Physics Quick Hits

Lots of interesting papers today. Little time to write, so only minimal commentary for now.

The reactor antineutrino anomaly still isn't real.

The Reactor Antineutrino Anomaly refers to the deficit observed between the average event rate measured in reactor antineutrino experiments with respect to the theoretical prediction. This anomaly was first identified in 2011 (2.5σ) as a consequence of the Huber-Muller reactor antineutrino flux calculation. It was thought to be resolved in 2021 as a result of new reactor antineutrino flux calculations, with a reduction to about 1σ. In this work, we examine the latest reactor antineutrino flux calculation published in 2023 by a French research group. This work represents the first summation model to include a comprehensive uncertainty budget. The result indicates a revival of the Reactor Antineutrino Anomaly at the level of 2.2σ. We also consider the usual simplest explanation of the Reactor Antineutrino Anomaly by active-sterile neutrino oscillations. We present the constraints on the oscillation parameters and we derive a tension of 3.8σ with the results of gallium source experiments (Gallium Anomaly) taking into account also the solar neutrino and KATRIN bounds, that of the combined short-baseline reactor spectral ratio measurements, and that of the Daya Bay search for a sub-eV sterile neutrino. Since the tension may be due to underestimated systematic uncertainties and the main tension is between the gallium data and the other data, we finally present the results of a global analysis with enlarged gallium uncertainties, which reduce the global tension to 1.3σ.

C. Giunti, Y.F. Li, R.P. Zhang, "Revival of the Reactor Antineutrino Anomaly" arXiv:2605.10353 (May 11, 2026).

Intriguing.

The charged-lepton Koide relation remains a striking empirical regularity in Standard-Model flavor data. We prove that for any positive mass set with Koide ratio Q0, the one-particle extension Q(m1,…,mN,x) has a unique global minimum Qmin=Q0/(1+Q0) at m∗=[(∑imi)/(∑imi‾‾‾√)]2. This exact kinematic result defines a unique extension benchmark. For the measured charged leptons it gives mℓ∗=1.25534(16)GeV and Qexp4,min=0.3999978(43); in the ideal Koide limit QKℓ=2/3, the corresponding minimum is exactly 2/5. In the effective-participant language Neff≡1/Q, the optimal one-particle extension increases Neff by one, while the equal-k multiplet extension increases it by k. The one-particle Neff profile is exactly Lorentzian in a dimensionless share-mismatch coordinate u, which we interpret kinematically rather than dynamically. Using charged-lepton pole masses with the PDG~2024 own-scale MS⎯⎯⎯⎯⎯⎯⎯⎯⎯ charm mass gives Q(e,μ,τ,c)=0.4000025(64), i.e. 11.7ppm above the measured-input benchmark and 6.2ppm above 2/5. This intentionally mixed-definition comparison is treated only as a phenomenological coincidence. To calibrate it within a stated benchmark class, we perform an exhaustive common-scale scan over non-neutrino Standard Model 2-body and 3-body seeds with one added mass. The charged-lepton-plus-charm continuation ranks 33/12,720 in the raw trial set, 24/2,640 after collapsing repeated scale realizations, and 6/756 within the fermion-only collapsed subset. We present the charm case as an empirically calibrated example of the theorem, not as a dynamical flavor model.

K. Hübner, "A minimization theorem for the Koide ratio and its Standard Model calibration" arXiv:2605.09651 (May 10, 2026).

So what?

Koide's charged-lepton relation suggests that (me‾‾‾√,mμ‾‾‾√,mτ‾‾‾√) is the natural family vector. We construct an effective compact-cycle model in which this vector is sampled from one real amplitude Z(ϕ) on an internal circle, while the masses are quadratic overlaps, ma∝|Z(2πa/3)|2. The amplitude is built from the two lowest antiperiodic modes on the circle; their symmetric square is periodic and gives the minimal three-harmonic family space e^iϕ,1,e^−iϕ. A reality condition together with the requirement that the amplitude comes from the square of one two-component spinor fixes the relative weights required by Koide's 45º geometry. The remaining orientation angle is fixed by matching one C3 family shift to transport on the full circle: integrating out the higher Fourier harmonics gives the Berry dressing that enters the determinant term and selects θℓ=−2/9. Using me and mμ as inputs, the model predicts mτ=1776.97MeV.

Kirill Shulga, "Charged-Lepton Koide Geometry from a Green-Dressed Compact Family Cycle" arXiv:2605.10245 (May 11, 2026).

Similar to another recent paper.

We show how, by exploiting the process of Coherent Elastic neutrino (v) Nucleus Scattering (CEvNS), neutrinos produced by nuclear reactor experiments appear to corroborate the evidence of the so-called X17 particle, which has been invoked to explain the ATOMKI anomaly. We base our analysis primarily on CONUS+ and Dresden-II data, which, when combined with CEvNS data from COHERENT and neutrino oscillation data from IceCube, single out a unique region of couplings to neutrinos and nuclei.

Johan Rathsman, Joakim Cederkäll, Yasar Hicyilmaz, Else Lytken, Stefano Moretti, "The X17 Existence Hinted at by Nuclear Reactor Neutrinos" arXiv:2605.10689 (May 11, 2026) (Short version of 2603.15246 using a different model for the X17).

Neutrinos do not have negative mass, so something isn't quite right in the model to estimate its masses from cosmology.

Recent baryon acoustic oscillation (BAO) distance measurements, when combined with Cosmic Microwave Background (CMB) observations in the ΛCDM framework, lead to a preference for negative neutrino masses. We investigate whether this neutrino mass anomaly can be alleviated by a class of astrophysically motivated reionization histories. Using a frequentist analysis, we find that some reionization histories can move the best-fit value of ∑mν to a positive value and bring ∑mν ≃ 0.06 eV into the 95% confidence interval. To separate the effect of the total optical depth from that of the details of the reionization history, we compare a high-τ history with a two-step tanh-like reionization history of the same τ. The resulting Δχ2(∑mν) profiles are nearly identical. This indicates that the effect is mainly driven by the total optical depth, while the details of the reionization history play only a minor role.

Yi Cheng Dai, Wei Liao, "Reionization History and Neutrino Mass" arXiv:2605.10116 (May 11, 2026).

As expected.

Modified Newtonian Dynamics (MOND) is a paradigm that can do away with dark matter at galaxy scales, but displays a residual missing mass discrepancy in galaxy clusters. Prompted by the updated JWST-based gravitational lens model of the Bullet Cluster, I confirm here that this cluster exhibits the same residual missing mass discrepancy as other clusters of similar mass in the MOND context. Moreover, this missing mass should be mostly collisionless, since it is centred on the galaxies of the Bullet Cluster.

Benoit Famaey, "On the residual missing mass of the Bullet Cluster" arXiv:2605.10022 (May 11, 2026).

Color me skeptical. It will take a closer look to poke holes in it, however. I suspect that while it may point out problems in toy-model MOND and some other models, this data could actually point the way towards a better modified gravity theory rather than towards dark matter particles which have myriad problems of their own that are ignored in this study.

Modified gravity theories such as Modified Newtonian Dynamics (MOND) and Scalar-Tensor-Vector Gravity (STVG) have been proposed as alternatives to dark matter, but decisive tests have been hindered by degeneracies between baryonic structure and gravitational laws. Here we break this degeneracy using independent, high-precision constraints: the Milky Way radial rotation curve, vertical phase-space spirals from Gaia, and a broken-exponential stellar disk. A joint reconstruction of the radial and vertical gravitational fields reveals a structural inconsistency in modified gravity -- no model can simultaneously reproduce both observations. Our results strongly disfavor MOND at >13σ and STVG at >4σ. In contrast, dark matter halo models naturally explain the observations, providing a self-consistent test of gravity on galactic scales.

Zheng-long Wang, Yue-Lin Sming Tsai, Lan Zhang, Yin Wu, Haining Li, Xiang-Xiang Xue, Hongsheng Zhao, Yi-Zhong Fan, "Milky Way Dynamics Favor Dark Matter over Modified Gravity Models" arXiv:2605.10857 (May 11, 2026).

A Notable Coincidence Related To The Proton Mass And Charge Radius

There is a functional relationship between the mass of the proton and the charge radius of the proton that is consistent with experimental measurements of those quantities, that doesn't have an obvious cause.

The simple proton mass and charge radius relationship

From @dandb at Physics Stack Exchange on May 5, 2016 (ten years ago). This can also be stated another way:

The charge radius of the proton is almost exactly four times the reduced Compton wavelength of the proton.

The reduced Compton wavelength is a natural representation of mass on the quantum scale and is used in equations that pertain to inertial mass, such as the Klein–Gordon and Schrödinger equations.

Equations that pertain to the wavelengths of photons interacting with mass use the non-reduced Compton wavelength. A particle of mass m has a rest energy of E = mc^2. The Compton wavelength for this particle is the wavelength of a photon of the same energy.

The reduced Planck's constant, h-bar, is Planck's constant divided by 2π. So, this relationship could also be stated as r = 2h/πmc, for Planck's constant h, the proton charge radius r, and the proton mass m.

This relationship is consistent with experimental measurements made to 0.05% precision

The uncertainty in the "predicted" value of the charge radius of the proton from this relationship, which is 0.84124 to five significant digits, is negligible, because the speed of light (c) and the reduced Planck's constant (h-bar) are quantities used to define SI units of measurement which are thus known "exactly" in terms of SI units of measurement, and the mass of the proton is known to the exquisite precision of about one part per hundred billion. See the Particle Data Group table of physical constants.

The Particle Data Group world average value is currently 0.8409(4) fm, i.e. a one sigma range of 0.8405 to 0.8413 This is a relative uncertainty of 0.048% (i.e. about one part per two thousand).

The PDG value is also consistent with a February 11, 2026 measurement of the charge radius of the proton with a relative uncertainty of 0.18% published in the prestigious peer reviewed journal Nature found it to be rp = 0.8406(15) fm, i.e. a one sigma range of 0.8392 to 0.8421 fm. 

So, the conjectured relationship is consistent with the experimentally measured value of the charge radius of the proton. 

At the time that this Physics Stack Exchange post was written, there was a discrepancy between the electron measurement of the proton charge radius and the muon measurement of the proton charge radius, but that has since been resolved. The muon measurement was found to be correct, and the electron measurement was found to have been incorrect due to experimental measurement errors not fully reflected in the stated uncertainty of the measurement.

This "prediction" is also notable because it is a testable hypothesis. As measurements of the proton charge radius grow more precise, we can find out if the experimentally measured value continues to be consistent with this prediction.

For example, if this hypothesis is merely numerology with no deeper meaning, it would be highly likely that it would grow less consistent with the experimental measurement if the experimental measurement's precision were increased by a factor of ten. And, in fact, experiments to do that are on the agenda of the physics community.

Analysis

What makes this relationship surprising?

Since the charge radius of the proton and the mass of the proton are both, in principle, derived quantities in the Standard Model, that this isn't actually a "coincidence" so much as it is a simple relationship arising from Standard Model physics whose source isn't trivially obvious.

The reason that it isn't trivially obvious is that the calculation of the mass and charge radius of the proton in the Standard Model are primarily functions at leading order of (1) the QCD coupling constant (which describes the strength of the "strong force") evaluated with non-perturbative QCD, (2) the mass of the up quark, (3) the mass of the down quark, and (4) the electromagnetic coupling constant. Yet, none of these experimentally measured physical constants have a functional relationship to Planck's constant or the speed of light.

There are comparatively minor contributions to these quantities that tweak their value beyond the leading order values from the masses of the other quarks (especially the strange quark), the weak force coupling constant, the W boson mass, and the CKM matrix elements (especially the  two elements of the nine elements in the matrix involving up-down quark transitions and up-strange quark transitions).

The reason that this relationship is surprising is that there is no known functional relationship between the reduced Planck's constant or the speed of light, and the other experimentally measured determinants of the proton mass and the proton charge radius (such as the Standard Model coupling constants, the quark masses, and the CKM matrix elements).

Three possible explanations

The stack exchange thread linked above contains some speculations as to why this is true, some more credible than others, but they are only speculations. For example, Michell Porter notes that:

Via P.R. Silva (eqn 6), I have run across a heuristic model of the nucleon in which M = 4/R (in natural units). Here R is the radius of the bag in the "bag model". See Xiangdong Ji, "Mass of the hadron", slide 20. I have not found where this argument originates, but a remark in a 1994 paper by Ji (see paragraph beginning "In the chiral limit...", on the final page) hints at it.

One possibility, which is to some extent the default one, is that this numerical coincidence of these two values has no deep meaning or connection and doesn't point to anything. In other words, this relationship just happens to hold for one hadron out of hundreds, for one of a large set of possible combinations of other physical constants that have no actually physical relationship to each other.

Another reason that this could be true is that the contributions of the experimentally measured constants cancel out in the combination of the proton mass and the proton charge radius, since the same experimentally measured constants enter into both calculations.

If true, this would suggest that should be a way of calculating the proton charge radius from first principles that more transparently and obviously reveals this cancelation.

This would be very interesting, would provide us to a deeper understand of the Standard Model and hadron physics. 

It would also suggest that this relationship ought be to generalizable in some way to the relationship between hadron mass and hadron charge radius for many hadrons (hadrons are composite particles made up of quark and/or gluons bound by the strong force of the Standard Model).

A calculation in this form would also have practical use, because the first principles Standard Model calculation of the proton mass has less than one part per thousand precision (vastly less than the precision of the experimentally measured value). And, in general, this would provide a quick and easy way to calculate hadron charge radii (which are no more precise than first principles calculations of hadron masses using current methods, see also here) which could then be compared to experimental measurements of hadron charge radii.

A third possibility, which would be even more grand, is that the values of the physical constants of the Standard Model that go into calculating the mass and charge radius of the proton actually have some deep functional connection to Planck's constant and the speed of light that has not previously been recognized or hypothesized.