is the key to the puzzle of matter-antimatter asymmetry in the universe.

Or, perhaps the "missing fermion rest mass" (about 25 GeV if all from a single particle), corresponds to the sum of the square of the rest masses of fundamental particles other than those in the Standard Model which do not participate in electroweak interactions and hence aren't part of equations involving the Higgs field - perhaps something in the "dark matter" sector, or a see-saw sterile neutrino, or the some significant measure of the dynamically created mass of gluons that are not "at rest" that have a negative rather than a positive contribution to the boson side of the equation.

Or, perhaps this imbalance relates to the cosmological constant in some way (another constant that is almost, but not quite, zero).

Open Thread: The Oops Files

One of the next posts that I plan on doing is a compilation of the most notable cases of scientific or anthropological results that were later discredited.  Comments suggesting examples of this to include in the post are welcome.

I am primarily interested in good faith errors by legitimate professionals, although examples of notable hoaxes and notable cases of faked data are also welcome.

Göbekli Tepe marked dog star's appearance in Anatolian sky

The circular stone enclosures known as the temple at Göbekli Tepe in southeastern Turkey remain the oldest of its kind, dating back to around the 10th millennium B.C.

But Göbekli Tepe may also be the world's oldest science building.

Giulio Magli of the Polytechnic University of Milan hypothesizes it may have been built due to the “birth” of a “new” star; the brightest star and fourth brightest object of the sky, what we call Sirius (Greek for "glowing"). . . .

Precession at the latitude of Göbekli Tepe would have sent Sirius under the viewing horizon of those in ancient Turkey around 15,000 BC, where it remained unseen again until around 9,300 B.C. To those residents it was a new star appearing for the first time. . . .

"The extrapolated mean azimuths of the structures (taken as the mid-lines between the two central monoliths) are estimated as follows":

Structure D 172°
Structure C 165°
Structure B 159°

Those azimuths match the rising azimuths of Sirius: 

Structure D 172° 9,100 BC
Structure C 165° 8,750 BC
Structure B 159° 8,300 BC

From here.

The case that this pre-Neolithic structure was built to track a newly appeared star described above is quite convincing.

Ireland's First Neolithic Revolution Failed

Around 3700 BCE,Ireland had a full fledged sedentary farming village society. In the three hundred years that followed, apparently due to a worsening climate, this society collapsed. The people of Ireland returned to a hunting and foraging method of food production where the island remained for about 1200 years. A return to sedentary farming didn't begin until around 2200 BCE. There may have been similar developments in Britain. Instances of a return to hunting and foraging after a brief period of farming, before an ultimate return to farming, driven by climate, are also known in Scandinavia thousands of years later.

Among other things this means that for much of Northern and Western Europe, an era of hunting and foraging was much more recent at the advent of the historical record than an estimate based upon the earliest Neolithic archaeological traces would suggest. It also suggests that the relationship between megalithic cultural remnants and food production method may be more nuanced than earlier analysis had suggested.

CMS Measures Fundamental Constants

The CMS experiment at the Large Hadron Collider has measured the strong force coupling constant at Z boson mass-energy to be 0.1151 +/- 0.0033.  This compares to and is consistent with a  four and a half times more precise previous measurement of 0.1184 +/- 0.0007.

It also measured top quark pole mass at 176.7 + 3.8 -3.4 GeV/c^2, which compares to and is consistent with a previous more accurate Tevatron measurement of 173.18 +/- 0.94 GeV/c^2.  The new result, again, is several times less precise than the current world standard estimate.

While the results are not terribly precise, because they are obtained using a different methodology than most previous measurements of these quantities, the results make the average measurements more robust and less subject to systemic errors that could be shared by all of the other experiments.

CMS has also made the most precise measurement ever of the relative momentum of up quarks and down quarks within the proton, something that could ultimately be used to more accurately estimate their masses, two of the least accurately known constants in the Standard Model.  These measurements now have more precision than the theoretically calculated prediction.

In January of this year, I summarized how precisely the various Standard Model constants have been measured.  In March of this year, I summarized how global electroweak precision fits fine tune some of these measurements by trying to reconcile individual measurements with their known relationships to each other.

Absolute Dates In Ancient Egyptian Prehistory Refined

A new paper has made progress in firmly establishing absolute chronological dates for various phases of ancient Egyptian prehistory.

More Analysis of Neanderthal Introgression

"The timing and history of Neandertal gene flow into modern humans." S. Sankararaman et al.

   Previous analyses of modern human variation in conjunction with the Neandertal genome have revealed that Neandertals contributed 1-4% of the genes of non-Africans with the time of last gene flow dated to 37,000-86,000 years before present. Nevertheless, many aspects of the joint demographic history of modern humans and Neandertals are unclear. We present multiple analyses that reveal details of the early history of modern humans since their dispersal out of Africa. 

   1.We analyze the difference between two allele frequency spectra in non-Africans: the spectrum conditioned on Neandertals carrying a derived allele while Denisovans carry the ancestral allele and the spectrum conditioned on Denisovans carrying a derived allele while Neandertals carry the ancestral allele. This difference spectrum allows us to study the drift since Neandertal gene flow under a simple model of neutral evolution in a panmictic population even when other details of the history before gene flow are unknown. Applying this procedure to the genotypes called in the 1000 Genomes Project data, we estimate the drift since admixture in Europeans of about 0.065 and about 0.105 in East Asians. These estimates are quite close to those in the European and East Asian populations since they diverged, implying that the Neandertal gene flow occurred close to the time of split of the ancestral populations.  

[Ed. This is probably in the time frame of ca. 50,000 to 86,000 years ago within the range of estimated admixture times.]

   2.Assuming only one Neandertal gene flow event in the common ancestry of Europeans and East Asians, we estimate the drift since gene flow in the common ancestral population. We show that an upper bound on this shared drift is 0.018. Because this is far less than the drift associated with the out-of-Africa bottleneck of all non-African populations, this shows that the Neandertal gene flow occurred after the out-of-Africa bottleneck.  

[Ed. Note that if the effective population size of Out of Africa modern humans fell before it recovered, the bottleneck could have happened well after the initial Out of Africa migration.]

   3.We use the genetic drift shared between Europeans and East Asians, in conjunction with the observation of large regions deficient in Neandertal ancestry obtained from a map of Neandertal ancestry in Eurasians, to estimate the number of generations and effective population size in the period immediately after gene flow. These analyses suggest that only a few dozen Neandertals may have contributed to the majority of Neandertal ancestry in non-Africans today.

[Ed. I'd love to get a look at this data.]

Via a Dienekes Anthropology Blog post on the 2013 ASHG conference abstracts (emphasis his; bracketed comments mine).

* Notably, this study does not discriminate between a single admixture event in a single genetic population followed promptly by a population split into Western and Eastern components, and two similar parallel admixture events, one with proto-West Eurasians and one with proto-East Eurasians, that takes place after the populations split.

Point one does, however, confirm inferences I have made previously from the small amount of overlap found in the particular Neanderthal genes found in West Eurasians and East Eurasians respectively, which you would not expect if Neanderthal admixed genes had reached fixation in a single unstructured population very long before the West Eurasian-East Eurasian split of "Out of Africa" modern humans into two separate populations with very little gene exchange.

* Point two is expected from the absence of Neanderthal genes in Africans except to the extent of gene flow from back migration from the Out of Africa population, and from the presence of Neanderthal genes in all non-Africans.

While understated in the abstract, the bigger revelation of point two is that Neanderthal gene flow probably took place quite a while after the Out of Africa event, rather than at the outset when one might naively have expected the Out of Africa population to be at its smallest prior to its expansion into "virgin territory."  Other studies have suggested based on statistical analysis of modern population genetic data that the Out of Africa population contracted before it expanded.

Neanderthal admixture may have happened not long after the effective Out of Africa population size hit bottom, or perhaps more accurately, Neanderthal admixture prior to then while the effective population size was falling was likely to be lost to the gene pool through drift, while Neanderthal admixture during the immediately following population expansion was likely to be preserved in the expanding population.

* Point three, suggesting that there were only a few dozen instances of Neanderthal admixture that account for almost all Neanderthal genes in modern humans is the most fascinating when it comes to building a narrative and understanding how this happened.

Assuming an effective population size around that time for Out of Africa modern humans of 3,000 to 20,000 and a time span of admixture that may have been somewhere in the range of 900 to 24,000 years (about 30 to 800 generations), we are talking about an entire modern human Out of Africa population the size of a small city in which there were one or two half-Neanderthal children born each generation or so (of course, more concentrated and more sparse scenarios are possible to some extent).

Also, based on reasoning from the absence of Neanderthal Y-DNA and mtDNA, I have previously concluded that Neanderthal hybrids who were born into modern human communities probably almost always had modern human mothers and Neanderthal fathers, and that live births were overwhelmingly of half-Neanderthal girls rather than boys due to issues of hybrid compatibility often expressed as Haldane's law.  An abstract of a recent paper by Reich in the same post corroborates the notion that hybrid incompatibility was an issue from direct genetic evidence:

We built a map of Neandertal ancestry in modern humans, using data from all non-Africans in the 1000 Genomes Project. We show that the average Neandertal ancestry on chromosome X of present-day non-Africans is about a fifth of the genome average. It is known that hybrid incompatibility loci concentrate on chromosome X. Thus, this observation is consistent with a model of hybrid incompatibility in which Neandertal variants that introgressed into modern humans were rapidly selected away due to epistatic interactions with the modern human genetic background.

Source Paper: "Insights into population history from a high coverage Neandertal genome. 

D. Reich for the Neandertal Genome Consortium.

In my view, this evidence, taken as a whole, supports a scenario in which modern human-Neanderthal couplings were episodic events, perhaps one night stands, perhaps seasons affairs, perhaps rapes, rather than sustained, marriage-like relationship in which a Neanderthal individual was integrated permanently into a modern human community, or visa versa.  There may have been an undetectable small number of exceptions that proved the rule, of course.

* I also continue to think that the Neanderthal introgression legacy in modern humans probably shows only half the picture.  Hybrid offspring of modern human men and Neanderthal women were probably also born, but if hybrid children were matrilocal, they would have disappeared when their Neanderthal tribes, in general, went extinct.

Are Archaic Ancestry Percentages A Function Of Phenotypic Invisibility?

One point it would be interesting to work out would be how long it would take before Neanderthal introgression reached fixation in the community and hybrid Neanderthals ceased to be a distinct and recognizable sub-community within Out of Africa modern humans.  In similar models that I have run (aims at understanding the future of race relations), it takes surprisingly few generations (five to ten or so) for a population to become almost completely admixed in the absence of endogamy norms, but in a community where some people are strongly endogamous and a minority are not, unadmixed people are very swiftly comprised only of people who have a strong endogamy norm.

Ultimately, no unadmixed populations persisted in either West Eurasia or East Eurasia, presumably because after a few generations of admixture people with a small percentage of Neanderthal admixture became phenotypically indistinguishable from people with none.  But, at first, it is hard to imagine that discernibly hybrid Neanderthal girls would have been on a completely level playing field in finding mates as girls without any Neanderthal admixture.  

One would expect that a Neanderthal ancestry proportion that was phenotypically indistinguishable from a non-admixed individual would have a proportion of Neanderthal admixture similar to the amount which is indistinguishable for instance, in a black-white mixed race individual, since Neanderthals and modern humans would have been more phenotypically distinct from each other than any two modern humans.  

Experience tends to show that a black-white mixed race individual can "pass for white" in the vicinity of 1/8th to 1/16th African ancestry, about 6.25%-12.5%.  The current Neanderthal admixture level in modern humans is just a little bit below that threshold (which would have been a bit lower for Neanderthal-modern human mixed species individuals due to the greater differences between the two to start with).  Indeed, one might wonder if this "pass for modern human" threshold played an important part in determining the ultimate level of admixture that took place on the theory that only people who could pass for modern human would have been fully integrated into the modern human community and contribute genetically to the population in the long run.  

Otzi the Iceman and the estimated peak level of admixture in Denisovan introgressed populations both seem to be close to 8% archaic admixed, again suggesting the phenotypic indistinguishability fraction as a cultural threshold with important long term effects.

A Defense of Bohmian Pilot Wave Theory

Lubos has posted a guest post making a vigorous defense of the Bohmian Pilot Wave Theory interpretation of quantum mechanics in response to his recent post arguing that the theory was fundamentally flawed.  The other main interpretations of quantum mechanics are the Copenhagen interpretation (which is the mainstream version) and the many worlds interpretation (aka inconsistent histories).

Lubos argued that the Bohmian interpretation does not produce the same results as other interpretation.  This criticism is taken to task and the main benefit of the Bohmian interpretation, which is that it dispenses with the need for a meta-theory about the "collapse of the wave function" is dispensed with in Bohmian interpretations with an additional equation.  Bohmian interpretations also try to give quantum mechanics a less "magical" PR spin via resort to hidden variables and in particular the "pilot wave".

But, Bohmian quantum mechanics, like the other kinds, involves subtle points that are easy to get wrong which is was the defense argues that Lubos has done - in effect arguing against a straw man flawed version of the theory when better versions exist.

In another forum the same author discusses why Lorentz invariance might plausible break down at small scales without breaking down at long distance sccales.

Planck 2013 CIB Anisotropy Data Released

The original release of the Planck 2013 CIB (cosmic infrared background radiation) data in March of this year excluded critical data on anisotropies that took longer to analyze.  Some of that data was released today in an analysis of tightened boundaries on models of star formation, which includes some quite model dependent assumptions about dark matter that are not present in the overall six parameter cosmological model.  But, the much awaited increased precision with which various cosmological inflation models can be discriminated from each other is not yet available.

These releases are a big deal because Planck's data are not just precise, but are measurements that are precise as it is theoretically possible to measure of a singular astronomical phenomena.  Once the full set of Planck data are release it may be a thousand years before deep space probes make better data available.

A Tidal Wave Of New Ancient DNA and Population Genetic Data

Dienekes' Anthropology blog recounts abstracts of conference papers providing an immense number of new ancient DNA data sets from Europe and North Africa, some from ISABS 2013 and some from EAA 2013.  None of the papers, taken individually, is really game changing.  But, collectively, the vastly expanded ancient DNA data set is solidifying and refining conjectures made based upon early ancient DNA results into well established results.

Among the most notable results are:

* the extent to which North Africa has been predominantly one corner of the West Eurasian in genetic macro-population (as opposed to sub-Saharan African) as far back as 23,000 years ago with sub-Saharan African contributions attributable to relatively recent low level population exchanges across the Sahara;

* the increasingly clear reality that there have been several important demic migration waves in Europe from the advent of the Neolithic revolution and Bronze Age collapse; and

* another solid archaeological example of megalithic architecture by people with forager economies.  The case of large scale social organization and religion preceding rather than following the Neolithic revolution is strengthening.

Physics Conjectures Galore!

The plenary opening and closing addresses at academic conferences are often hotbeds of cutting edge conjecture by the gray beards of the discipline.  Chris Quigg's paper "DIS and Beyond" (August 30, 2013) does not disappoint on that score.  He notes:

* Optimistic prospects for new discoveries within QCD.

* An interesting conjectural relationship between the mass of the top quark and the mass of the proton (hat tip to Mitchell's theory blog).

* The notion that a good place to look for a GUT or supersymmetry would be in the bending of the running of the coupling constants of the Standard Model that might be observable at the LHC (and which if not observed would undermine motivation for SUSY).

* A discussion of alternative means by which electroweak symmetry breaking can take place.

* He closes by noting that remarkable success of the Standard Model against other contenders which is particularly evidence in the absence of flavor changing neutral currents predicted in many beyond the Standard Model theories but which are too rare to detect in the Standard Model.  He closes his talk by stating:

I regard the persistent absence of flavor-changing neutral currents as a strong hint that a new symmetry or new dynamical principle may be implicated, or that new physics is more distant than hierarchy-problem considerations had indicated.

In sum, the short paper is definitely worth a read.