Neutrino Oscillation CP Violation Parameter Measured

Ignore the discussion of the matter-antimatter asymmetry of the universe that is thrown in as a journalistic convention anytime that someone tries to explain CP violation observations in news reporting and in the paper itself as a contextualizing preface. Simply put, even with this observation of near maximal CP violation (with immense uncertainty) the magnitude of the CP violating parameters that are observed in the Standard Model just aren't big enough to produce the existing magnitude of matter and antimatter imbalance from a universe that began in matter-antimatter balance. The paper doesn't claim otherwise, it is simply reporting a measurement of an experimental measurement of a Standard Model fundamental constant.

But, a best ever measurement of one of the least precisely known fundamental constants in the Standard Model is still a big deal, and our understanding of neutrinos remains nebulous in a field where so much is definitively established. The pertinent part of the abstract is as follows: 

Until now, the value of δCP has not been substantially constrained by neutrino oscillation experiments. Here we report a measurement using long-baseline neutrino and antineutrino oscillations observed by the T2K experiment that shows a large increase in the neutrino oscillation probability, excluding values of δCP that result in a large increase in the observed antineutrino oscillation probability at three standard deviations (3σ). The 3σ confidence interval for δCP, which is cyclic and repeats every 2π, is [−3.41, −0.03] for the so-called normal mass ordering and [−2.54, −0.32] for the inverted mass ordering.

From here via Science Daily.

The key result from the body text of the paper (in radians) is as follows:

We find the data shows a preference for the normal mass ordering with a posterior probability of 89%, giving a Bayes factor of 8. We find sin2 (θ23) = 0.53+0.03 −0.04 for both mass orderings. Assuming the normal (inverted) mass ordering we find ∆m2 32 = (2.45 ± 0.07) × 10^−3 (∆m2 13 = (2.43±0.07)×10^−3 ) eV^2 /c^4. For δCP our best fit value and 68% (1σ) uncertainties assuming the normal (inverted) mass ordering are −1.89 +0.70 −0.58 (−1.38 +0.48 −0.54), with statistical uncertainty dominating. Our data show a preference for values of δCP which are near maximal CP violation (see Figure 3), while both CP conserving points, δCP = 0 and δCP = π, are ruled out at T2K measurement [8]. Here, we also produce 99.73% (3σ) confidence and credible intervals on δCP . In the normal ordering the interval contains [−3.41,−0.03] (excluding 46% of the range of parameter space), while in the inverted ordering the interval contains [-2.54,-0.32] (excluding 65% of the parameter space). The 99.73% credible interval marginalized across both mass orderings contains [−3.48,0.13] (excluding 42% of the parameter space). The CP-conserving points are not both excluded at the 99.73% level. However, this is the first time closed 99.73% (3σ) intervals on the CP-violating phase δCP have been reported (taking into account both mass orderings) and a large range of values around +π/2 are excluded.

Figure 3 referenced above is this one:

Expressed differently, the best fit value is -0.60π + 0.22π -0.18π. This is consistent at a one standard deviation level with maximal CP violation which is -0.50π. 

This result is in line with previous results from the T2K experiment. In July of 2018 it found that: "The best fit value for a CP violating phase based upon the latest T2K measurements is -0.6π. Maximal CP violation is -0.5π. Zero CP violation (zero or pi) is excluded at more than two sigma significance."

The press release in Science Daily explains that:

To get the new result, the team fired beams of muon neutrinos and antineutrinos from the J-PARC facility at Tokai, Japan, and detected how many electron neutrinos and antineutrinos arrived at the Super-Kamiokande detector 295km away.  

They looked for differences in how the neutrinos or antineutrinos changed flavour, finding neutrinos appear to be much more likely to change than antineutrinos.  

The available data also strongly discount the possibility that neutrinos and antineutrinos are as just likely as each other to change flavour. Dr Dunne said: "What our result shows is that we're more than 95 per cent sure that matter neutrinos and antineutrinos behave differently. This is big news in itself; however we do already know of other particles that have matter-antimatter differences that are too small to explain our matter-dominated universe.

Astronomy observations favor a "normal ordering" for the neutrino masses even more strongly than the 89% preference for this derived from oscillation data alone by the T2K experiment. See, e.g., this March 18, 2020 review paper summarizing constraints on neutrino properties from multiple sources rather than a single experiment which shows a 3.5 standard deviation preference for "normal ordering" over an "inverted ordering" of the neutrino masses.

The newly published paper is: Abe, K., Akutsu, R., Ali, A. et al., "Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations." Nature (April 15, 2020). DOI: 10.1038/s41586-020-2177-0. The open access full text pre-print of this paper was released in October of 2019.

N.B. It is worth noting that the particular numerical values reported above are convention dependent, which means that they depend upon who you define the parameters of the PMNS matrix of which this phase is one of four, although the physical consequences are the same without regard to which parameterization convention is used.

The Reference Frame comments.

Deur Makes Another Prediction About Gravity In Disk Galaxies

Deur's work on gravity (which he considers to be within general relativity but which deviates from how it is conventionally applied in significant ways) is one of the most promising approaches to understanding dark matter and dark energy phenomena. In his latest paper, below, he predicts and confirms as association between disk thickness and the magnitude of dark matter phenomena observed.

Relativistic corrections to the rotation curves of disk galaxies

Alexandre Deur

(Submitted on 10 Apr 2020)

We present a method to investigate the effect of relativistic corrections arising from large masses to the rotation curves of disk galaxies. The method employs a mean-field approximation and gravitational lensing. Applying it to a basic model of disk galaxy, we find that these corrections become important and magnified at large distances. The magnitude of the effect is sufficient to explain the galactic missing mass problem without requiring a significant amount of dark matter. A prediction of the model is that there should be a strong correlation between the inferred galactic dark mass and the galactic disk thickness. We use two independent sets of data to verify this.

Comments:	7 pages, 6 figures
Subjects:	Astrophysics of Galaxies (astro-ph.GA); General Relativity and Quantum Cosmology (gr-qc)
Cite as:	arXiv:2004.05905 [astro-ph.GA]
	(or arXiv:2004.05905v1 [astro-ph.GA] for this version)

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From: Alexandre Deur [view email]

[v1] Fri, 10 Apr 2020 11:23:04 UTC (1,188 KB)

The introduction to the latest paper explains that:

The total mass of a nearby disk galaxy is typically obtained from measuring its rotation curve and deducing from it the mass using Newton’s dynamics. The rationale for this non-relativistic treatment is the small velocity of stars: v/c << 1 sufficiently far from the central galactic black hole. However, the assumption that relativistic corrections are negligible may be questioned on several grounds. Inspecting the post-Newtonian [1] Lagrangian, e.g. for two masses M1 and M2 separated by r, shows non-Newtonian potential terms of the type G^2M1M2(M1+M2)/2r^2 (G is the gravitational constant) that are independent of v, thus not suppressed at small v, and can be non-negligible for large enough M1 and M2. These terms express the non-linear nature of General Relativity (GR), which arises from its field self-interaction: the gravitational field has an energy and hence gravitates too.

Field self-interactions are well-known in particle physics: Quantum Chromodynamics (QCD), the gauge theory of the strong force between quarks, features color-charged fields that self-interact. In fact, GR and QCD have similar Lagrangians, including self-interacting terms, as can be seen when the Einstein-Hilbert Lagrangian of GR is expanded in a polynomial form [2, 3]. Field self-interaction in QCD, which causes quark confinement, exists even for static sources, as shown by the existence of numerous heavy quark bound states (in which v ≈ 0 for quarks) [4] and by classic numerical lattice calculations for v = 0 quarks [5]. This, as well as the correspondence between the respective terms of the GR and QCD Lagrangians, shows that for bodies massive enough a relativistic treatment is required regardless of their velocity. Finally, the measured speeds at the rotation curve plateaus are of several hundreds of km/s, e.g. 300 km/s (or v/c = 0.1%) for NGC 2841. They are similar to that of stars orbiting the central black hole of our galaxy and clearly display the relativistic dynamics expected in the strong regime of GR [6]. 

These arguments suggest that one should investigate the importance of relativistic dynamics in galaxies and how it affects the missing mass problem. From experience with QCD, a non-perturbative approach is required to fully account for field self-interaction, making post-Newtonian formalism inadequate. In Refs. [2, 3], a nonperturbative numerical lattice method was used. Here, we propose to approach the problem with a mean-field technique combined with gravitational lensing. There are several advantages of the approach compared to the lattice method used in [2, 3]: (1) it is an entirely independent method, thereby providing a thorough check of the lattice result; (2) it is not restricted to the static limit of the lattice method and can be applied to systems with complex geometries; (3) it is significantly less CPU-intensive than a lattice calculation, and hence much faster; (4) it clarifies that the effect calculated in Refs. [2, 3] is classical. The lattice approach – an inherently quantum field theory (QFT) technique – used in Refs. [2, 3] may misleadingly suggest that a quantum phenomenon is involved. In fact, the classical nature of the effect is consistent with these lattice calculations being performed in the high-temperature limit in which quantum effects disappear, as discussed in Ref. [3]; (5) the lensing formalism is more familiar to astrophysicists and cosmologists, in contrast to lattice techniques with its QFT underpinning and terminology.

I don't recall if I blogged his 2019 paper on gravity (which was updated in January of this year) or not, so rather than checking, I am cutting and pasting that here as well. Notably, he has two collaborators on the 2019 paper. I have updated my permanent page on Deur's gravitational work to reflect both of these papers.

Significance of Gravitational Nonlinearities on the Dynamics of Disk Galaxies

Alexandre Deur, Corey Sargent, Balša Terzić

(Submitted on 31 Aug 2019 (v1), last revised 11 Jan 2020 (this version, v2))

The discrepancy between the visible mass in galaxies or galaxy clusters, and that inferred from their dynamics is well known. The prevailing solution to this problem is dark matter. Here we show that a different approach, one that conforms to both the current Standard Model of Particle Physics and General Relativity, explains the recently observed tight correlation between the galactic baryonic mass and its observed acceleration. Using direct calculations based on General Relativity's Lagrangian, and parameter-free galactic models, we show that the nonlinear effects of General Relativity make baryonic matter alone sufficient to explain this observation.

Subjects:	Astrophysics of Galaxies (astro-ph.GA); General Relativity and Quantum Cosmology (gr-qc)
Cite as:	arXiv:1909.00095 [astro-ph.GA]
	(or arXiv:1909.00095v2 [astro-ph.GA] for this version)

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From: Balša Terzić [view email]

[v1] Sat, 31 Aug 2019 00:02:04 UTC (278 KB)

[v2] Sat, 11 Jan 2020 04:32:06 UTC (1,168 KB)

From Part II:

Field self-interaction makes GR non-linear. The phenomenon is neglected when Newton’s law of gravity is used, as typically done in dynamical studies of galaxies or galaxy clusters. However, such a phenomenon becomes significant once the masses involved are large enough. Furthermore, it is not suppressed by low velocity—unlike some of the more familiar relativistic effects—as revealed by e. g. the inspection of the post-Newtonian equations (Einstein et al. 1938). In fact, the same phenomenon exists for the strong nuclear interaction and is especially prominent for slow-moving quark systems (heavy hadrons), in which case it produces the well-known quark confining linear potential. 

The connection between self-interaction and non-linearities is seen e.g. by using the polynomial form of the Einstein-Hilbert field Lagrangian (see e.g. Salam 1974; Zee 2013)  

L = sqrt(det(gµν)) gµνR µν 16πG = sigma(∞ to n=0) (16πGM) n/2 [ϕ n ∂ϕ∂ϕ] (1) 

where gµν is the metric, Rµν the Ricci tensor, M the system mass and G is the gravitational constant. In the natural units (~ = c = 1) used throughout this article, [G] = energy−2 . The polynomial is obtained by expanding gµν around a constant metric ηµν of choice, with ϕµν ≡ gµν − ηµν the gravitational field. The brackets are shorthands for sums over Lorentz-invariant terms (Deur 2017). Field self-interaction originates from the n > 0 terms in Eq. (1), distinguishing GR from Newton’s theory, for which the Lagrangian is given by the n = 0 term. One consequence of the n > 0 terms is that they effectively increase gravity’s strength. It is thus reasonable to investigate whether they may help to solve the missing mass problem. In fact, it was shown that they allow us to quantitatively reproduce the rotation curves of galaxies and the dynamics of clusters without need for dark matter, also providing a natural explanation for the flatness of the rotation curves (Deur 2009). 

The phenomenon underlying these studies is ubiquitous in Quantum Chromodynamics (QCD, the gauge theory of the strong interaction). The GR and QCD Lagrangians are similar and both contain field self-interaction terms. In QCD, their effect is well-known as they are magnified by the large QCD coupling, typically αs = 0.1 at the transition between perturbative and strong regimes (Deur et al. 2016). In GR, self-interaction becomes important for non-negligible values of the coupling sqrt(GM/L) (L is the system’s characteristic scale, used here to form the dimensionless coupling needed to heuristically assess self-interaction’s importance), typically for sqrt(GM/L) > 10^−3 (Deur 2017). In QCD, a critical effect of self-interaction is a stronger binding of quarks, resulting in their confinement. In GR, self-interaction likewise increases gravity’s strength, which can explain the missing mass problem (Deur 2009). 

One may question the relevance of field self-interaction at large galactic radii r, where on the one hand the matter density is small, so field self-interaction is negligible, and where the matter density is small, so field self-interaction is negligible, but where the missing mass problem grows worst. However, once the gravity field lines are distorted at small r due to large matter density there, they evidently remain so even if the matter density becomes negligible (no more field self- interaction, i.e. no further distortion of the field lines), preserving a form of potential different to that of Newton. Thus, even if the gravity field becomes weak, the deviation from Newton’s gravity remains1. 

A key feature for this article is the suppression of self-interaction effects in isotropic and homogeneous systems (Deur 2009): 

• In a two-point system, large p GM/L or αs values lead to a constant force between the two points (and a vanishing force elsewhere), i.e. the string-like flux-tube, well-known in QCD. 

• For a homogeneous disk, because of the symmetry, the flux collapses only outside the disk plane. The resulting force between the disk center and a point in the disk at distance r decreases as 1/r. 

• For a homogeneous sphere, the force recovers its usual 1/r^2 behavior since the flux has no particular direction or plane of collapse. 

This symmetry dependence has led to the discovery of a correlation between the missing mass of elliptical galaxies and their ellipticity (Deur 2014). This also illustrates the point of the previous paragraph: even if the matter density in the disk decreases quickly with r, the missing mass problem—which in our approach comes from the difference between the GR and Newtonian treatments—grows worst since the difference between the 1/r GR force in the 2D disk and the 1/r^2 Newtonian force grows with r. This offers a simple explanation for the relation reported in MLS2016: although densities, and thus accelerations, are largest at small r, the 1/r − 1/r^2 difference between the GR and Newtonian treatments remains moderate. However, it becomes important at large r although accelerations are small. Furthermore, at small r, the 1/r^2 force is restored for GR due to finite disk thickness hz , since isotropy is restored for r < hz . Moreover, since disk galaxies often contain a central high-density bulge that is usually nearly spherical (M'endez-Abreu et al. 2008), self-interaction effects are suppressed there by the near-spherical symmetry, and the departure from the 1/r^2 behavior occurs after the bulge-disk transition.

1 An analogous phenomenon exists for QCD: the parton distribution functions (PDFs) that characterize the structure of the proton are nonperturbative objects even if they are defined and measured in the limit of the asymptotic freedom of quarks where αs tends to zero. Thus, PDFs are entirely determined by the self-interaction/non-linearities of QCD, although those are negligible at the large energy-momentum scale where PDFs are relevant. 

From the conclusion:

Our findings support the possibility that GR’s self-interaction effects increase the gravitational force in large, nonisotropic mass distributions. When applied to disk galaxies, the increased force on the observed matter transposes to the missing mass needed in the traditional Newtonian analyses. We have thus proposed a plausible explanation for the correlation between the luminous mass in galaxies and their observed gravitational acceleration shown in MLS2016. That this correlation is encapsulated in our basic, parameter-free, models indicates its fundamental origin.  

The explanation proposed here is natural in the sense that it is a consequence of the fundamental equations of GR and of the characteristic magnitudes of the galactic gravitational fields, and in the sense that no fine tuning is necessary. This contrasts with the dark matter approach that necessitates both yet unknown particles and a fine tuning in galaxy evolution and baryon-dark matter feedbacks (see e.g. Ludlow et al. 2017). We used several approaches that are quite different, thus leading to a robust conclusion.  

The work presented here adds to a set of studies that provide straightforward and natural explanations for the dynamical observations suggestive of dark matter and dark energy, but without requiring them nor modifying the known laws of Nature. This includes flat rotation curves of galaxies (Deur 2009), the Bullet cluster (Clowe et al. 2006; Deur 2009), galaxy cluster dynamics (Deur 2009), and the evolution of the universe (Deur 2019). The TullyFisher relation (Tully & Fisher 1977) also finds an immediate explanation (Deur 2009). There are compelling parallels between those observations and QCD phenomenology, e.g. the equivalence between galaxies’ Tully-Fisher relation, and hadrons’ Regge trajectories (Deur 2009, 2017), plausibly due to the similarity between GR’s and QCD’s underlying fundamental equations. The fact that these phenomena are well-known for other areas of Nature that possess a similar basic formalism; the current absence of natural and compelling theory for the origin of dark matter (supersymmetry being now essentially ruled out); and the yet unsuccessful direct detection of a dark matter candidate or its production in accelerators despite coverage of the phase-space expected for its characteristics; all support the approach we present here as a credible solution to the missing mass problem.

A Tocharian Love Poem From 600 CE

 

. . .  a thousand years, you will tell our story. 

I thus announce, heretofore there was no human being dearer to me than you; likewise hereafter there will be no one dearer to you than me. 

Your love, your affection, my jubilant song rises up! 

Along with life itself, this should not come to an end for my whole life. 

I was thinking: "I will live with one love well for the whole of my life, without any deceit, without…" 

The God of Karma alone recognized this, my thought. Thus he provoked a quarrel; it ripped out my heart that belonged to you. It led you afar, it tore me apart, it turned me into a partaker of all sorrows; he took away the consolation I had in thee. 

. . . my life, spirit, and heart, day-by-day.

From here.  The ellipsis reflect gaps in the fragmentary manuscript (an image of which is above) that can't be inferred from the remaining portions of the text.

The original was written in the dead Tocharian language, a branch of the Indo-European language family which was the language of the people of the Tarim Basin in what is now Inner Mongolia, China, in 600 CE, by the ancestrally West Eurasian people who lived there from about 2000 BCE until about 600 CE. It was written shortly before that language and culture died and was succeeded by the ethnogenesis of the Uyghur people (who are genetically a roughly even mix between West Eurasian and East Eurasian ancestors).

While a script brought by Buddhists to whose religion the people of the Tarim Basin had converted is used, the character of the poem bears no similarity to other Buddhist or South Asian poetry and appears to reflect the character of the Tocharian culture.

800,000 Year Old Hominin DNA

Details regarding the autosomal DNA of an archaic hominin from 800,000 years ago, half a million years before modern humans evolved, has been inferred from proteins that it produced which were then fossilized. This revealed that the DNA of the archaic hominin species Homo antecessor was closer to the genomes of modern humans, Neanderthals and Denisovans than expected, and was probably a sister clade to the shared ancestor species those three hominin species.

It also bears mentioning how amazing a scientific achievement this study is. This is twenty times older than any previously ancient DNA sequencing. It was widely believed that it would be impossible to do this. It replaces a vague hypothetical ghost population with a hard data point. If you had asked me a week ago when I thought this would be possible, I would have said either "never" or several decades in the future.

The press release provided to Science Daily explains:

[S]cientists retrieved the oldest human genetic data set from an 800,000-year-old tooth belonging to the hominin species Homo antecessor. 

"Ancient protein analysis provides evidence for a close relationship between Homo antecessor, us (Homo sapiens), Neanderthals, and Denisovans. Our results support the idea that Homo antecessor was a sister group to the group containing Homo sapiens, Neanderthals, and Denisovans," says Frido Welker, Postdoctoral Research Fellow at the Globe Institute, University of Copenhagen, and first author on the paper. 

By using a technique called mass spectrometry, researchers sequenced ancient proteins from dental enamel, and confidently determined the position of Homo antecessor in the human family tree. The new molecular method, palaeoproteomics, developed by researchers at the Faculty of Health and Medical Sciences, University of Copenhagen, enables scientists to retrieve molecular evidence to accurately reconstruct human evolution from further back in time than ever before. 

The human and the chimpanzee lineages split from each other about 9-7 million years ago. . . . "Much of what we know so far is based either on the results of ancient DNA analysis, or on observations of the shape and the physical structure of fossils. Because of the chemical degradation of DNA over time, the oldest human DNA retrieved so far is dated at no more than approximately 400,000 years," says Enrico Cappellini, Associate Professor at the Globe Institute, University of Copenhagen, and leading author on the paper. "Now, the analysis of ancient proteins with mass spectrometry, an approach commonly known as palaeoproteomics, allow us to overcome these limits," he adds. 

The fossils analyzed by the researchers were found by palaeoanthropologist José María Bermúdez de Castro and his team in 1994 in stratigraphic level TD6 from the Gran Dolina cave site, one of the archaeological and paleontological sites of the Sierra de Atapuerca, Spain. 

Initial observations led to conclude that Homo antecessor was the last common ancestor to modern humans and Neanderthals, a conclusion based on the physical shape and appearance of the fossils. In the following years, the exact relation between Homo antecessor and other human groups, like ourselves and Neanderthals, has been discussed intensely among anthropologists. Although the hypothesis that Homo antecessor could be the common ancestor of Neanderthals and modern humans is very difficult to fit into the evolutionary scenario of the genus Homo, new findings in TD6 and subsequent studies revealed several characters shared among the human species found in Atapuerca and the Neanderthals. In addition, new studies confirmed that the facial features of Homo antecessor are very similar to those of Homo sapiens and very different from those of the Neanderthals and their more recent ancestors. 

"I am happy that the protein study provides evidence that the Homo antecessor species may be closely related to the last common ancestor of Homo sapiens, Neanderthals, and Denisovans. The features shared by Homo antecessor with these hominins clearly appeared much earlier than previously thought. Homo antecessor would therefore be a basal species of the emerging humanity formed by Neanderthals, Denisovans, and modern humans," adds José María Bermúdez de Castro, Scientific Co-director of the excavations in Atapuerca and co-corresponding author on the paper.

The abstract and the citation to the paper are as follows:

The phylogenetic relationships between hominins of the Early Pleistocene epoch in Eurasia, such as Homo antecessor, and hominins that appear later in the fossil record during the Middle Pleistocene epoch, such as Homo sapiens, are highly debated. For the oldest remains, the molecular study of these relationships is hindered by the degradation of ancient DNA. However, recent research has demonstrated that the analysis of ancient proteins can address this challenge. Here we present the dental enamel proteomes of H. antecessor from Atapuerca (Spain) and Homo erectus from Dmanisi (Georgia), two key fossil assemblages that have a central role in models of Pleistocene hominin morphology, dispersal and divergence. We provide evidence that H. antecessor is a close sister lineage to subsequent Middle and Late Pleistocene hominins, including modern humans, Neanderthals and Denisovans. This placement implies that the modern-like face of H. antecessor—that is, similar to that of modern humans—may have a considerably deep ancestry in the genus Homo, and that the cranial morphology of Neanderthals represents a derived form. By recovering AMELY-specific peptide sequences, we also conclude that the H. antecessor molar fragment from Atapuerca that we analysed belonged to a male individual. Finally, these H. antecessor and H. erectus fossils preserve evidence of enamel proteome phosphorylation and proteolytic digestion that occurred in vivo during tooth formation. Our results provide important insights into the evolutionary relationships between H. antecessor and other hominin groups, and pave the way for future studies using enamel proteomes to investigate hominin biology across the existence of the genus Homo. 

Frido Welker, et al., "The dental proteome of Homo antecessor." Nature (April 1, 2020). DOI: 10.1038/s41586-020-2153-8

UPDATE April 2, 2020: Razib Khan's take.

Anomalous Magnetic Moment Of The Muon Predictions Reviewed

The anomalous magnetic moment of the muon is a measurable quantity that can be predicted, in principle, in the Standard Model of Particle Physics. Most parts of the Standard Model calculation are much more precise than any possible experiment, but the portions that involve the strong force of the Standard Model (i.e. the contribution from quantum chromodynamics or QCD), while a small part of the total value account for most of the error in the prediction.

The current experimental value is about 3.5 to 3.7 standard deviations away from the best theoretical estimate at the time it was made, which makes it one of the most important anomalies between Standard Model predictions and experimental observations. 

This quantity, since it can be measured and calculated theoretically extremely precisely, and has some contributions from essentially all parts of the Standard Model, is a good global measure of the magnitude of the extent to which beyond the Standard Model physics are not properly captured by the Standard Model over a quite broad range of energy scales. 

On one hand, the existing anomaly relative to estimate margins of error in the calculations and measurement, tentatively points to some deviation from the Standard Model, and on the other, the very small deviation on a percentage basis between the predicted value and the measured value (about 2 parts per million), suggests that any deviation from the Standard Model isn't a huge one with much observable impact.

Efforts to refine the Standard Model theoretical prediction have been an active area of research. The table below (from here) summarizes various theoretical predictions in recent years and compares them to the state of the art experimental measurement announced on January 8, 2004.

The experimental number will receive a more precise update within one to two years from now from the Fermilab E989 experiment. Data has been collected in that experiment since 2018 and the precision of the measurement at the experiment should rival the previous one early this year, with an eventual precision four times that of the previous measurement. A final result was anticipated in 2020 as of January of 2017, but like all major government projects, it is somewhat behind schedule. As of May of 2019, data collection was expected to continue through 2019-2020, with a result announced sometime in late 2020 or in 2021. The J-PARC (E34) experiment is also measuring muon g-2 at greater precision experimentally in a method with different kinds of systemic error, but it probably at least two years behind E989 in producing a publishable measurement.

Many Lattice QCD based estimates from the last few years (including this one from late February of 2020) are consistent with the state of the art experimental measurement, suggestion that the tension is mostly due to an inaccurate theoretical prediction. But, many estimates using a different technique called an R-ratio, independent of, or in conjunction with Lattice QCD methods (including this one from March 2020), can only be reconciled with experiment if the new state of the art measurement is significantly lower than the last one. Lots of background can be found in this power point presentation from March 2018. The R-ratio seems to be "the ratio of the bare cross section for e +e − annihilation into hadrons to the pointlike muon-pair cross section at center-of-mass energy √ s."

Conventional wisdom is that the theoretical calculation and experimental result will converge with greater precision in each.

Astronomy Constraints On Neutrino Properties Are Strong And Robust

The astronomy observation based constraints on the number of neutrino types (which also bounds possible number of light sterile neutrino species), and on the sum of the neutrino masses, are robust to a wide range of assumptions about the dark sector of cosmology made in the calculations made based upon observations. 

Both support Standard Model assumption that there are exactly three kinds of neutrinos and strongly favors the proposition that the sum of their masses arise from a "normal" neutrino hierarchy (i.e. in which the most frequent mass eigenstate of electron neutrinos is smaller than the most frequent mass eigenstate of muon neutrinos, which in turn is less massive than the most frequent mass eigenstate of tau neutrinos).

Thus, unless there is something profoundly wrong at a theoretical level which that way that we infer the number of neutrino types form astronomy observations, the equivocal hints of "sterile neutrino" species that oscillate with the three active neutrino types from more direct nuclear reactor produced neutrino experiments are extremely strongly disfavored. But, astronomy observations sensitive to neutrinos don't "see" neutrino types of more than about 10 electron volts in mass (which is roughly a factor of two hundred more massive the the most massive of the three Standard Model neutrino mass eigenstates). A sterile neutrino type heavier than that would escape the astronomy observation based constraints, but would also be pretty much outside the mass range suggested by nuclear reactor produced neutrino experiments. The reactor anomalies, where they have been observed (not consistently with each other), favor a fourth "sterile neutrino" that oscillates with the active neutrinos with a mass on the order of 1 electron volt. 

"Active neutrinos" (i.e. those that interact via the weak force at full strength) are ruled out experimentally up to about 62,500,000,000,000 milli-electron volts (because W and Z boson decays rule them out up to about 45,000,000,000,000 milli-electron volts, and an active neutrino with a mass of more than that would radically disturb the decays of the Higgs boson to a far greater extent than is consistent with observations of Higgs boson decays to date).

We know to a fair precision the differences in mass between the least massive and second least massive, and the second least massive and most massive neutrino mass eigenstate from neutrino oscillation experiments. This sets a floor to neutrino masses and also insures that the three neutrino masses are highly correlated. 

This, together with the cap of the sum of the three neutrino masses that is derived from astronomy observation constraints, leaves a quite narrow range of masses for the possible lightest neutrino mass eigenstate of about 17 milli-electron volts (with 95% confidence), favoring the middle to low end of that range. By comparison, the mass of an electron is approximately 511,000,000 milli-electron volts. The is a very small absolute margin of error, although the relative error is very high for the first neutrino mass eigenstate (accurate to roughly a factor of 100), and on the order of 150%+ for the second neutrino mass eigenstate, and on the order of 35%+ for the third neutrino mass eigenstate.

Upper bounds on neutrino mass (1) from direct measurements and (2) from the lowest frequencies for which neutrinoless beta decay has been ruled out, are much less constraining than those derived from astronomy observations.

As it is currently understood, any of the three kinds of neutrino types can have one of three neutrino masses called eigenstates, but the probabilities of each type of neutrino type having a particular mass varies by type.

A new article and its abstract on the topic are as follows:

Dynamical Dark sectors and Neutrino masses and abundances

Weiqiang Yang, Eleonora Di Valentino, Olga Mena, Supriya Pan

(Submitted on 27 Mar 2020)

We investigate generalized interacting dark matter-dark energy scenarios with a time-dependent coupling parameter, allowing also for freedom in the neutrino sector. The models are tested in the phantom and quintessence regimes, characterized by an equation of state wx<−1 and wx>−1, respectively. Our analyses show that for some of the scenarios the existing tensions on the Hubble constant H0 and on the clustering parameter S8 can be significantly alleviated. The relief is either due to (a) a dark energy component which lies within the phantom region; or (b) the presence of a dynamical coupling in quintessence scenarios. 

The inclusion of massive neutrinos into the interaction schemes does not affect neither the constraints on the cosmological parameters nor the bounds on the total number or relativistic degrees of freedom Neff, which are found to be extremely robust and, in general, strongly consistent with the canonical prediction Neff=3.045. The most stringent bound on the total neutrino mass Mν is Mν<0.116 eV and it is obtained within a quintessence scenario in which the matter mass-energy density is only mildly affected by the presence of a dynamical dark sector coupling.

Comments:	16 pages, 9 tables and 8 figures; comments are welcome
Subjects:	Cosmology and Nongalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc)
Cite as:	arXiv:2003.12552 [astro-ph.CO]
	(or arXiv:2003.12552v1 [astro-ph.CO] for this version)