Muon g-2 Predictions Recapped

A new 192 page paper prepared by a huge collaboration of authors and led by Fermilab exhaustively reviews the latest efforts to theoretically calculate the property of anomalous magnetic moment of the muon, called muon g-2 reports on the latest state of that effort. Another big review came out earlier this year in March.

The tension between experiment and theoretical prediction of this quantity is one of the leading unexplained problems in physics today. A September 9, 2019 post at this blog also examined the discrepancy in detail. As I summarized then, using slightly different source numbers from this paper (which, if anything assigns a larger share of the error to the QCD component):

The errors in theoretical calculation by component are summarized roughly as follows (in comparable units):

QED 0.08 (i.e. 0.2% of the total)
Weak Force 1.00 (i.e. 2.9% of the total)
QCD 33.73 (i.e. 96.9% of the total). . . .

Proportion of total value from each component:

QED 99.994% (116 584 718.95)
Weak Force 0.00013% (153.6)
QCD 0.006% (6931)

Relative error percentage:

QED 0.000 000 0686%
Weak Force 0.65%
QCD 4.88%

On one hand, muon g-2 is predicted to exquisite seven significant digit accuracy, suggesting the general correctness of the Standard Model used to calculate it. On the other hand, a strong tension with the most recent precise experimental measurement of that quantity, remains, dashing the hope that much of the discrepancy might have been due to uncertainties in the most uncertain part of the calculation. This review is timely because a new, four times more precise experimental measurement will be available in a year or two.  

Improvements of the precision in the theoretical estimate, which are predominantly from the quantum chromodynamics component of the calculation that make the smallest contribution to the absolute value of this measurable quantity are also expected in the near term.

Conventional wisdom is that the tension will ease, producing an experimentally measured value closer to the theoretically predicted one, despite the much greater precision of the new measurement. 

But, if this does not happen, the quantity muon g-2 is a good global indicator of the existence and magnitude of beyond the Standard Model physics, although it is not a very good tool for determining the precise nature of the new physics because it is affected by essentially all parts of the Standard Model when measured with the precision that is now possible.

A third possibility is that scientists are making some shared conceptual error in how they do their theoretical predictions of the value of muon g-2 that doesn't really amount to new physics. Gravitational corrections, if any, however, should be negligible in magnitude compared to other uncertainties. 

Cheat Sheet For When Experimental Results Are Announced

The current state of the art Brookhaven measurement was:

116,592,089(63) x 10^−11.

The headline that will be used when the experimentally measured value announced later this year or next year can be determined by referring the the cheat sheet below where the number listed is the new experimental result.

Less than or equal to 116,591,582 x 10^-11:

New physics has been discovered contradicting the Standard Model more definitively than any prior measurement in physics. The Brookhaven measurement was deeply flawed.

116,591,581 to 116,591,718 x 10^-11:

There is tension with the Standard Model prediction in the opposite direction from the Brookhaven measurement. The Brookhaven measurement was deeply flawed. At the high end of this range it will be called a "slight tension", at the low end of this range it will be called a "strong tension."

116,591,718 to 116,591,901 x 10^11:

The new measurement has confirmed the Standard Model prediction. Any new physics that impact muon g-2 are too small to observe experimentally.

116,591,902 to 116,592,037 x 10^11:

There is tension with the Standard Model prediction. At the low end of this range it will be called a "slight tension", at the high end of this range it will be called a "strong tension."

Greater than or equal to 116,592,038 x 10^11:

New physics has been discovered contradicting the Standard Model more definitively than any prior measurement in physics.

The Facts

The new paper and its abstract are as follows:

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. 

This is performed in a perturbative expansion in the fine-structure constant 

α and is broken down into pure QED, electroweak, and hadronic contributions. 

The pure QED contribution is by far the largest and has been evaluated up to and including (α5) with negligible numerical uncertainty. The electroweak contribution is suppressed by (mμ/MW)2 and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at (α2) and is due to hadronic vacuum polarization, whereas at (α3) the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads aSMμ=116591810(43)×10−11 and is smaller than the Brookhaven measurement by 3.7σ. 

The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics.

T. Aoyama, et al., "The anomalous magnetic moment of the muon in the Standard Model" arXiv (June 8, 2020).

The conclusion is as follows:

In this paper we provide a detailed analysis and review of the SM calculation of the muon anomalous magnetic moment aµ. The emphasis is on the hadronic contributions, since they dominate the final uncertainty, but the QED and electroweak contributions are also discussed in detail and up-to-date numbers are provided. 

The QED contribution, which has been calculated up to tenth order in the perturbative expansion, i.e., O(α 5 ), is reviewed in Sec. 6. The final number depends on the input used for the fine-structure constant α and at present there are two independent determinations that differ by about 2.4 standard deviations. The impact of this discrepancy on the final number for aµ is however well below the uncertainty of the QED contribution itself, which is dominated by the estimated effect of the O(α 6 ) contribution. As final number we take the one based on the value of α obtained from atom-interferometry measurements of the Cs atom [117], see Eq. (6.30), and the latest QED calculations from Refs. [33, 34]: 

a QED µ (α(Cs)) = 116 584 718.931(104) × 10−11 . (8.1) 

Electroweak contributions are reviewed in Sec. 7: they have been calculated up to two loops and an estimate of the leading logarithmic contribution beyond two-loop level is also included in the final estimate. The hadronic loops, which appear at two-loop level, are also included and dominate the uncertainty of the EW contribution. The final result Eq. (7.16) (mainly based on Refs. [35, 36]) reads 

a EW µ = 153.6(1.0) × 10−11 , (8.2) 

with an uncertainty ten times larger than the QED one, but still negligible with respect to the hadronic uncertainties. 

In the section on data-driven evaluations of HVP we reviewed both the available data sets for the e + e − → hadrons cross section and the techniques applied for the evaluation of the HVP dispersive integral. In particular, we provide a detailed discussion of the differences between these approaches and the current limitations of the dispersive HVP evaluation, as they arise from the published experimental uncertainties as well as, crucially, from unresolved tensions among the data sets, especially in the dominant ππ channel. As the main result, Eq. (2.33), we devised a merging procedure that adequately takes into account these tensions, which also drive the differences between the available HVP evaluations. The resulting estimate, based on Refs. [2–7] as well as the main experimental input from Refs. [37– 89], 

a HVP, LO µ = 6931(40) × 10−11 (8.3) 

should provide a conservative but realistic assessment of the current precision of data-driven HVP evaluations. In the same framework, the LO result is complemented by NLO [7] and NNLO [8] HVP iterations, see Eq. (2.34) and Eq. (2.35), 

a HVP, NLO µ = −98.3(7) × 10−11 , 

a HVP, NNLO µ = 12.4(1) × 10−11 , (8.4) 

leading to the sum 

a HVP, LO µ + a HVP, NLO µ + a HVP, NNLO µ = 6845(40) × 10−11 . (8.5) 

Finally, we discussed the prospects for future improvements, including new data from several e + e − experiments as well as the possibility to measure HVP independently in electron–muon scattering. 

The status of lattice QCD+QED calculations of HVP is reviewed in Sec. 3. While lattice calculations can, in principle, provide an alternate, ab initio determination of the HVP contribution, they are, at present, not precise enough to confront the data-driven evaluations. The current “lattice world average,” obtained in Sec. 3.5.1 from a conservative combination of current, published lattice QCD+QED results, is consistent with the data-driven result of Eq. (8.3) but with a large enough uncertainty to also cover the “no new physics” scenario: 

a HVP, LO µ = 7116(184) × 10−11 , (8.6) 

based on Refs. [9–17]. 

The phenomenological estimate of HLbL scattering as reviewed in Sec. 4 is essentially based on a dispersive approach, in analogy to HVP. The various contributions to HLbL can be collected into three main pieces depending on how they have been estimated: (1) the numerically dominant contributions from the single-pseudoscalar poles and large parts of the two-pion intermediate states, both of which rely on data-driven approaches and are under good control; (2) the model-dependent estimates for the sum of scalar, tensor, and axial-vector contributions, as well as the impact of short-distance constraints; all of these still suffer from significant uncertainties, which in the total have been added linearly; (3) the c-quark contribution, which can be estimated using perturbative QCD, with a conservative uncertainty estimate in view of the low scale and potential nonperturbative effects. The final estimates for HLbL from Table 15 (mainly based on Refs. [18–30] and, in addition to e + e − → hadrons cross sections, the experimental input from Refs. [90–109]) and HLbL at NLO [31] from Eq. (4.91) read as follows: 

a HLbL µ = (69.3(4.1) + 20(19) + 3(1)) × 10−11 = 92(19) × 10−11 , (8.7) 

a HLbL, NLO µ = 2(1) × 10−11 , (8.8) 

where the first line gives the three pieces in the same order as discussed above and the total in the second line is obtained by adding the central values of the three contributions and combining the errors in quadrature. The final error is about 20% and is completely dominated by the model estimates of a numerically subdominant part of the total. 

The lattice determination of HLbL scattering is reviewed in Sec. 5. The lattice methodology for this quantity has advanced significantly in the last years [110–116] and has now reached a mature stage, resulting in a calculation [32] with reliable estimates of both statistical and systematic uncertainties (Eq. (5.49)): 

a HLbL µ = 78.7(30.6)stat(17.7)sys × 10−11 . (8.9) 

There have been extensive checks between different groups working on the lattice HLbL as well as internal checks of the calculations such as the regression against the leptonic loop or pion-pole contributions. These checks are explained in detail in Sec. 5. 

To obtain a recommendation for the full SM prediction we proceed as follows: for HLbL scattering, there is excellent agreement between phenomenology and lattice QCD, to the extent that it is justified to consider a weighted average. Taking into account that the lattice-QCD value does not include the c-quark loop, we first average the light-quark contribution and add the c quark as estimated phenomenologically in the end. This produces 

a HLbL µ (phenomenology + lattice QCD) = 90(17) × 10−11 , (8.10) 

and, using Eq. (8.8), 

a HLbL µ (phenomenology + lattice QCD) + a HLbL, NLO µ = 92(18) × 10−11 . (8.11) 

For HVP, the current uncertainties in lattice calculations are too large to perform a similar average and the future confrontation of phenomenology and lattice QCD crucially depends on the outcome of forthcoming lattice studies. For this reason, we adopt Eq. (8.3) as our final estimate, emphasizing that the uncertainty estimate already accounts for the tensions in the e + e − data base. Combined with the QED and EW contributions, we obtain 

a SM µ = a QED µ + a EW µ + a HVP, LO µ + a HVP, NLO µ + a HVP, NNLO µ + a HLbL µ + a HLbL, NLO µ = 116 591 810(43) × 10−11 . (8.12) 

This value is mainly based on Refs. [2–8, 18–24, 31–36], which should be cited in any work that uses or quotes Eq. (8.12). It differs from the Brookhaven measurement [1] 

a exp µ = 116 592 089(63) × 10−11 , (8.13) 

where the central value is adjusted to the latest value of λ = µµ/µp = 3.183345142(71) [751], by 

∆aµ := a exp µ − a SM µ = 279(76) × 10−11 , (8.14) 

corresponding to a 3.7σ discrepancy. In constructing Eqs. (8.5), (8.11), and (8.12), we have taken into account the correlations between the uncertainties in the leading and subleading HVP contributions as well as the partial correlation in the case of HLbL, with numbers rounded including subleading digits from the individual contributions. 

The prospects for near-term and long-term improvements of the uncertainties in the SM prediction are excellent. As discussed in Sec. 2, a new measurement of the crucial 2π channel by SND is currently under review, and more measurements of the 2π channel and others are forthcoming, leading to the realistic prospects of reducing the dispersive HVP error by a factor of 2. In addition, independent data-driven input could be provided by the MUonE project. The past five years have seen great progress in the development of methods to address the challenges associated with lattice determinations of a HVP, LO µ at the target precision, as discussed in detail in Sec. 3. This is also evident in the recent high-precision lattice result for a HVP, LO µ [392], which, however, still needs to be scrutinized in detail. With these methods now in place, and with sustained, dedicated effort, lattice results with permil-level precision will be forthcoming. The phenomenological determination of HLbL scattering has been consolidated at a level well below the Glasgow consensus, see Sec. 4, with the dominant contributions derived using data-driven methods in analogy to the dispersive HVP approach. With expected progress on the subleading contributions, a 10% calculation of HLbL scattering now appears feasible. Finally, we expect more independent lattice calculations of the HLbL to appear in the next years. Building on the newly developed methodologies, a 10% lattice calculation of the HLbL also appears feasible by the end of the Fermilab experiment.

Early Chinese Art and Early Hominin Bone Tools

Hunter-gatherers weren't as unsophisticated as they are often assumed to have been. This small sculpture of a bird from Chine predates the invention of agriculture there by more than five thousand years. 

Pottery also arose in East Asia prior to agriculture (primarily in sedentary communities that relied upon fishing for subsistence). In contrast, in the Levant, farming came first and pottery came second.

A tiny statuette of a bird carved from burnt bone about 13,500 years ago reveals the origins of Chinese art, embodying a style different from prehistoric three-dimensional artwork by people in other parts of the world, researchers said on Wednesday. 

The figurine, found at a site called Lingjing in Henan Province in central China, depicts a standing bird on a pedestal and was crafted using stone tools employing four sculpting methods - abrasion, gouging, scraping and incision, the researchers said. 

It is the oldest-known three-dimensional art from China and all of East Asia by 8,500 years, although there are primitive abstract engravings on bone and stone and personal ornaments made of animal teeth and shells predating it. . . . 

Humankind’s earliest-known three-dimensional carvings, made of mammoth ivory, date to 40,000 years ago from southern Germany. . . .  It is still unclear whether three-dimensional artwork arose independently in various locales or by diffusion from a prehistoric center of origin. The figurine differs in size, style and technology from older and contemporaneous carvings from Europe and Siberia, d’Errico said, suggesting it belongs to a distinctive Chinese artistic tradition.

From here.

Henan, China (image via Wikipedia)

The paper is:

The recent identification of cave paintings dated to 42–40 ka BP in Borneo and Sulawesi highlights the antiquity of painted representations in this region. However, no instances of three-dimensional portable art, well attested in Europe since at least 40 ka BP, were documented thus far in East Asia prior to the Neolithic. 

Here, we report the discovery of an exceptionally well-preserved miniature carving of a standing bird from the site of Lingjing, Henan, China. Microscopic and microtomographic analyses of the figurine and the study of bone fragments from the same context reveal the object was made of bone blackened by heating and carefully carved with four techniques that left diagnostic traces on the entire surface of the object. Critical analysis of the site’s research history and stratigraphy, the cultural remains associated with the figurine and those recovered from the other archeological layers, as well as twenty-eight radiometric ages obtained on associated archeological items, including one provided by a bone fragment worked with the same technique recorded on the object, suggest a Late Paleolithic origin for the carving, with a probable age estimated to 13,500 years old. The carving, which predates previously known comparable instances from this region by 8,500 years, demonstrates that three-dimensional avian representations were part of East Asian Late Pleistocene cultural repertoires and identifies technological and stylistic peculiarities distinguishing this newly discovered art tradition from previous and contemporary examples found in Western Europe and Siberia.

Zhanyang Li, et al., "A Paleolithic bird figurine from the Lingjing site, Henan, China" PLOS One (June 10, 2020) https://doi.org/10.1371/journal.pone.0233370

Middle Paleolithic Bone Tools In China 

Another interesting paper from PLOS One with one of the same investigators from the same location involves an extremely early site whose hominin occupants may have been modern humans but could also have been archaic hominins of some kind.

Bone tools have thus far been found almost exclusively in association with modern humans and are extremely rare more than about 75,000 years ago. The authors conservatively assume that these tools were made and used by archaic hominins. 

Most Chinese lithic industries dated between 300,000 and 40,000 are characterized by the absence of Levallois debitage, the persistence of core-and-flake knapping, the rarity of prepared cores, their reduction with direct hard hammer percussion, and the rarity of retouched flakes. 

Here we report the discovery of seven bone soft hammers at the early hominin Lingjing site (Xuchang County, Henan) dated to 125,000–105,000. These artefacts represent the first instance of the use of bone as raw material to modify stone tools found at an East Asian early Late Pleistocene site. 

Three types of soft hammers are identified. The first consists of large bone flakes resulting from butchery of large herbivores that were utilized as such for expedient stone tools retouching or resharpening. The second involved the fracture of weathered bone from medium size herbivores to obtain elongated splinters shaped by percussion into sub-rectangular artefacts. Traces observed on these objects indicate intensive and possibly recurrent utilization, which implies their curation over time. The last consists of antler, occasionally used. 

Lingjing bone tools complement what we know about archaic hominin cultural adaptations in East Asia and highlight behavioural consistencies that could not be inferred from other cultural proxies. This discovery provides a new dimension to the debate surrounding the existence of the Middle Palaeolithic in the region. The attribution of East Asian sites to the Middle Palaeolithic assumes that cultural traits such as the Levallois method represent evolutionary hallmarks applicable to regions of the world different from those in which they were originally found. Here, we promote an approach that consists in identifying, possibly from different categories of material culture, the original features of each regional cultural trajectory and understanding the behavioural and cognitive implications they may have had for past hominin populations.

Luc Doyon, et al., "Discovery of circa 115,000-year-old bone retouchers at Lingjing, Henan, China" PLOS One (March 12, 2018) https://doi.org/10.1371/journal.pone.0194318

Hard Science Isn't Immune To Current Events

Both of the defining events of 2020 have had an impact on arXiv, the repository of free, open access, scientific journal pre-prints that I scour several times a week.

Quote Of The Day

Not only do they make up everything, they are also feckless, because they are prone to acting randomly.

Hat tip to Dr. Jennifer Grant of the University of Wisconsin-Stout.

Bonus gag:

Meta: This blog is actually two posts in excess of its 3% humor quota, so I guess I'm going to have to dial it back now.

Maize Was Primarily A Liquor Ingredient For More Than Four Thousand Years After Its Domestication

Maize was domesticated in the Americas around the same time as the independent Neolithic revolutions in the Fertile Crescent (ca. 8000 BCE), in both North and South China respectively (ca. 6000 BCE for Millet farming in the Yellow River Basin in the north, and around the same time for rice cultivation in the Yangtze River Basin in southern China) and in the highlands of Papua New Guinea (also around the same time).[1] 

But, this didn't lead to a full fledged Neolithic revolution with attendant civilizational and technological advances in the Americas until roughly four thousand years later (i.e. in the time period from 2700 BCE to 2000 BCE, predating the Classical Mayan period by more than a thousand years), according to a new study. 

Until then, Maize was a crop used predominantly to make alcoholic drinks, a bit like modern niche crops like agave and hops today, by people who were basically hunter-gatherers.

"Farming allowed us to live in larger groups, in the same location, and to develop permanent villages around food production. These changes ultimately led in the Maya area to the development of the Classic Period city states of the Maya between 3,000 and 1,000 years ago. However, until this study, we did not know when early Mesoamericans first became farmers, or how quickly they accepted the new cultigen maize as a stable of their diet. Certainly, they were very successful in their previous foraging, hunting, and horticultural pursuits before farming, so it is of considerable interest to understand the timing and underlying processes," he said. 

Radiocarbon dating of the skeletal samples shows the transition from pre-maize hunter-gatherer diets, where people consumed wild plants and animals, to the introduction and increasing reliance on the corn. Maize made up less than 30 percent of people's diets in the area by 4,700 years ago, rising to 70 percent 700 years later. 

Maize was domesticated from teosinte, a wild grass growing in the lower reaches of the Balsas River Valley of Central Mexico, around 9,000 years ago. There is evidence maize was first cultivated in the Maya lowlands around 6,500 years ago, at about the same time that it appears along the Pacific coast of Mexico. But there is no evidence that maize was a staple grain at that time. 

The first use of corn may have been for an early form of liquor.

From Science Daily.

The paper and its abstract are as follows:

Maize is a cultigen of global economic importance, but when it first became a staple grain in the Americas, was unknown and contested. 

Here, we report direct isotopic dietary evidence from 52 radiocarbon-dated human skeletons from two remarkably well-preserved rock-shelter contexts in the Maya Mountains of Belize spanning the past 10,000 years. 

Individuals dating before ~4700 calendar years before present (cal B.P.) show no clear evidence for the consumption of maize. Evidence for substantial maize consumption (~30% of total diet) appears in some individuals between 4700 and 4000 cal B.P. Isotopic evidence after 4000 cal B.P. indicates that maize became a persistently used staple grain comparable in dietary significance to later maize agriculturalists in the region (>70% of total diet). These data provide the earliest definitive evidence for maize as a staple grain in the Americas.

Douglas J. Kennett et al., "Early isotopic evidence for maize as a staple grain in the Americas." 6(23) Science Advances eaba3245 (June 3, 2020) (open access).

[1] Some other background and context regarding the history of agriculture follows.

Other independent Neolithic Revolutions. There were three other independent Neolithic revolutions that each occurred several thousand years after the four main independent Neolithic revolution events in the Fertile Crescent, North China, South China and Papua New Guinea. And, while the Papuan Neolithic's first crops were domestically early (just as they were in Meso-America), the full Papuan Neolithic package may not have been sufficiently assembled to allow a conversion to a food producing lifestyle until 3000 BCE to 2000 BCE.

There was an independent Neolithic Revolution in Ethiopia and across the Sahel to West Africa. 

There was a second independent Neolithic Revolution in the eastern United States which was superseded by the Meso-American agricultural package in late pre-Columbian times. 

And, there was a third independent Neolithic Revolution in the Amazon River Basin in South America which petered out without spreading widely or being replaced by the Meso-American package for reasons that are currently unknown, but were probably related to climate changes.

Assembling Neolithic Domesticate Packages. Further, each of the independent Neolithic revolutions didn't take hold until several domesticates sufficient to constitute working "package" of domesticated plants and animals sufficient to make it possible to transition from a hunter-gather means of subsistence to a herding and/or farming means of subsistence was assembled.

In the Fertile Crescent case, different components of the package of domesticates that made a Neolithic package viable with domesticated, respectively, in Mesopotamia and the Zargos Mountains, in the Anatolian highlands, and in the Levant.

In Meso-America, the "three sisters" (corn, beans and squash) were domesticated in different places at different time.

The Neolithic revolutions didn't occur anywhere in the world prior to this time for reasons related to climate change.

Derived Neolithic Revolutions. Elsewhere in the world, agriculture was largely derived from one or more of these independent Neolithic revolutions in Pre-Columbian times.

In Europe, North Africa, Iran, the Indus River Valley, and Central Asia the primary source was the Fertile Crescent Neolithic package. 

The Meso-American Neolithic package (once fully assembled and used for staple subsistence) spread to both North America and South America.

Elsewhere in East Asia and in Southeast Asia, Oceania and Northeast India, the primary source was the Chinese Neolithic package, which in many cases happened after the North Chinese Neolithic package and the South Chinese Neolithic package had integrated.

The Sahel African Neolithic package was exports to South India where it was integrated to some extent with select components of the Fertile Crescent Neolithic package.

The Neolithic packages of the highlands of Papua New Guinea, of the Eastern United States, and of the Amazon were never widely exported.

Local Neolithic Package Enhancements Places that received a particular based independent Neolithic package often added some secondary domesticated animals and crops that were domesticated locally at a later date, and often shared with other places that had agriculture based upon the same package of domesticates.

For example, guinea pigs, yams and the llama were added to the Meso-American Neolithic package in the highlands of Pacific coastal South America. Cotton and the donkey were added to the Fertile Crescent Neolithic package in Egypt. One kind of camel was added to the Fertile Crescent Neolithic package in North Africa and the Middle East, and another kind of camel was added in North Asia along the Silk Road. Horses were added to the Fertile Crescent Neolithic package in the Pontic-Caspian steppe. Some secondary grains and vegetables and cows were added to the Fertile Crescent Neolithic package in the Southeast Europe. Bananas were added to the Chinese Neolithic package in Indonesia. The indica strain of rice was added to the Fertile Crescent Neolithic package in northern India.

Likewise, some of the original crops in these Neolithic packages, like the "ancient grains" of the original Fertile Crescent Neolithic package have subsequently been abandoned or superseded.

Modern Global Agricultural Integration By the "age of exploration" starting in the late 15th century CE, regular, bidirectional maritime trade at global distances had started the process of integrating particular domesticated plants and animals from other packages into the local agricultural package. 

This has happened only sporadically before then (e.g. the merger of the North and South Chinese Neolithic packages facilitated by the development of a non-tropical strain of East Asian rice and the importation of Indian strain rice, the arrival of the yam from South America to Oceania, and the transmission of Indonesian domesticates from Borneo to Africa by Austronesian mariners).

Some of the most notable age of exploration exports to the wider world to grow domestically New World crops including spicy peppers which were rapidly adopted globally in warmer climates, the potato, the yam, and corn, the spread of wheat and cotton to North America, and the spread of coffee to Indonesia and South America. 

Other domesticated crops, like tea from Southeast Asia and tobacco from the Americas, soon became widely exported, but did not result in much cultivation outside the areas where they were already established.

Quebec As A Natural Experiment

The National Geographic channel (which is included in the newly initiated Disney+ streaming service), has a new historical fiction TV drama series called "Barkskins" about the Filles du Roi (aka King's Daughters) who were sent to New France by King Louis XIV (who died in 1715 CE) to correct the gender imbalance in the colony. 

Mostly, they ended up in Quebec.

Quebec is a hot spot for international genetics research related to the multi-generational inheritance of genetic traits that can be benchmarked against theoretical models to test their reliability, as a long running natural experiment. 

This is because it has high quality and very complete birth, death and marriage records for about 400 years, with additional descriptive data because lots of people journaled or wrote vivid letters to family that were preserved, going all of the way back to this generation of men and women.

Also, there was not massive migration to or from Europe after this era, or to or from the rest of North America (except a pretty much one time, one directional migration to Louisiana), in part due to language barriers, since no new Francophone territories were left after the Louisiana Purchase in 1809. So, while this is certainly an oversimplification (as a comprehensive capsule history of Quebec from below the fold points out in detail) you still have a comparatively isolated gene pool pretty much until the 20th century, for a dozen generations or so after the women depicted in the new drama. And, because the habitable part of Quebec has essentially no natural geographic barriers and few strict endogamy inducing cultural divisions, Quebec can be studied as a first approximation of a single, unstructured, closed gene pool, which is what lots of widely used population genetic models try to approximate.

For example, in the case of many rare genes found among people in Quebec, it is possible to identify the names of specific named women from this founding population group, who we know something about beyond a mere tombstone information, who introduced the trait into the gene pool of Quebec.

This makes it possible, for instance, to quantify exactly the statistical impact of a gene on the fertility and mortality of those who carried it, and to precisely quantify mutation rates of genes present in the founding populations by looking at all descendants of that person who inherited either the original version or a mutated version of the original gene.

There are a few other places where that can be done (e.g. Iceland and Korea have 500+ year time series of accurate vital statistics records at the individual by individual level), that capture essentially a complete and isolated gene pool, but not many. In lots of other places that were keeping good written vital statistics records from the late 17th century or earlier, wars, fires and natural disasters destroyed the records at some point.

So you can use the example of Quebec to compare mathematically idealized multi-generational population genetic models with reality to see what factors differ enough from mathematical ideals (from the fact that there is no such thing as a fractional child in real life, to the fact that "panmixia" isn't a realistic assumption even in a very weakly structured population) that need to be included in a model that accurately describes reality.

Selected references from this body of the scientific literature and a detailed capsule history of Quebec from the body text of one of those articles, appear below the fold.

A Project To Sequence The Genome Of Every Vertebrate Species Is Underway

A project to develop high quality reference genomes for each of the 70,000+ known species of vertebrates is underway.

High-quality and complete reference genome assemblies are fundamental for the application of genomics to biology, disease, and biodiversity conservation. However, such assemblies are only available for a few non-microbial species. 

To address this issue, the international Genome 10K (G10K) consortium has worked over a five-year period to evaluate and develop cost-effective methods for assembling the most accurate and complete reference genomes to date. 

Here we summarize these developments, introduce a set of quality standards, and present lessons learned from sequencing and assembling 16 species representing major vertebrate lineages (mammals, birds, reptiles, amphibians, teleost fishes and cartilaginous fishes). We confirm that long-read sequencing technologies are essential for maximizing genome quality and that unresolved complex repeats and haplotype heterozygosity are major sources of error in assemblies. Our new assemblies identify and correct substantial errors in some of the best historical reference genomes. 

Adopting these lessons, we have embarked on the Vertebrate Genomes Project (VGP), an effort to generate high-quality, complete reference genomes for all ~70,000 extant vertebrate species and help enable a new era of discovery across the life sciences.

Arang Rhie, "Towards complete and error-free genome assemblies of all vertebrate species" bioRxiv (May 23, 2020).

What Would Have Been Different If The Persians Had Defeated The Greeks? UPDATED

Feel free to discuss and consider this proposition in the comments. 

I will briefly comment that during a visit to Greece, and in particular, some tours in Athens last summer, the Greco-Persian War was vibrantly alive in the hearts and minds of the Greek people and still felt relevant today.

Of all the many counterfactuals, those “what-ifs” posed by history, perhaps the most arresting, if only because the most sweeping, asks: "what if the Persians had defeated the Greeks in the Greco-Persian War of 490–479 B.C.?" 

Had this happened, there might have been no Plato, no Aristotle, no Roman Empire, no Christianity, no Western Civilization. A Great King, a lineal descendant of Darius, might still rule the world. All might worship the Zoroastrian god Ahura Mazda, with men going about in turbans, women remaining at home or in harems. But that, as every counterfactual invariably ends—generally accompanied by a sigh of relief—didn’t happen.

From this book review reviewing Peter Green, Xerxes at Salamis (1970, reissued as The Greco-Persian Wars).

I'll also note that the answer is multi-faceted. 

One aspect of the question is a question of what matters in terms of historical causation.

If you are believer in the "Great Men" and "key moments" theory of history, events like this really can make an immense difference. 

But, if you think that history is largely a function of big, long term fundamental forces like climate and technology and inevitable secular trends (an approach often associated with Marxist historical interpretation but by not means so ideologically bound), you may be inclined to say that if the Persians had defeated the Greeks in the Greco-Persian War of 490–479 B.C., the fortunes of the parties probably would have been reversed in a second Greco-Persian War of 453-444 B.C., without leaving the world notable changed in the long run.

In this view, "Great Men" may change the finer grained details of history, but only rarely the overarching long term trends that matter in the long run. The alternative history would surely be different in some respects, because history does not repeat itself, but it would rhyme with the world we live in, taming our utopian and dystopian instincts.

In the language of mathematics, historical causation is a "chaotic" process, i.e. one in which small changes in the conditions in one moment are capable of producing big differences in outcome down the line due to the non-linear processes involved in how events unfold. But, historical trajectories have an "attractor" to which the non-linear processes' developments tend to gravitate, although the strength of these attractors is not a matter upon which there is a strong consensus, even when it is possible to meaningful define or describe that strength with more than a mere gut feeling. 

Even then, however, a question like this opens up the question of what is really fundamental, and what is window dressing.

An absence of Plato and Aristotle does not imply that the Persian tradition might have offered us equally formidable philosophers and proto-scientists. Cf. Hindu philosophy was mathematical. Indeed, some non-Western figures readily present themselves as alternatives. 

We might not have "Western Civilization" but that is not to say that Persian civilization under the different conditions it would have encountered in the scenario suggested would have been all that different in the ways that matter. Surely, an ascendant global Persian civilization would have still been more similar to our "Western Civilization" than the civilizations of India, China, Japan, the expansionist Bantu tribes of Africa, or the Aztecs.

A Persian Empire, had it extended to Hadrian's Wall, would probably have turned out more similar to the Roman Empire than the Persian Empire of our history books, but it would surely also have been quite distinct in myriad particulars. The notion that "A Great King, a lineal descendant of Darius, might still rule the world", likewise, seems about as plausible as the notion that because the Greeks won, a Roman Emperor still rules the world.

The Roman Empire with late Iron Age technology, was not sufficient robust to survive to the modern day, and neither would a Persian Empire.

Arguably, the therapeutic deism of the typical layman with little training in religious doctrine, who is nominally Christian, is actually closer, doctrinally, to Zoroastrianism than to Christianity or Judaism understood at the level of the doctrines that matter to educated elites.

It could be that 19th century businessmen might have ended up wearing turbans rather than bowler hats or beaver caps and silk neckties, if this had come to pass. But, anyone who thinks that fashion has much intrinsic value vastly overestimates the importance of function over form.

And, the suggestion that in world where the Persians rather than the Greeks prevailed that we would have women remaining at home or in harems, misapprehends the extent to which women's roles are functions of economics more than culture. 

King Solomon is a household name to every small town Christian and Jew in America, and he generally has a very high favorability rating. But, that doesn't mean that modern Americans maintain vast harems in order to follow his allegedly wise example. And, women remained at home to a much greater extent than they do today as recently as the 1950s and early 1960s Baby Boom in the United States.

IMPORTANT UPDATE (July 6, 2020):

One noteworthy aspect of Zoroastrianism is that, in contrast to other ancient religions (including Judaism, and later, Christianity), Zoroastrianism appears to have banned slavery on spiritual grounds. This is important to bear in mind in the context of discussing the Persian War, below. The Greeks thought of the war as the defense of their glorious traditions, including the political participation of citizens in the state, but it was the Greeks who controlled a society that was heavily dependent on slavery, whereas slavery was at least less prevalent in Persia than in Greece (despite the religious ban, slavery was clearly still present in the Persian Empire to some degree).

From here.

The Nucletouch Periodic Table

A new periodic table is designed to highlight the numbers of protons in a nucleus that make an atom most stable from a nuclear perspective, as opposed to the properties of the orbiting electrons that give rise to the chemical properties of an atom.

Over 150 years have passed since Dmitri Mendeleev discovered the periodic law that lead him to propose the classic periodic table. He even had the foresight to add space for elements that were still unknown in his time. 

"Fundamentally, it comes down to the electrons in each atom. Atoms are considered to be stable when electrons completely fill their 'shell' of orbits around the nucleus," continues Maeno. 

"So-called 'noble gases', inert elements such as helium, neon, and argon, rarely react with other elements. Their most stable electron numbers are 2, 10, 18, 36, and so on." 

Maeno decribes these as atomic 'magic numbers', and importantly the same principle can also be applied to protons. Imagining that protons in a nucleus exist in 'orbits' may seem like a stretch, but the discovery of the concept was awarded the 1963 Nobel prize in physics. 

Protons have different stable magic numbers: 2, 8, 20, 28, and so on. Among these are familiar elements such at helium, oxygen, and calcium. The Nucletouch table places these 'magic nuclei' at its center, providing a new perspective on the elements. 

"Similar to electrons, when nuclear orbits are filled with protons, they form stable nuclei, analogous to the noble-gas elements," says collaborator Kouichi Hagino. 

"In our nuclear periodic table, we also see that nuclei tend to be spherically-shaped near the magic numbers, but deformed as you move away from them."

From a press release at Science Daily. 

A nuclear periodic table based on the proton magic numbers. The rightmost column shows the elements with the proton magic and semi-magic numbers. The other elements are arranged according to the nuclear shell structure shown in Fig. 1, for which the single-particle levels for the valence protons are denoted with different colors. In the legend for the single-particle levels, those without j include both of the spin orbit partners, e.g. f for f5/2+f7/2. The elements shown in round-corner boxes are those whose nuclei are deformed in the ground state (see Möller et al. (Möller et al. 2016) for the actual values for the deformation parameter). Elements with black symbols have stable nuclei, while those with white symbols represent those with all the isotopes unstable. Even though Bi and Th are unstable, we do not include them in the unstable elements since their decay half-lives are of the order of the age of the universe or longer. Likewise, we do not include U in the unstable elements, since the half-life is similar to the age of the earth.

A nuclear periodic table similar to Fig. 2, but a version in which the elements are arranged symmetrically around the shell closures.

A paper model of the nuclear periodic table shown in Figs. 2 and 3. Corresponding to a similar model for the atomic periodic table known as “Elementouch” (Maeno 2002), we propose to call this model “Nucletouch”

From here.