Tuesday, May 31, 2022

Evidence Of Lepton Flavor Universality Violation Weakens With Better Analysis

Tensions between experiment and the Standard Model prediction regarding lepton universality violations (i.e. that all charged leptons behave identically except for differences flowing from their different masses) is the most important hint of beyond the Standard Model physics at the Large Hadron Collider (LHC). As the paper explains in the introduction, reviewing work before this presentation:

But a new analysis reported in a recent conference paper argues that the differences between tau leptons and muons is not statistically significant even in these decays. It finds a predicted R(D*) on a purely theoretical Standard Model basis to be: 0.275 ± 0.008 (about 1.3 sigma).
At this point, a natural question arises: why is the SM HFLAV theoretical average in Eq. (4) so different from the DM estimate in Eq. (19)? The answer has to be found in the shape of the FFs [ed. Form Factors]. 

Form factors are one of the most technical parts of quantum chromodynamics. (QCD), right on the frontier of what we understand, so its a natural place for a discrepancy to arise.

If so, the likelihood that the LHC will see no beyond the Standard Model physics surges.

This tends to favor my hypothesis that the source of the discrepancy is a separate additional source of electrons in B meson decays which isn't being screened out as expected, or isn't properly considered in the analysis, for some reason. The conclusion of the conference paper states:
We have reviewed the main properties of the Dispersion Matrix approach, which is an attractive tool to implement unitarity and LQCD calculations in the analysis of exclusive semileptonic decays of mesons and baryons. It has several interesting properties. In particular, it does not rely on any assumption about the momentum dependence of the hadronic form factors and it can be based entirely on first principles (i.e. unitarity and analiticity) and on non-perturbative inputs. 
We have discussed the application of the DM method to the b → c and the b → u quark transitions and the resulting theoretical determinations of the LFU observables. In this sense, our main result is that the anomalies in semileptonic charged-current B decays have been strongly lightened. In fact, we have consistency between theory and experiment at the 1.3σ level for both R(D) and R(D∗ ), separately. 
To achieve this goal, it is fundamental to avoid the mixing among theoretical calculations and experimental data to describe the shape of the FFs of interest.
The caution about mixing theoretical calculations and experimental data is also at the heart of the discrepancy between the two leading calculations of the Standard Model prediction for muon g-2, which the calculation that mixes the two strongly discrepant and in tension with experiment, and the one which is purely theoretical in much less tension with the experimental result, just as in this LFU violation comparison.

One of the strongest reasons to think that the LFU violation hints are misleading us is that many other processes with the same W boson mediated mechanism as the one believed to be at work in B meson decays and which governs these decays in the Standard Model show no sign of LFU violation to great precision.

The new conference paper and its abstract are as follows:
We present the results of the application of the unitarity-based Dispersion Matrix approach to semileptonic charged-current B decays. This method allows to achieve a non-perturbative and completely model-independent determination of the hadronic form factors. Starting from lattice results available at large values of the momentum transfer, the behaviour of the form factors in their whole kinematical range is obtained without introducing any explicit parameterization of their momentum dependence. 
We will focus on the analysis of Lepton Flavour Universality by computing the τ/μ ratios of the branching fractions of the B→D(∗)ℓν and B→πℓν decays. The most important result is that, for the first time, the discrepancies between the SM expectation values and the measurements of the Lepton Flavour Universality ratios for the B→D(∗)ℓν decays are reduced at the 1.3σ level for each of the two channels, separately.
Guido Martinelli, et al., "LFU ratios in B decays using Lattice QCD and Unitarity" arXiv:2205.13952 (May 27, 2022) (Contribution to "La Thuile 2022, XXXV Rencontres de Physique de la Vallée d'Aoste").

Footnote Regarding The CKM Matrix

The paper also notes another B meson decay anomaly.
On the one hand, we have the so-called |Vcb| puzzle, i.e. the discrepancy between the inclusive and the exclusive determinations of the CKM matrix element |Vcb|. According to the FLAG Review 2021 [1], there is a ∼ 2.8σ tension between the exclusive estimate (that depends on the form factors parametrization) and the inclusive one, namely
A new more precise estimate of the inclusive value has also recently appeared [2], namely |Vcb|incl = 42.16(50), which is compatible with the inclusive FLAG value in Eq. (1).

But, this discrepancy is less notable, despite having a similar statistical significance, because it is very common for inclusive and exclusive measurements to have discrepancies in the direction observed (something that is also the case, for example, for the mean lifetime of free neutrons), and because global tests of the CKM matrix can point us to the value which is closer to the truth.

A global fit of the CKM matrix via the Particle Data Group, as of 2021, favors a value of Vcb of 40.53 +0.83/-0.61 x 10^3, i.e. a two sigma spread of 39.31 x 10^3 to 42.19 x 10^3, which is between and consistent with both the global average inclusive and global average exclusive measured values of this CKM matrix element. The uncertainty in Vcb constrained by the necessity of a global fit is about ± 2%.

. . .

Highlights from previous posts on related topics

Over the last eight years disparate experimental results and disparate calculations of the Standard Model expectations related to lepton flavor universality tests have produced mixed results. Some have disfavored lepton flavor universality violations (LFUV), either generally, or in particular kinds of decays, while others have shown continued evidence for LFUV in semi-leptonic decays of certain kinds of B mesons to certain kinds of D mesons.

Twenty-one posts at this blog, in addition to this post over those eight years (excluding overall reviews of the state of high energy physics or unsolved problems in physics), have tracked those developments, almost back to the point when experimental hints of LFUV were first reported.

The main conclusions of the twenty-one other posts regarding the existence of LFUV (some of which discuss more than one paper or experimental results, and others of which analyze multiple previously blogged results when taken together) are recapped below. I have largely omitted the discussions of experimental models that could explain what is observed if the observations of LFUV discrepancies with Standard Model expectations persist given new experimental data, improved analysis of both the data, and improved calculations of the Standard Model expectations for selected LFUV sensitive obserbables.

* A New Experimental Challenge To Lepton Universality Overstates Significance (November 30, 2021) ("Rather than being a five sigma discovery class evidence in a new decay channel for LFU violation, this result is actually consistent with LFU at the two sigma level, and actually, as a result, if anything, it tends to disfavor the conclusion that LFU violation is present in any context outside of semi-leptonic B meson decays. But given the great uncertainty in the ratio of the two values, this new experiment, honestly, doesn't really tell us anything one way or the other.")

* Another Search For Lepton Universality Violation Comes Up Empty (October 18, 2021) (finding no LFU violation in semi-leptonic decays of neutral and charged B mesons to kaons of like charge).

* Lepton Universality Violation Considered Again (April 13, 2021) (suggesting cherry picking issues since lepton universality violations are not found in tau lepton decays or pion decays, and are not found in anti-B meson and D* meson decays or in Z boson decays. There is no evidence of LFV in Higgs boson decays either; that many new physics models that explain the intriguing anomalies in the b-quark flavour sector are severely constrained by Bs-mixing; and discussing the coincidence that the ratio could be explained by additional pion path decays if the data collection cutoffs which should exclude decays in this path failed to do so).

* Lepton Universality Not Violated In Top Quark Decays (February 26, 2021) (the title says it all and is notable since these decays should almost all have intermediate b quark paths).

* Belle Experiment At LHCb Finds No Evidence Of Lepton Flavor Universality Violations (January 12, 2021) (finding no LFU violation in semi-leptonic decays of neutral and charged B mesons to kaons of like charge).

* Apparent Lepton Universality Violations Are Probably Measurement And Statistical Errors (December 22, 2020) (in a semileptonic decay of a b quark, the leptons arise from one or two subsequent leptonic W boson decays. So, if W boson decays don't display violations of lepton universality, then either the leptons observed in semileptonic b quark decays are produced by some means other than an intermediate W boson decay, exclusive to b meson decays, which decays preferentially to lighter leptons, or there is some error in the observation. The latter result is infinitely more likely.)

* How Big Are The Lepton Universality Violation Tensions With The Standard Model? (September 16, 2020) (The flavor anomalies reported in RK, RK∗, P′5 and (Bs→ϕμ+μ−) indicate lepton flavor universality violation in b→sl+l− quark level transition decays. The deviation from the SM prediction reported in the underlying flavor observables currently stand at the level of 2.5σ, 2.4σ, 3.3σ and 3.7σ, respectively).

* ATLAS Finds No Evidence Of Lepton Universality Violations In W-Boson Decays (July 29, 2020) (the ratio of the rate of decay of W bosons to τ-leptons and muons, R(τ/μ)=B(W→τντ)/B(W→μνμ) . . . is found to be 0.992±0.013[±0.007(stat)±0.011(syst)] and is in agreement with the hypothesis of universal lepton couplings as postulated in the Standard Model. This is the most precise measurement of this ratio, and the only such measurement from the Large Hadron Collider, to date).

* B Meson Decay Anomalies Getting Smaller With More Data (September 9, 2019) (Belle collaboration announced their new measurements on RD and RD∗ which are in agreement with their Standard Model (SM) predictions within 1.2σ. After inclusion of these measurements, the discrepancy between the world averages and the SM predictions of RD-RD∗ comes down from 4.1σ to 3.1σ)).).. . . . . . The higher values of RD and RD∗ are assumed to occur due to new physics (NP) contribution to the b → c τ ν¯ decay. New physics in b → c {e/µ} ν¯ is ruled out by other data.)

* How Not To Write An Abstract (June 24, 2019) (In summary, BESIII has . . . [a] LFU test at a very high precision (1.5% for Cabbibo favoured decays and 4% for Cabbibo suppressed decays) has been performed while no evidence of violation is found. Search for charm semileptonic decays to scalar mesons were performed at BESIII and the current results are in favor of the SU(3) nonet tetraquark description of a0(980), f0(500) and f0(980). Moreover, our sensitivity to rare charm leptonic and semileptonic decays has been improved by several magnitudes with the huge statistics at LHCb, and strong constraints have been set for various new physics models with recent measurements.)

* Lepton Flavor Violations In B Meson Decays Still Seen In Experimental Evidence (updated March 27, 2019) (Following the updated measurement of the lepton flavour universality (LFU) ratio R_K in B -> Kll decays by LHCb, as well as a number of further measurements, e.g. R_K* by Belle and B_s -> mu mu by ATLAS, we analyse the global status of new physics in b -> s transitions in the weak effective theory at the b-quark scale, in the Standard Model effective theory at the electroweak scale, and in simplified models of new physics. We find that the data continues to strongly prefer a solution with new physics in semi-leptonic Wilson coefficients . . . After the completion of this work, new preliminary results on RD and RD∗ using semileptonic tags were presented by Belle [109]. The new results, that are slightly closer to the SM predictions compared to an average of previous Belle results, are not yet included in our analysis).

* A Review Of Lepton Universality In B Meson Decays (September 18, 2018) (A possible violation of LU is hinted at in two different classes of semileptonic b-quark decays. The measurements are obtained from experiments at the B-factories (BaBar, Belle and soon Belle-II) as well as at the LHC (LHCb). For these processes the SM predictions can be computed using an effective Hamiltonian approach that separates short and long-distance contributions, and require non-perturbative inputs (e.g. form factors) obtained through diverse theoretical methods. Tensions at the level of 4–5 σ are observed in b→ clν [charm quark, negative charged lepton, corresponding anti-neutrino] decays, which are mediated at tree level through a W± boson in the SM, when the branching ratios of decays with l = τ and l = e, µ are compared. Deviations at the level of 3–4 σ are also present in b→ sll [strange quark, lepton and anti-lepton] decays, which are mediated through a loop in the SM, when comparing the branching ratios for l = e and l = µ.)

* B Quark Decays Still Anomalous (June 25, 2018) (it seems that the probability of getting a muon pair from particular interactions is about three-quarters of the probability of what the Standard Model says it should be.)

* Maybe b quark decays aren't weird after all (January 18, 2018) (Many new physics models that explain the intriguing anomalies in the b-quark flavour sector are severely constrained by Bs-mixing, for which the Standard Model prediction and experiment agreed well until recently. New non-perturbative calculations point, however, in the direction of a small discrepancy in this observable. Using up-to-date inputs to determine ΔMSMs, we find a severe reduction of the allowed parameter space of Z′ and leptoquark models explaining the B-anomalies. Remarkably, in the former case the upper bound on the Z′ mass approaches dangerously close to the energy scales already probed by the LHC.; B decays proceeding via b→cℓν transitions with ℓ=e or μ are tree-level processes in the Standard Model. They are used to measure the CKM element Vcb, as such forming an important ingredient in the determination of e.g. the unitarity triangle; hence the question to which extend they can be affected by new physics contributions is important, specifically given the long-standing tension between Vcb determinations from inclusive and exclusive decays and the significant hints for lepton flavour universality violation in b→cτν and b→sℓℓ decays. We perform a comprehensive model-independent analysis of new physics in b→cℓν, considering vector, scalar, and tensor interactions, including for the first time differential distributions of B→D∗ℓν angular observables. We show that these are valuable in constraining non-standard interactions. Specifically, the zero-recoil endpoint of the B→Dℓν spectrum is extremely sensitive to scalar currents, while the maximum-recoil endpoint of the B→D∗ℓν spectrum with transversely polarized D∗ is extremely sensitive to tensor currents. We also quantify the room for e-μ universality violation in b→cℓν transitions, predicted by some models suggested to solve the b→cτν anomalies.)

* Some B Meson Decay Anomalies Disappear In Run-2 Data (May 10, 2017) (After Run 1 of the LHC, global fits to b→sℓℓ observables show a deviation from the Standard Model (SM) with a significance of ∼ 4 standard devations. An example of a b→sℓℓ process is the decay of a B0s meson into two muons (B0s→μ+μ−). The latest analysis of B0(s)→μ+μ− decays by LHCb with Run 1 and Run 2 data is presented. The B0s→μ+μ− decay is observed for the first time by a single experiment. In addition, the first measurement of the B0s→μ+μ−effective lifetime is performed. No significant excess of B0→μ+μ− decays is observed. All results are consistent with the SM and constrain New Physics in b→sℓℓ processes.)

* Experimental Confirmation Of Koide's Rule And Lepton Universality In Tau Leptons (September 28, 2017) (The experiment confirmed this prediction of the Standard Model comparing a ratio of two experimental results that should be 1.0 if lepton universality is correct. The measured value of that ratio is: 1.0016 ± 0.0042. Thus, the experimental outcome was again less than half of a standard deviation due to experimental uncertainty from the predicted value and lepton universality is confirmed.)

* Mixed Results In A Test Of Lepton Universality (December 17, 2016) (in semilepton B meson decays to kaons a new experimental result finds a local 2.6 sigma deviation from the Standard Model expectation of charged lepton universality in particular kinds of B meson decays. But, after considering look elsewhere effects, it is consistent with the Standard Model.)

* Another Experimental Confirmation of Lepton Universality (December 5, 2016) (semileptonic B decays to τ leptons (semitauonic decays) . . . for the decay process B¯ → D(∗) τ −ν¯τ. The decays B¯ → D(∗) τ −ν¯τ have been studied by the Belle, BaBar and LHCb experiments. Most of these studies have measured ratios of branching fractions, defined as R(D(∗) ) = B(B¯ → D(∗) τ −ν¯τ )/B(B¯ → D(∗) l−ν¯l−). The denominator is the average of l− = e−, µ− for Belle and BaBar, and l− = µ− for LHCb. The ratio cancels numerous uncertainties common to the numerator and the denominator. The current averages of the three experiments are R(D) = 0.397 ± 0.040 ± 0.028 and R(D∗ ) = 0.316 ± 0.016 ± 0.010, which are 1.9 and 3.3 standard deviations (σ) away from the SM predictions of R(D) = 0.299 ± 0.011 or 0.300 ± 0.008 and R(D∗ ) = 0.252±0.003, respectively. The overall discrepancy with the SM is about 4σ. . . .Our study includes an R(D∗) measurement independent of the previous studies, in which leptonic τ decays have been used.)

* Tau Decays Still Match Standard Model Expectations (September 8, 2015) (While other experiments have shown what could be noise, or could be weak evidence of violations of lepton universality or lepton flavor violations, a new LHCb experiment paper finds no violations of lepton universality, no lepton flavor violations, no lepton number violations and no baryon number violations in tau lepton decays. All of the tau lepton decays observed are in accord with the Standard Model expectation and the bounds on lepton or baryon number violations derived are very strict. . . . A study of pion decays released this past June likewise confirms lepton universality to high precision. There has been weak evidence of lepton universality violations and lepton flavor non-conservation in B meson decays and Higgs boson decays, but those could just be statistical flukes or due to systemic error. It is not easy to imagine why lepton universality might be violated with B meson decays, but not pion or tau lepton decays.)

* New Experiment Tends To Confirm Electron-Muon Universality (June 22, 2015) (a new experimental results, looking at the decays of positively charged pions to electrons and muons respectively, confirms Standard Model prediction of muon-electron universality to within 0.1%.)

* Interesting LHCP 2013 (Barcelona) Higgs Conference Abstracts (June 9, 2014) (Present measurements of b->c tau nu and b->u tau nu transitions differ from the standard model predictions of lepton flavor universality by almost 4 sigma. . . . Some of the strongest evidence for beyond the Standard Model behavior involves Lepton flavor violations where decays to electrons are about 25% more common than decays to muons, contrary to a Standard Model expectation of equal frequencies. This is a promising place to look for new physics. Motl discusses the results in a post here.)

Thursday, May 26, 2022

Yes, There Were Lost Civilizations In the Amazon

For a long time, the conventional wisdom was that the Amazon was inhabited by small tribes of hunter-gatherers from the time that the first modern humans arrived in the region, ca. 14,000 years ago until well into the post-Columbian period. But, increasingly, there is evidence of farming and moderate density sedentary settlements there that existed, at least on and off, for many thousands of years that collapsed with European disease and colonial impacts.

The one discussed below was one of at least several such civilizations in the Amazon. Another was contemporaneous in the Brazilian Amazon (see also here and here). A much earlier Amazonian farming civilization is discussed here. See also here (for ancient rice domestication and farming in South America).

Science News explains the new find in the Amazon made possible with aerial lidar surveys (see also the press release here): 

A massive urban landscape that contained interconnected campsites, villages, towns and monumental centers thrived in the Amazon rainforest more than 600 years ago. In what is now Bolivia, members of the Casarabe culture built an urban system that included straight, raised causeways running for several kilometers, canals and reservoirs. . . . 
Such low-density urban sprawl from pre-Columbian times was previously unknown in the Amazon or anywhere else in South America. . . . a substantial Casarabe population spread out in a network of small to medium-sized settlements that incorporated plenty of open space for farming. . . . 
Earlier excavations indicated that Casarabe maize farmers, fishers and hunters inhabited an area of 4,500 square kilometers. For about a century, researchers have known that Casarabe people fashioned elaborate pottery and constructed large earthen mounds, causeways and ponds. But these finds were located at isolated forest sites that are difficult to excavate, leaving the reasons for mound building and the nature of Casarabe society, which existed from about the year 500 to 1400, a mystery. . . . it is obvious that the mounds are platforms and pyramids standing on artificial terraces at the center of well-planned settlements. . . . 
These sites raise questions about whether only places with centralized governments that ruled over people who were packed into neighborhoods on narrow streets, such as 6,000-year-old Mesopotamian metropolises, can be defined as cities.

Some past urban settlements organized around crop growing spanned up to 1,000 square kilometers or more in tropical regions. These include locales such as Southeast Asia’s Greater Angkor roughly 700 to 800 years ago and interconnected Maya sites in Central America dating to at least 2,300 years ago. . . . Clusters of interconnected Casarabe settlements ranged in area from 100 square kilometers to more than 500 square kilometers. Spread-out settlements of comparable area include 6,000-year-old sites from Eastern Europe’s Trypillia culture. . . . 

Casarabe culture’s urban sprawl must have encompassed a considerable number of people in the centuries before the Spanish arrived and Indigenous population numbers plummeted, largely due to diseases, forced labor and slavery.
The paper and its abstract are as follows:
Archaeological remains of agrarian-based, low-density urbananism have been reported to exist beneath the tropical forests of Southeast Asia, Sri Lanka and Central America. However, beyond some large interconnected settlements in southern Amazonia, there has been no such evidence for pre-Hispanic Amazonia. 
Here we present lidar data of sites belonging to the Casarabe culture (around AD 500 to AD 1400) in the Llanos de Mojos savannah–forest mosaic, southwest Amazonia, revealing the presence of two remarkably large sites (147 ha and 315 ha) in a dense four-tiered settlement system. 
The Casarabe culture area, as far as known today, spans approximately 4,500 km^2, with one of the large settlement sites controlling an area of approximately 500 km^2. The civic-ceremonial architecture of these large settlement sites includes stepped platforms, on top of which lie U-shaped structures, rectangular platform mounds and conical pyramids (which are up to 22 m tall). The large settlement sites are surrounded by ranked concentric polygonal banks and represent central nodes that are connected to lower-ranked sites by straight, raised causeways that stretch over several kilometres. Massive water-management infrastructure, composed of canals and reservoirs, complete the settlement system in an anthropogenically modified landscape. 
Our results indicate that the Casarabe-culture settlement pattern represents a type of tropical low-density urbanism that has not previously been described in Amazonia.
H. Prümers et al. Lidar reveals pre-Hispanic low-density urbanism in the Bolivian Amazon. Nature. Published May 25, 2022. doi: 10.1038/s41586-022-04780-4.

Wednesday, May 18, 2022

Denisovan Remains Found In Laos

Denisovans were an archaic hominin species that was a sister to Neanderthals and admixed with modern humans in Southeast Asia. Previously, Denisovan remains were found in Siberia and Tibet. 

Now, the tooth of a Denisovan female which is at least 131,000 years old, was found in Cobra Cave in Laos. The species identification and gender were based upon morphology and tooth enamel proteins, rather than ancient DNA per se. The presence of Denisovan's in the region was expected based upon Denisovan DNA in Asians and Australians and Papuans. The New York Times discusses the find further.

The paper and its abstract are as follows:

The Pleistocene presence of the genus Homo in continental Southeast Asia is primarily evidenced by a sparse stone tool record and rare human remains. Here we report a Middle Pleistocene hominin specimen from Laos, with the discovery of a molar from the Tam Ngu Hao 2 (Cobra Cave) limestone cave in the Annamite Mountains. The age of the fossil-bearing breccia ranges between 164–131 kyr, based on the Bayesian modelling of luminescence dating of the sedimentary matrix from which it was recovered, U-series dating of an overlying flowstone, and U-series–ESR dating of associated faunal teeth. Analyses of the internal structure of the molar in tandem with palaeoproteomic analyses of the enamel indicate that the tooth derives from a young, likely female, Homo individual. The close morphological affinities with the Xiahe specimen from China indicate that they belong to the same taxon and that Tam Ngu Hao 2 most likely represents a Denisovan.

Fabrice Demeter, et al.,"A Middle Pleistocene Denisovan molar from the Annamite Chain of northern Laos" 13 Nature Communications volume 13, Article number: 2557 (May 17, 2022) (open access).

Tuesday, May 17, 2022

Ancient DNA Insight Into Ashkenazi Jewish Ancestry

Consistent with the paradigm prior to a new preprint, 14th century DNA samples from Ashkenazi Jews show that their ethnogenesis predated this time period and that their Eastern European ancestry was more recent, and hence, more variable in amount, at that time.

Image from here.

The Paper
We report genome-wide data for 33 Ashkenazi Jews (AJ), dated to the 14th century, following a salvage excavation at the medieval Jewish cemetery of Erfurt, Germany. 
The Erfurt individuals are genetically similar to modern AJ and have substantial Southern European ancestry, but they show more variability in Eastern European-related ancestry than modern AJ. A third of the Erfurt individuals carried the same nearly-AJ-specific mitochondrial haplogroup and eight carried pathogenic variants known to affect AJ today
These observations, together with high levels of runs of homozygosity, suggest that the Erfurt community had already experienced the major reduction in size that affected modern AJ. However, the Erfurt bottleneck was more severe, implying substructure in medieval AJ. Together, our results suggest that the AJ founder event and the acquisition of the main sources of ancestry pre-dated the 14th century and highlight late medieval genetic heterogeneity no longer present in modern AJ.
Shaman Waldman, et al., "Genome-wide data from medieval German Jews show that the Ashkenazi founder event pre-dated the 14th century" BioRxiv (May 16, 2022) (Supplementary Material here).

Where Did Ashkenazi Jews Get East Asian Ancestry?

Davidski at Eurogenes, however, pulls some additional insights from the paper. He notes that:
The fact that the authors are using modern-day Russians to model Eastern European-related ancestry in these Ashkenazi ancients from Central Europe tells me that they're somewhat confused.

They did this because some of the Jews harbor significant Slavic ancestry and minor but perceptible East Asian ancestry, and Russians are Slavs who carry some Siberian ancestry, which is closely related to East Asian ancestry. Thus, broadly speaking, in terms of the right mix of DNA, Russians do the job.

However, as per the preprint, based on historical data, these Jews probably sourced their Slavic ancestry from Bohemia, Moravia and/or Silesia, and the Slavic speakers in these regions carry very little, if any, East Asian or Siberian ancestry. I'm sure the authors can verify this claim without too much trouble.

Ergo, it's likely that the Erfurt Jews received their Slavic and East Asian admixtures from different sources, and possibly at different times.

Thus, a new open question in historical genetics and Jewish ethnogenesis is how in some time period prior to the 14th century, Ashkenazi Jews got their small proportion East Asian ancestry.

I would differ with the statement that "Jews probably sourced their Slavic ancestry from Bohemia, Moravia and/or Silesia" which is stronger than the evidence. The Jews with elevated Eastern European ancestry who migrated into this German community in the late 1300s were from these places, but there is very thin evidence regarding the source of the baseline of Eastern European ancestry in this community among non-recent migrants.

Also, data from the Human Origins database (see, e.g. pdf page 16), which doesn't have a Polish sample, shows that Ukrainian, Belorussian, Lithuanian and Estonian gene pools, adjacent or near Poland, have a significant affinity to Han Chinese-like East Asian ancestry (f4 test 0.004 to 0.0045) albeit less than that of Russians, Finns and Mordavians in Russia (f4 test about 0.0052) and the Chuvash in Russian (f4 test about 0.0072) and Finnish Saami (f4 test about 0.008) and also closely tracks ANE ancestry.

A source elsewhere in Eastern Europe is still a possibility, as is a source in Southern Italy, perhaps derived from "barbarian" invaders during the later days of the Roman Empire and the early Middle Ages prior to the Ashkenazi Jewish bottleneck.

Ashkenazi Jewish History 

Wikipedia provides the following summary of the mainstream view of Ashkenazi Jewish history as follows:

A substantial Jewish population emerged in northern Gaul by the Middle Ages, but Jewish communities existed in 465 CE in Brittany, in 524 CE in Valence, and in 533 CE in Orléans. Throughout this period and into the early Middle Ages, some Jews assimilated into the dominant Greek and Latin cultures, mostly through conversion to Christianity. King Dagobert I of the Franks expelled the Jews from his Merovingian kingdom in 629. Jews in former Roman territories faced new challenges as harsher anti-Jewish Church rulings were enforced.

Charlemagne's expansion of the Frankish empire around 800, including northern Italy and Rome, brought on a brief period of stability and unity in Francia. This created opportunities for Jewish merchants to settle again north of the Alps. Charlemagne granted the Jews freedoms similar to those once enjoyed under the Roman Empire. In addition, Jews from southern Italy, fleeing religious persecution, began to move into Central Europe. 
Returning to Frankish lands, many Jewish merchants took up occupations in finance and commerce, including money lending, or usury. (Church legislation banned Christians from lending money in exchange for interest.) 
From Charlemagne's time to the present, Jewish life in northern Europe is well documented. By the 11th century, when Rashi of Troyes wrote his commentaries, Jews in what came to be known as "Ashkenaz" were known for their halakhic learning, and Talmudic studies. They were criticized by Sephardim and other Jewish scholars in Islamic lands for their lack of expertise in Jewish jurisprudence and general ignorance of Hebrew linguistics and literature. 
Yiddish emerged as a result of Judeo-Latin language contact with various High German vernaculars in the medieval period. It is a Germanic language written in Hebrew letters, and heavily influenced by Hebrew and Aramaic, with some elements of Romance and later Slavic languages.

Historical records show evidence of Jewish communities north of the Alps and Pyrenees as early as the 8th and 9th centuries.
By the 11th century, Jewish settlers moving from southern European and Middle Eastern centers (such as Babylonian Jews and Persian Jews) and Maghrebi Jewish traders from North Africa who had contacts with their Ashkenazi brethren and had visited each other from time to time in each's domain appear to have begun to settle in the north, especially along the Rhine, often in response to new economic opportunities and at the invitation of local Christian rulers. Thus [ed. in the 11th century] Baldwin V, Count of Flanders, invited Jacob ben Yekutiel and his fellow Jews to settle in his lands; and soon after the Norman conquest of England, William the Conqueror likewise extended a welcome to continental Jews to take up residence there. Bishop Rüdiger Huzmann [ed. in the 11th century] called on the Jews of Mainz to relocate to Speyer. In all of these decisions, the idea that Jews had the know-how and capacity to jump-start the economy, improve revenues, and enlarge trade seems to have played a prominent role. Typically, Jews relocated close to the markets and churches in town centres, where, though they came under the authority of both royal and ecclesiastical powers, they were accorded administrative autonomy. In the 11th century, both Rabbinic Judaism and the culture of the Babylonian Talmud that underlies it became established in southern Italy and then spread north to Ashkenaz.
Numerous massacres of Jews occurred throughout Europe during the Christian Crusades. Inspired by the preaching of a First Crusade, crusader mobs in France and Germany perpetrated the Rhineland massacres of 1096, devastating Jewish communities along the Rhine River, including the SHuM cities of Speyer, Worms, and Mainz. The cluster of cities contain the earliest Jewish settlements north of the Alps, and played a major role in the formation of Ashkenazi Jewish religious tradition, along with Troyes and Sens in France. Nonetheless, Jewish life in Germany persisted, while some Ashkenazi Jews joined Sephardic Jewry in Spain. 
Expulsions from England (1290), France (1394), and parts of Germany (15th century), gradually pushed Ashkenazi Jewry eastward, to Poland (10th century), Lithuania (10th century), and Russia (12th century). 
Over this period of several hundred years, some have suggested, Jewish economic activity was focused on trade, business management, and financial services, due to several presumed factors: Christian European prohibitions restricting certain activities by Jews, preventing certain financial activities (such as "usurious" loans) between Christians, high rates of literacy, near-universal male education, and ability of merchants to rely upon and trust family members living in different regions and countries.

Text Relevant To East Asian Ancestry In Jews

The text that Davidski is referencing to in the paper notes, in part, that:

Ashkenazi Jews (AJ) emerged as a distinctive ethno-religious cultural group in the Rhineland and Northern France in the 10th century. The AJ population since expanded substantially, both geographically, first to Eastern Europe and recently beyond Europe, and in number, reaching about 10 million today. The AJ population today harbors dozens of recessive pathogenic variants that occur at higher frequency than in any other population, implying that AJ descend from a small set of ancestral founders. This Ashkenazi “founder event” is also manifested by four mitochondrial haplogroups carried by as many as 40% of AJ. More recently, studies found high rates of identical-by-descent (IBD) sharing in AJ, that is, near-identical long haplotypes present in unrelated individuals, a hallmark of founder populations. Quantitative modeling suggested that AJ experienced a sharp reduction in size (a “bottleneck)” in the late Middle Ages and that the (effective) number of founders was in the hundreds

The origins of early Ashkenazi Jews, as well as the history of admixture events that have shaped their gene pool, are subject to debate. In historical research, there are two main hypotheses regarding the identity of the early AJ: either Jews who lived at the Germanic frontiers since late Roman times, or medieval migrants from the established Jewish communities of the Italian peninsula (SI 1). Genetic evidence supports a mixed Middle Eastern (ME) and European (EU) ancestry in AJ. This is based on uniparental markers with origins in either region, as well as autosomal studies showing that AJ have ancestry intermediate between ME and EU populations. Recent modeling suggested that most of the European ancestry in AJ is consistent with Southern European-related sources, and estimated the total proportion of European ancestry in AJ as 50-70%. While the Ashkenazi population is overall highly genetically homogeneous, there are subtle average differences in ancestry between AJ with origins in Eastern vs Western Europe. . . . 

The Erfurt Jewish community existed between the late 11th century to 1454, with a short gap following a 1349 massacre. We report 33 genomes from individuals whose skeletons were extracted in a salvage excavation. Our results demonstrate that Erfurt Ashkenazi Jews (EAJ) are genetically highly similar to modern Ashkenazi Jews (MAJ), implying little gene flow into AJ gene since the 14th century. Further analysis demonstrated that EAJ were more genetically heterogeneous than MAJ, with multidisciplinary evidence supporting the presence of two sub-groups, one of which had higher Eastern European affinity compared to MAJ. The EAJ population shows strong evidence of a recent sharp bottleneck, based on the distribution of mitochondrial haplogroups, high levels of runs of homozygosity, and the presence of AJenriched alleles, including pathogenic variants. 
. . .  
The first Jewish community of Erfurt (pre-1349) was the oldest in Thuringia, and its cemetery also served nearby towns. During the 1349 pogrom, most Jews of Erfurt and nearby communities were murdered or expelled. Jews returned to Erfurt around 1354 to form the second community, which was one of the largest in Germany. The individuals we studied were buried in the south-western part of the medieval Jewish cemetery of Erfurt, which underwent salvage excavations in 2013. 
. . .

An ADMIXTURE analysis demonstrated that EAJ are genetically similar to MAJ, but with higher variance, consistent with the PCA findings. Individuals classified based on the PCA as ErfurtEU had higher EU-related ancestry. The results also revealed a small but consistent East-Asian-related component, especially in the Erfurt-EU group (means of 2.7% and 1.6% in Erfurt-EU and all EAJ, as previously observed. This suggests either a minor gene flow event from East-Asia, as previously attested by mtDNA, or gene flow from Eastern European populations, who carry (at least today) a minor component of this ancestry. 
. . .

[A]ny hypothetical admixture event between AJ and Eastern Europeans in the past ≈20 generations must have been limited to replacing at most 2-4% of the total AJ gene pool (this would correspond to at most 0.2% replacement per generation). 
. . . 

We modeled EAJ as a mixture of the following modern sources: Southern European (South-Italians or North-Italians), Middle Eastern (Druze, Egyptians, Bedouins, Palestinians, Lebanese, Jordanians, or Syrians), and Eastern European (Russians). To avoid bias due to ancient DNA damage, we only used transversions. 
Most of the models with a South-Italian source were plausible (P-value >0.05; Table S7), which would be consistent with historical models pointing to the Italian peninsula as the source for the AJ population. The mean admixture proportions (over all of our plausible models; Table S7) were 68% South-EU, 17% ME, and 15% East-EU (Figure 2A). However, the direct contribution from the Middle East is difficult to estimate given historical ME admixture in Italy [49] (see the Discussion). Indeed, a model with North-Italians as a source (which was only plausible with a Lebanese source; Table S7) had ancestry proportions 44% South-EU, 44% ME, and 12% East-EU (Figure 2A). 
We validated that the results did not qualitatively change when we tested the same models using all available SNPs, a different outgroup population, or fewer SNPs (Table S7, Figure S16). Models with a Western European source (Germans) instead of Russians were not plausible (Table S7), and there was no support for an East-EU-independent contribution of East-Asians (Methods Section 4). Interestingly, Erfurt-ME could be modeled based on Turkish (Sephardi) Jews (97% admixture proportion) and Germans (3%) as sources. 

Figure S12  

Figure S12 shows East Asian ancestry (orange in K=7 charts, yellow in K=8 charts) in various populations. It is present at low levels in modern Ashkenazi Jews, in Russians, and in Erfurt-EU (one of two Eufurt subpopulations notable for higher levels of European ancestry than the other subpopulation Erfurt-ME). This component is absent in Italian, Lebanese (except one individual) and German populations. It is found in some Caucasus and Eastern European samples in the chart as well.

The Erfurt-EU population has a strong affinity of Russia and other places in Eastern Europe indicated by a low z-score, while the Erfurt-ME population has a weak connection to these populations as indicated by a high z-score. The affinity to Russia is strongest, but not that much stronger than Ukraine, Belorussia, and Poland.
This chart shows that the Erfurt-ME population shows a much strong affinity to the populations of the Levant and Arabia than the Erfurt-EU population, and a much weaker affinity to Russia, the Baltic states for which samples are available, and to a slightly lesser extent Poland and Ukraine.

 Figure S16

The Middle Eastern proxy used doesn't impact the ancestry predictions much. The Erfurt-EU population has much more ancestry described as Russian for the Eastern European proxy used in an effort to model them as a mix of Lebanese, Russian and Northern Italian (which unlike Southern Italian lacks Middle Eastern admixture in non-Jews), than Erfurt-ME does, with many Erfurt-ME subpopulation members having no discernible East European ancestry. Thus, East Asian ancestry is not found in Erfurt individuals that lack East European ancestry, ruling out a source in the Italian source population for Ashkenazi Jews, or in the Western European intermediate homeland of Ashkenazi Jews (where there isn't any East Asian ancestry). So, the East Asian ancestry appears to be mediated through East Asian admixture in Eastern Europeans.

Table S7

The two most left charts in Table S7 examine whether Northern Italy or Southern Italy are a better fit for a source population for Erfurt individuals, when in combination with with one of eight possible Middle Eastern populations and a Russian European population. The first, third and fourth looking only at SNPs available in the ancient DNA samples (which have missing data) and the second looks at all SNPS. The third uses the same populations as the first two, but a different outgroup. The far right chart in Table S7 use a German European population rather than a Russian one. A high p-score indicates that this is a more likely possibility, while a low p-score indicates that the combination of source populations is disfavored.

The Lebanese-Southern Italian-Russian combination is favored with or without all SNPs and regardless of outgroup over the alternatives, and the Lebanese-Southern Italian combination is the most favored of the German combinations. The fact that these source populations are preferred favors some narratives of Ashkenazi origins and ethnogenesis over others, although it isn't completely definitive.

Southern European source populations

Across the board, a Southern Italian source for Erfurt Jews (who are basically ancestral to modern Ashkenazi Jews except that their Eastern European/East Asian ancestral component is not yet as homogenous) is strongly preferred over a Northern Italian source, even though a Northern Italian source isn't entirely ruled out in the case of a Lebanese Middle Eastern population and a Russian European population. 

The preference for a Southern Italian source over a Northern Italian source is supported by the historical record.

Middle Eastern source populations

Across the board, a Lebanese Middle Eastern population is favored with Syrian and Bedouin B as runners up, and Druze, Egyptian, Bedouin A, Palestinian and Jordanian comparatively disfavored.  

The data sets which are part of the Human Origins dataset are described here, which notes that Bedouin B has significant North African admixture, with the distinction between Bedouin A and Bedouin B apparently first made in this paper based upon cluster analysis of the paper's Negev Bedouin samples (from the Negev desert in Southern Israel): 
Investigation of surnames identified cluster A as one of the oldest, well established clans in the Negev. On the other hand, cluster B is composed of related tribes, probably from a common founder, that migrated from Gaza to the Negev around 300 years ago. Thus, it seems that clan B, as opposed to clan A, allows interactions with tribes outside the clan.
This result supports the Biblical tradition that puts the ultimate source of people who became Jews in Lebanon, although the Bible states that after Egyptian exile they end up ruling areas that, prior to the 20th century, were inhabited by Palestinians to whom Ashkenazi Jews have a much weaker affinity. 

This data suggests the possibility that Jews in this Iron Age Jewish state had a weak demographic impact on the region that they ruled (and in Egypt where they apparently remained endogamous if indeed their people spend time there as the Book of Exodus claims), and may have been a demographically distinct elite ruling caste that largely relocated away from the region while the people they ruled stayed, upon and before the destruction of the Second Temple in 70 CE and the resulting Jewish diaspora.

Non-Southern European source population

In all cases, a German source population is disfavored, despite the fact that the earliest Ashkenazi Jews were in France and Germany and elsewhere in Western Europe, such as in Flanders Flanders, where they were welcomed until the First Crusade (although these Jews were apparently were strongly endogamous at this time) and despite the fact that Yiddish is a mostly Germanic rather than being a Slavic language. 

Instead, non-Southern Italian ancestry in Ashkenazi Jews is Eastern European rather than Western European, a place where Ashkenazi Jews had started to migrate in the 10th to 12th centuries (both before and after the 11th century period in which Western European leaders were welcoming them) which aligns with the time period of the Ashkenazi population bottleneck. 

The Erfurt-EU subpopulation, which had admixed with Eastern Europeans (mostly by marrying local women) sometime after the 10th century, and then joined the Erfurt community in the late 14th century apparently represented a back migration to the German west. The combined population was quite typical of the population that eventually expanded to form the modern Jews right at the cusp of its post-bottleneck expansion.

It could also be the case that Ashkenazi Jews in Western Europe were not much more endogamous than their Eastern European co-ethnics, but that Ashkenazi Jews with Western European admixture mostly were either killed in the Rhineland massacres of 1096 and subsequent pogroms, or migrated to Moorish Spain to join the Sephardic Jewish population there, with few Western European Ashkenazi Jews actually migrating to Eastern Europe after the 11th-12th centuries. This would have left the lion's share of the surviving Jewish population that did not join the Sephardic Jews in Spain in Eastern Europe. 

Expulsions from England (1290), France (1394), and parts of Germany (15th century) may have had little demographic impact on Jews in Central and Eastern Europe, because most Jews in the areas of Western Europe from which they were ultimately expelled had taken the hint that they were not wanted after numerous pogroms much earlier than these expulsions, or fled to Spain rather than Central and Eastern Europe when they ultimately were expelled.

Multiple lines of evidence suggest that the EAJ population had already experienced a “bottleneck” shared with MAJ: the high frequency of Ashkenazi founder mtDNA haplogroups; and the presence of Ashkenazi-specific pathogenic variants, other AJ-enriched alleles, and long runs of homozygosity. Carriers of the K1a1b1a mtDNA founder haplogroup seem to have descended from an even smaller set of founders. In agreement with previous studies, we date the onset of the expansion in AJ population size to about 20-25 generations ago

Our ancient DNA data allowed us to identify patterns in the history of AJ that would not have been otherwise detectable from modern genetic variation. Specifically, our genetic results suggest that the AJ population was structured during the Middle Ages. Within Erfurt, one group of individuals had an enrichment of Eastern European-related ancestry, while the other had ancestry very close to that of MAJ of Western European origin and modern Sephardi Jews. The two groups also had significantly different levels of enamel δ18O. Medieval AJ may have been structured even beyond Erfurt, based on our inferred demographic model. In contrast, present-day AJ is a remarkably homogeneous population. This suggests that even though the overall sources of ancestry remained very similar between medieval and modern AJ, endogamy and within-AJ mixture since medieval times have contributed to the homogenization of the AJ gene pool. 

We found that a plausible model for the ancestral sources of EAJ include groups related to people in South-Italy (about 70%, who themselves plausibly might harbor Middle East-related ancestry), the Middle East (about 15%), and Eastern Europe (about 15%). Models with North-Italians as a source were also plausible, with an ancestry proportion of about 45% to each of North-Italians and Middle Easterners. The ancestry proportion estimates using North-Italians are closer to previous estimates using modern SNP and sequencing data, but a North-Italian source was less favored by qpAdm. While these results could be consistent with a model where the Middle Eastern ancestry in AJ has not been as large as previously thought, complicating the picture are (i) our inability to identify a satisfactory model for modern AJ; (ii) the historically variable levels of Middle Eastern ancestry in Italy; and (iii) the possible problems when modeling an ancient population with modern sources. 
. . . 
Therefore, the direct contribution of ME sources to AJ ancestry may be higher than estimated. Either way, the substantial Southern European ancestry we inferred adds weight to the evidence that early AJ descended, at least partly, from Italian Jews. The estimate of about 15% Eastern European-related ancestry is consistent with a previous study. 
The identification of this source as Eastern European relies on the f4 results and the qpAdm models; however, this ancestry might derive from a broad area across Central or Eastern Europe, which may accord with recorded migration into Erfurt from Bohemia, Moravia, and Silesia. For an additional discussion on the historical interpretation of these results, see SI 2. 
. . .
4.3. qpAdm

Here too, we used the option "allsnps:YES". The reference populations (right populations) for the qpAdm analyses were: Mbuti, Ami, Basque, Biaka, Bougainville, Chukchi, Eskimo_Naukan, Han, Iranian, Ju_hoan_North, Karitiana, Papuan, Sardinian, She, Ulchi, and Yoruba. Mbuti was used as the outgroup (provided to AdmixTools as the first in the list of reference populations) in all analyses. In robustness tests, we replaced Mbuti with Ami as the outgroup. As in the qpWave analyses, in models with South-Italians we used samples of Sicilian and Italy_South together as one group. In models with ancient Germans, we used samples from [45], not including individuals with elongated skulls or with Southern European ancestry. The ancient Levant (Canaanite) samples included samples from [46] of Bronze-Age Megiddo (Megiddo_MLBA) and the ancient Rome samples included samples from [47] of Late Antiquity (Italy_LA.SG) and Imperial Rome (Italy_Imperial.SG).

For the analyses at the individual level, we used all SNPs, as the coverage of many individuals was already low. To guarantee that using all SNPs did not bias the results, we repeated the analyses at the population level with all SNPs instead of just transversions, and verified that the results remained qualitatively unchanged (Figure S16A). We included first-degree relatives in the individual-level analysis, but omitted the low-coverage individuals (<50k SNPs). For individuals for which the Eastern- EU ancestry proportion was inferred to be negative (Figure 2), we re-ran qpAdm with only Southern-EU and Middle Eastern sources.

To evaluate the potential contribution of East-Asians to the ancestry of EAJ, we tested models where the sources were Lebanese, South-Italians or North-Italians, Russians, and Han Chinese (Han were dropped from the reference populations for this analysis). The models had P-values of 1.9·10^-10 and 1.8·10^-6 with South- and North-Italians, respectively. When the target was Erfurt-EU, the P-values were 7.5·10^-8 and 1.8·10^-4, respectively. Given that the same models for EAJ without Han had plausible P values (Table S7), we conclude that there is no detectable East-Asian ancestry in EAJ.

To quantify the difference in the Eastern European ancestry between MAJ and Erfurt-ME, we used qpAdm to model MAJ as the target of admixture between Erfurt-ME and Russians. We used only transversion SNPs. The model was plausible with P=0.76, with ancestry proportions 87% for Erfurt-ME and 13% for Russians. The model was plausible also with Germans as a source instead of Russians (P=0.74; ancestry proportions 86% for Erfurt-ME and 14% for Germans). To quantify the relation between Erfurt-ME and Sephardi Jews, we used qpAdm to model Erfurt-ME using Turkish Jews and Germans as sources. We again used only transversion SNPs. The model was plausible with P=0.96, with ancestry proportions 97% for Turkish Jews and 3% for Germans. A model with Russians instead of Germans was also plausible (P=0.96; ancestry proportions 96% for Turkish Jews and 4% for Russians). 
. . . 

The information on the origin of Jewish families who migrated to Erfurt comes mainly from records of home rentals from 1354 to 1407. Most persons in these records are mentioned with surnames, which often name the town where they lived before. Information in topographic surnames is limited, as surnames can change, and as the time period when a person has lived in the other town could vary. But in some cases, we have independent sources validating the former place of residence. From 1354, and especially in the 1360s, many families moved to Erfurt whose surnames refer to former places of residence in Bohemia, Moravia, and Silesia. For example, several families came from Breslau (Wrocław) after a pogrom in 1360, some after moving to Wrocław from other Silesian towns. After 1400, there are no known cases of families migrating into Erfurt from the East. Towns in Silesia (present-day Poland) from where families moved into Erfurt include Bunzlau/Bolesławiec (one family, first mentioned in the records in 1383), Liegnitz/Legnica (two related families in 1360), Löwenberg/Lwówek Śląski (one person whose family was originally from Brno), Breslau/Wrocław (one family in 1355/6, more families after 1360), Striegau/Strzegom (one family in 1366), Schweidnitz/Świdńica (one person in 1389), and Glatz/Kłodzko (one family in 1380). Towns in Bohemia and Moravia (present-day Czech Republic) from where families moved into Erfurt include the neighboring towns Braunau/Broumov and Náchod (two families in 1360 or later, who moved through Wrocław), Prag/Praha (one family in 1366), Pilsen/Plzeň (one family in 1365), Eger/Cheb (one family in 1359), and Brünn/Brno (one family in 1363, with a son-in-law in Vienna). We note that one man moved to Erfurt from Poland in 1327 (i.e., in the first community). . . .

Our results provide new evidence for (although do not definitely prove) the theory of AJ origins in Italy, given the good fit of qpAdm models that had Italy as a source, particularly Southern Italy. Southern Italy is one of the very few places in Europe where there is evidence for Jewish demographic and cultural continuity from the late Roman into the early Medieval period and beyond. During this timeframe, the Jewish communities of Southern Italy were at the crossroads of Jewish Mediterranean life. They were in direct contact with the Jewish communities of Byzantine and early Muslim Palestine from whom they received liturgical traditions that they transmitted into Europe and that later turned up in the AJ prayer book. They were also in touch with Jewish communities elsewhere in the Eastern Mediterranean by virtue of the fact that Southern Italy was part of the Byzantine Empire into the late 11th century. 

All the evidence currently available indicates that during the Roman and early Medieval periods Jews were highly integrated in Southern Italy. There is historical evidence that there was at least some gene flow between Jews and non-Jews in Southern Italy, because, in the late Roman and early Medieval periods, imperial and ecclesiastical authorities tried to prevent the practice of intermarriage between Jews and Christians, as well as the phenomenon of conversion of non-Jews to Judaism. When, in due course, highly accomplished and connected Jews from Southern Italy started moving north, they were joined by others from central and northern Italy. For example, the Kalonymus family—a Jewish family from Rome, but with roots in Southern Italy—is known to have had major impact on AJ intellectual life in 10th-century Mainz and Speyer. This was the multilayered migratory legacy that may be reflected in the Southern European genetic ancestry we observed in our models for the genomes of Erfurt Jews. 

Our qpAdm models with a South-Italian source suggested that only a small proportion of EAJ ancestry derived from Middle Eastern populations. This may be interpreted to imply that present-day AJ derive only a small proportion of their ancestry from ancient Judaeans; and if so, most AJ ancestry would owe its origin to European converts. While this is one possible explanation, modern Italians themselves have had much higher proportions of ME admixture since at least European Imperial Roman times and this is especially the case in modern Southern Italy. Thus, an alternative explanation for these observations is that the true ME proportion in AJ is higher than in our fitting model, and that the actual contribution of Italians is not as large as suggested by this analysis. Under this scenario, good qpAdm fits are obtained when using Southern Italians as sources simply because Southern Italians are a modern population that harbors a relatively high proportion of ME ancestry with less impact from additional immigration waves that subsequently affected ME populations and may make modern ME populations relatively poor proxy sources for the ME ancestry in AJ. If this alternative explanation is right, the true ME proportion could be higher than in our fitting models, even higher than the ≈44% for the models using Northern Italians. At present, we believe both types of scenarios are plausible, along with scenarios that involve features of both. Co-analysis of ancient DNA data from the Middle East and the Italian peninsula from the periods of Antiquity and the early Medieval period would make it possible to distinguish them. 

Our genetic data suggest that some Erfurt individuals had elevated levels of European ancestry, likely Eastern European-related. A possible explanation is the documented migration into the second Erfurt Jewish community from Bohemia, Moravia, and Silesia. However, this requires that Jews living in these areas had previously admixed with local non-Jewish populations. Partly supporting this hypothesis may be the presence of names of Slavic origin among medieval Jewish women in Bohemia, particularly as it stands in contrast to naming practices common among Jews in medieval times

Finally, the genetic data suggested a high degree of endogamy in AJ through the last ≈700 years. Historical evidence indicates that the social practice of intermarriage between Jews and Christians was frowned upon by medieval Jewish and Christian authorities. Our genetic results suggest that in practice there was indeed very little gene flow into the Jewish community since this period. 

2.2. Timing demographic events in Ashkenazi history 

Our modeling of shared haplotypes dated the onset of the AJ bottleneck to ≈40-45 generations ago, or approximately about 1000-1200 years ago. This period is well before the time in the late 12th century when the persecution of Jews in the Rhineland became endemic. The appearance of a bottleneck in the early stages of the AJ community formation could reflect the historical evidence that the original AJ settlers comprised only a few dozen families, which were not always welcome and lacked the benefit of a fully developed Jewish community.

Our models dated the onset of expansion of AJ to about 20-25 generations ago, or approximately about 500-700 years ago. This confirms historical research pointing towards a gradual demographic growth within the Jewish community in German lands. The growth is hard to quantify numerically, but, especially from the 1300s onwards, it appears to have been substantial, considering the rapid increase in the number of towns that accommodated Jewish communities. 

In this work, we were unable to reliably estimate the dates of the historical admixture events of AJ in Europe. Our previous work inferred a minor post-bottleneck gene flow event from Eastern Europeans based on a depletion of EU ancestry in IBD segments (as such segments are expected to descend from ancestors who lived during the bottleneck). However, with a model of a prolonged bottleneck (about 20 generations), such a depletion may be observed also if the admixture event had happened late during the bottleneck. Our previous work estimated that admixture between Middle Eastern and European sources in AJ history occurred about 30 generations ago. This date may be associated with the admixture event with Eastern Europeans. Unfortunately, our EAJ genomes did not provide additional insight, as we found that a state-of-the-art tool for admixture time inference (DATES) provided unreliable results under simulations of AJ-like history.

A Case Study In Homogenization of Ancestry

It also highlights a point I've made about Paleoasian ancestry in indigenous population of the Amazon basin, which has a great deal of variation in proportion not only between tribal groups, but within tribal groups, all of which were endogamous with the Amazon basin through the time period of first contact for these tribes which was well after the 1492, and in most cases in the late 19th century or the 20th century.

In Ashkenazi Jews, variability in their proportions of Eastern European and East Asian ancestry vanished in about 700 years (about 24 generations) or less. 

There is simply no way that this variability in ancestry in Amazonian tribal populations could be sustained if it has a 14,000 years old source (in line with the founding population of the Americas), or even a 3,500 year old source (the timing of the Paleo-Eskimo ancestors of the Na-Dene people to the Americas).