Neutrinoless Quadruple Beta Decay

While detection of neutrinoless double beta decay is a sign that neutrinos are Majorana particles, neutrinoless quadruple beta decay in the absence of neutrinoless double beta decay is a sign that neutrinos have Dirac mass. So far, neither form of decay has been observed.

The observation of neutrinoless quadruple beta decay (0ν4β) in the absence of neutrinoless double beta decay (0ν2β) has been argued to provide a strong indication that neutrinos are Dirac particles. We report a search for 0ν4β decay of 136Xe using a total 136Xe exposure of 148.4 kg⋅yr, collected during the commissioning and the first science runs of the PandaX-4T experiment. No significant excess of events over the background is observed. A lower limit on the 0ν4β decay half-life of 136Xe is set at 6.01 x 10^24 yr at the 90% confidence level. This result establishes the most stringent constraint on this process in xenon, demonstrating the unique capability of the PandaX-4T detector in probing lepton number violation and shedding light on the fundamental nature of neutrinos.

PandaX Collaboration, "Search for neutrinoless quadruple beta decay of 136Xe in PandaX-4T detector" arXiv:2609.10048 (September 9, 2026).

Sterile Neutrino Parameter Space Further Constrained

Observations of high energy out space sourced neutrinos from an Earth based neutrino detector further constrain the parameter space of possible sterile neutrinos in a way that the LHC, reactor experiments, and an Antarctica based cosmic ray observatory do not.

While the sterile neutrino mass range probed (1-100 TeV) is vastly greater than the active neutrino mass range, this is a sterile neutrino mass range frequently considered in see saw neutrino mass models, so it is relevant for discriminating between hypotheses.

The money chart, below, is a bit difficult to explain, but the key point is that it adds new constraints that rule out sterile neutrinos with certain properties with masses ca. 12-120 TeV, that other experiments can't probe. 

We investigate the sensitivity of the Pierre Auger Observatory to physics beyond the Standard Model arising from magnetic-moment-induced transitions between active and heavy sterile neutrinos. Such dipole portal interactions can enhance neutrino-nucleon cross sections above a kinematic threshold set by the sterile neutrino mass, leading to observable modifications of neutrino detection rates at ultrahigh energies (UHE). 

We estimate the impact of these interactions on both down-going and Earth-skimming neutrino detection channels, the contrasting responses of which enable discrimination between an enhanced neutrino flux and a modified interaction cross section. Using the non-observation of UHE neutrino candidates, we derive neutrino-flux-dependent constraints with 90% confidence-level on the transition magnetic moment for sterile neutrino masses in the range 1 TeV-100 TeV. Under the assumed flux scenarios, the resulting flavor-independent limits extend existing bounds into previously unexplored parameter space.

Pierre Auger Collaboration, "Search for active-sterile neutrino transitions using Pierre Auger Observatory data" arXiv:2608.01496 (August 2, 2026).

The Model Dependence Of Cosmological Neutrino Mass Estimates

Even with greatly relaxed cosmology based bounds in neutrino mass that free it from the strong model dependence it has in the deeply flawed ΛCDM model, cosmology based limits on neutrino mass have a 90% confidence level upper bound that is about five times more strict than direct measurements of neutrino mass.

The relaxed less model dependent bound on neutrino mass still limits the lightest neutrino mass to about 60 meV in an inverted hierarchy scenario, and to about 73 meV in a normal neutrino mass hierarchy. In the restrictive and model dependent ΛCDM model estimation of the neutrino masses, there is a normal neutrino mass hierarchy and the lightest neutrino mass can't be much more than 2 meV which a best fit value that is much smaller than that.

Very low neutrino masses greatly limits the role that neutrinos can play to make up the gap between modified gravity theories that account for most, but not all, dark matter phenomena, such as MOND.

Neutrino oscillations establish that neutrinos are massive, providing the only laboratory detection of physics beyond the Standard Model. Direct kinematic experiments bound the electron-neutrino mass to m(νe) < 0.45 eV (KATRIN, 90% CL), implying ∑m(ν) ≲ 1.3 eV. 

Conversely, cosmology within ΛCDM is highly constraining: Planck CMB, CMB lensing, and DESI DR2 BAO yield ∑m(ν) < 0.056 eV (95% CL), in 2-3σ tension with the inverted-ordering floor (0.10 eV). However, this bound relies on ΛCDM, while data hint at an evolving dark energy. 

To determine the model dependence of cosmic neutrino mass bounds, we deconstruct each probe's sensitivity to late-time physics and pursue two robust routes to a ∑m(ν) bound: 

(i) The existing dark-energy-marginalized route, retaining all data and marginalizing over (w(0),w(a)), is shown to also be immune to flexible binned and cubic w(a) histories, yielding ∑m(ν) < 0.152 eV, sharpening to σ(∑m(ν)) ≈ 0.043 eV with Simons Observatory lensing and Spec-S5 BAO.

(ii) A new late-Universe-free route combines primary CMB, marginalizing over acoustic-peak smoothing via Alens, with the reconstructed lensing spectrum CκκL, removing late-time expansion dependence by construction. This yields ∑m(ν) < 0.41 eV today, tightening to 0.31 eV (Simons Observatory) and 0.28 eV (cosmic-variance limit) across all tested dark-energy models. These relaxed bounds trade statistical power for model independence. Interestingly, they land in the sensitivity range targeted by next-generation laboratory experiments like Project 8 (m(νe) ∼ 0.1 eV), motivating vital synergies between future cosmological and terrestrial neutrino measurements.

Frank J. Qu, et al., "Measuring Cosmic Neutrino Masses Independently of Dark Energy" arXiv:2607.24742 (July 27, 2026).

Neutrinos Are Very Likely Very Light

Adopting the cosmological bounds on the sum of the neutrino masses and making some other unambitious assumptions, this paper argues that the lightest of the three neutrino masses is less than 2.3 meV and considers a possible phenomenological relations between the three neutrino masses. Direct measurements of the electron neutrino mass at the Katrin experiment bound it at less than 450 meV with good prospects of reducing the bound to 200 meV, but that is still at least two orders of magnitude less than the likely true value.

By way of comparison, the mass of an electron is about 511,000,000 meV, and the first generation quarks are in the low single digit billions of meVs. 

Determining the absolute neutrino mass scale remains one of the most compelling challenges in particle physics. To constrain theoretical models, establishing precise relations among neutrino masses is essential. We propose a simple integral representation of the neutrino mass-squared differences Δm(ij)^2 that provides a complementary perspective on these oscillation parameters. We then demonstrate its utility through several examples. 

Specifically, assuming stringent cosmological bounds that confine the sum of neutrino masses near the normal ordering floor, we derive an analytical condition for the lightest neutrino mass, m(1) < √(61Δm(21)^2)/30. Using recent data from the JUNO experiment, this yields a competitive upper limit of m(1) < 0.0023 eV (95% C.L.). 

We also formulate practical analytical bounds for m(2) and m(3) adaptable to future data, and translate the results into allowed ranges for the effective electron and Majorana neutrino masses m(νe) and m (ββ). Finally, we show that neutrino mass relations of the Gatto-Sartori-Tonin type emerge directly from the proposed integral representation.

I. Alikhanov, "Integral representation of the neutrino mass-squared differences" arXiv:2607.19340 (July 21, 2026).

As a footnote, the body text has a very readable and useful introduction section that addresses many of the main outstanding elements of neutrino physics.

More Cosmology Limits On Neutrino Mass

In principle, the sum of the three neutrino masses and the number of neutrino types can be determined from astronomy observations in the context of a cosmology model. 

In practice, to a certain extent this determination is model dependent, although the estimates are consistently quite a bit less than 150 meV at the two sigma level. This is far less than the current 1410 meV lower bound (expected to be ultimately reduced to 660 meV) set by direct measurements of lightest of the three neutrino mass eigenstates in the Katrin experiment (currently 450 meV but expected to reach 200 meV once the experiment runs its course). 

Even fairly extreme tweaks to dark energy assumptions and a prior that the sum of the neutrino masses can't be less than the minimum established by neutrino oscillation experiments, in the paper below sets of cap of about 115 meV. So, the results are robust in the general vicinity of absolute neutrino masses, even if their specific limits vary by scores of meVs from each other.

Like other cosmology based absolute neutrino mass estimates, it doesn't absolutely rule out an inverted neutrino mass hierarchy, but it disfavors one in a statistically significant manner with fairly mild assumptions.

The effective number of neutrino types determined from cosmology measurements is more robust and overwhelming a fit to three types (plus an expected adjustment for radiation), ruling out additional sterile neutrinos with masses on the order of 10 eV or less (N(eff) is not sensitive to heavier neutrinos). 

This doesn't rule out seesaw neutrino mass models (which can involve very heavy sterile neutrinos) or sterile neutrino warm dark matter (which characteristically has keV scale masses), but it does seriously limit sterile neutrino explanations of anomalies in neutrino oscillation experiments (which tellingly are frequently inconsistent with each other).

We present a robust assessment of cosmological constraints on the sum of neutrino masses (∑mν) when relaxing the standard assumption of purely adiabatic primordial initial conditions. 

Allowing for a neutrino density isocurvature (NDI) component alongside the adiabatic mode, we analyse the latest CMB-SPA combination (Planck 2018, ACT DR6, and SPT-3G), DESI DR2 baryon acoustic oscillation data, and the DES Year 5 supernova sample. Within the ΛCDM model, the 95% upper limit weakens only marginally from ∑mν < 0.052 eV (purely adiabatic) to < 0.057 eV (including NDI), with the NDI amplitude consistent with zero. In the CPL dynamical dark energy model, the adiabatic limit is < 0.111 eV, shifting to < 0.115 eV with NDI, yet the isocurvature mode remains undetected. 

While these limits are robust against the inclusion of isocurvature perturbations, they are highly sensitive to both the assumed dark energy equation of state and the prior lower bound on ∑mν. Notably, the adiabatic ΛCDM limit of 0.052 eV lies below the minimum sum required by the normal neutrino mass hierarchy (0.05878 eV), indicating that this bound is an artifact of the statistical prior extending to zero. Imposing a physically motivated hierarchy-informed prior raises the limit to <0.092 eV. 

Our results demonstrate that current data show no evidence for NDI modes and that the inferred neutrino mass upper limit is robust against this extension, but a definitive, model-independent bound requires addressing prior dependencies and dark energy uncertainties. This work provides the first joint constraint on ∑mν and NDI using the full CMB-SPA+DESI DR2+DES dataset.

Hongsheng Hou, Sai Wang, Zhi-Chao Zhao, Xin Zhang, ""Constraints on the Sum of Neutrino Masses from ACT DR6 and DESI DR2 Considering Isocurvature Initial Conditions" arXiv:2606.17994 (June 16, 2026).

Data Combinations For Neutrion Oscillations

The PMNS matrix with non-zero CP conservation and a normal ordering of neutrino masses is still a good description of all of the available raw data from four leading neutrino experiments (without the need for right handed or otherwise sterile neutrinos, or non-standard neutrino interactions, or Majorana neutrino mass). 

This is hardly breaking news but provides yet another confirmation, independent of the major neutrino physics collaborations that this fairly simple model of neutrino physics works.

We present the first combined oscillation analysis of multiple atmospheric neutrino datasets, featuring data from Super-Kamiokande, IceCube-DeepCore, and KM3NeT/ORCA together with reactor data from Daya Bay. 

Such combinations have long been considered infeasible outside experimental collaborations; we demonstrate that a unified physics model can simultaneously describe all datasets with no significant parameter tensions. 

Fitting 839,048 events across 1536 bins with 91 parameters, our combined analysis yields competitive measurements of the neutrino mixing parameters, disfavors CP conservation, and prefers the Normal over the Inverted Mass Ordering.

Philipp Eller, "Atmospheric Neutrino Oscillations: the Full Picture" arXiv:2606.09714 (June 8, 2026).

The body text notes that:

We disfavor the absence of CP violation at ∆χ2 = 8.06 and the Inverted Ordering at ∆χ2 = 9.11.

These preferences are statistically significant at a more than 95% confidence level.

The preference for normal ordering is about three sigma (roughly a 99% confidence level). 

This preference is also corroborated by an independent statistically significant preference for a normal ordering from cosmology data that strengthens that preference when cosmology data is combined with terrestrial experimental data. But quantifying the cosmology data preference is challenging because it is cosmology model dependent (see also here). 

Cosmology data does, however, consistently favor a lightest neutrino mass eigenstate far less massive than the Katrin direct neutrino mass measurement experiments (by two or three orders of magnitude).

Neutrinoless beta decay experiments (which imply Majorana neutrino mass limits) aren't yet powerful enough to make meaningful statements about neutrino masses relative to other data sources for neutrino masses.

More Physics Quick Hits

A relationship between the Higgs boson, top quark, and Z boson masses

Maybe a coincidence, maybe meaningful. The only relation that fits, using pole masses, holds at 1.4 sigma, but tends to predict either a rather high Higgs boson mass, or a rather low top quark mass.

I have little doubt that there are deeper functional relationships between the fundamental constants of the Standard Model (or at least some of them) than are contained within the Standard Model (what I call "within the Standard Model new physics" as opposed to "beyond the Standard Model new physics"). And, even if this particular relationship is not actually true, it is close enough that it is fruitful to ask, if there is some deeper source for these experimentally measured physical constant values, what kind of relationship would produce a close coincidence like this one.

For example, I wonder if an approximation of this relationship is favored in some way by the LP & C relationship that the square of the Higgs vev is equal to the sum of the squares of the fundamental SM particle masses, or by the approximate, but not exact, equality between the sum of the squares of the fundamental fermion masses and the sum of the squares of the fundamental boson masses.

Indeed, the paper notes that: 

After the Higgs discovery the numerical observation M(H)^2 ≃ M(Z)*M(t) (1) was proposed as a possible electroweak mass coincidence involving the heaviest spin-0, spin-1/2 and spin-1 representatives of the Standard Model (SM) spectrum.

(The citation for this sentence is to a paper by the author of the current paper: E. Torrente-Lujan, "The Higgs mass coincidence problem: why is the Higgs mass M2 H = MZMt?", Eur. Phys. J. C 74 (2014) 2744, arXiv:1209.0474.)

This suggests that there might be a fuller relationship that involves addition masses on the Standard Model spectrum beyond the heaviest ones that might provide correcting terms bringing the relationship to a more exact one.

I also seem to recall that there theoretically expected mass of the W boson in the Standard Model is a function of the Z boson mass, the top quark mass, and the Higgs boson mass, based upon electroweak unification in some way, but have never seen that relationship spelled out in detail. I have only seen the abbreviated leading order relationship between the W boson mass and Z boson mass that is related to the electromagnetic force and weak force coupling constants. 

The paper doesn't evaluate the "arithmetic relation" with the theoretically predicted W boson mass of 80.357 ± 0.006 GeV, but because that value is lower than the PDG value of 80.3692 ± 0.0133 GeV, it should be a somewhat better fit with the theoretically predicted W boson mass. As it turns out, this difference doesn't matter much, and neither does the difference between the Higgs boson mass that they use of 125.2 ± 0.11 GeV and the lower value of the Higgs boson mass of 125.09 GeV that is sometimes used. Indeed, the greater precision of the theoretically estimated W boson mass may increase the statistical significance of the discrepancy somewhat.

The relation M(H)^2 ≃ M(Z)*M(t), previously proposed as a non-trivial Higgs mass coincidence, is reconsidered with present electroweak inputs and with a scheme-consistent matching analysis. With the 2025 PDG values for M(Z), M(W) and M(H), and the ATLAS-CMS direct top-mass combination, the pole-level ratio is ρ(Zt)=M(Z)*M(t)/M(H)^2 = 1.00362 ± 0.00261. Thus an exact pole-level geometric relation predicts either M(H) = 125.426 ± 0.120 GeV or M(t) = 171.898 ± 0.302 GeV, which is still a 1.4σ test rather than an exclusion. 

By contrast, the companion arithmetic relation gives ρ(Wt) = (M(W)+M(t))/(2M(H))=1.00994±0.00159 and is not a viable exact mass sum rule. 

We then evaluate the complete NNLO weak-scale MS bar matching formulae at μ=M(t). In the standard convention one obtains ρˆ(Zt(M(t)) = √(g(2)^2+g(Y)^2) * y(t)/(4√2λ) = 0.96714±0.00361. Consequently, the exact running-coupling boundary condition λ =  g(Z)y(t)/(4√2) at the top scale would predict M(H) = 123.19 ± 0.20 GeV, or equivalently M(t) = 177.81 ± 0.50GeV when M(H) is held fixed. This is incompatible with the measured point. 

A possible symmetry explanation must therefore act on pole-level threshold quantities, or provide a finite matching factor κ(th) = 1.0340 ± 0.0039 at the electroweak scale. We formulate this requirement as a target for custodial/top-Higgs or triality-like symmetry extensions.

E. Torrente-Lujan, "The Higgs-top-Z mass coincidence relation after NNLO matching" arXiv:2605.21721 (May 20, 2026) (Report number: FISPAC-TH/3145-26, UQBAR-TH/26-97234).

Another key chart from the paper is this one:

The Lambda predictions are very far from the mark, as are the "arithmetic relation" estimates. The other relationship still has some tension with the experimental results but isn't ruled out.

Bounds on new neutrino physics

The constraints on BSM physics continue to narrow. In the Standard Model, the neutrino magnetic moment is predicted to be far below the threshold of current experimental detection, and the neutrino has an exactly zero electromagnetic charge. These results are consistent with those predictions and thus constrain BSM neutrino physics to very slight deviations from the SM predictions. Non-standard interactions of neutrinos are likewise constrained materially.

CODATA 2022 gives the value:

     ${\displaystyle {\sin }^2{\theta }_{\mathsf{\text{w}}}=1-{\left(\frac{m_{\mathsf{\text{W}}}}{m_{\mathsf{\text{Z}}}}\right)}^2=0.22305(23).}$

So, the Weinberg angle measurement from the CONUS collaboration, while consistent with the world average measurement at the two sigma level, is too imprecise by two orders of magnitude to add meaningfully to our knowledge of that physical constant compared to the value obtained from simply plugging in the world average measured values of the W boson mass and the Z boson mass (or from calculating it in electroweak unification theory from the electromagnetic coupling constant and the weak force coupling constant so e^2/g^2 = sin^2 theta(W).

Its detections with pion-decay-at-rest, solar and recently with reactor antineutrinos by the CONUS collaboration render coherent elastic neutrino-nucleus scattering (CEνNS) an established tool for investigations within and beyond the Standard Model (SM). The CONUS experiment located at the nuclear power plants in Brokdorf (Germany) and Leibstadt (Switzerland) operates Germanium semiconductor detectors in a compact shield at close distance to the reactor core. An observation with 3.7σ significance is reported at the Leibstadt site, showing good agreement with its SM prediction.

Physics investigations performed with the last datasets collected at the Brokdorf reactor and with the first data obtained at the Leibstadt site are summarized. By using the experimental analysis framework, the presented results contain the full systematics that underlie the experiment. 

Previously determined limits with neutrino-electron scattering on the neutrino magnetic moment and a neutrino millicharge are improved to μ(ν) < 5.18⋅10^−11μB and q(ν) < 1.76⋅10^−12e0 (90% C.L). Further, the scale of new physics related to NSIs is improved to ΛNSI = 145 GeV and limits on the coupling of light new mediators are lowered down to 4⋅10−7 (90% C.L.) with the new data. Finally, the determination of the Weinberg angle with CEνNS and reactor antineutrinos yields sin(θ(W))^2  = 0.28 +0.03 −0.04 at a momentum transfer of ∼10 MeV.

N. Ackermann, et al., "New constraints on physics within and beyond the standard model from the latest CONUS datasets" arXiv:2605.22815 (May 21m 2026).

The abstract is unclear about what there is 3.7 sigma evidence of, but the body text clarifies that: "With data collected there since 2023, a successful CEνNS detection was reported with 3.7σ significance."

The body text explains some of the theoretical motivation for the paper:

On theory side CEνNS has become an interesting tool for investigations within and beyond the standard model (BSM) because of its flavor-blind and, in principle, threshold-free properties [21–27]. Within the SM it enables measurements of the Weinberg angle sin^2 θ(W) at the MeV scale with neutrinos and probe modifications of the involved couplings, i.e. via radiative correction [28–31] or investigation of the nuclear form factor when deviating from full coherence, i.e. with higher neutrino energies from πDAR sources [32–36]. BSM searches can be performed by testing for new neutrino interactions, for example in the context of heavy new physics via non-standard neutrino interactions (NSIs)[37–43] or new light mediators [44–53]. Neutrino (electromagnetic) properties [26, 27, 54–56] or emerging new particles may be probed as well [57–59]. Furthermore, future applications in the context of multi-messenger astronomy [60–62] or nuclear safeguarding seem promising [63, 64]. Experimental upscaling in the near future will allow such investigations via precision CEνNS measurements.

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).

Nailing Neutrino-Nucleus Interaction Rates

An experimental test of how frequently neutrinos interact with atomic nuclei has a best fit value of the Standard Model expectation and an uncertainty of less than ± 15%, which is impressive given how slight the interaction is, fit 10^22 trials yielding just 124 observed interactions.

The COHERENT collaboration reports the most precise measurement of the coherent elastic neutrino-nucleus scattering cross section to date. This measurement was performed with COHERENT's germanium detector array, Ge-Mini, at the Spallation Neutron Source at Oak Ridge National Laboratory. 

A cumulative exposure of 4.68 × 10^22 protons on target yielded a total number of observed counts of 124 + 14 −12 and a flux-averaged cross section of 1.00 ± 0.10 (statistical) ± 0.10 (systematic) relative to the standard-model expectation of 5.9 × 10^−39 cm^2. 

The well-understood energy and timing distributions of the neutrino source allow for independent measurements of muon- and electron-neutrino scattering rates. This information is used to improve constraints on non-standard neutrino interactions mediated by heavy particles.

M. Adhikari, et al., "Measurement of coherent elastic neutrino nucleus scattering on germanium by COHERENT" arXiv:2603.17951 (March 18, 2026).

Experimental Bounds On Baryon And Lepton Number Non-Conservation

Baryon number (B) conservation means that the number of quarks minus the number of anti-quarks in any interaction remains constant. Lepton number (L) conservation means that the number of leptons (electrons, muons, tau leptons, and neutrinos) minus the number of anti-leptons in any interaction remains constant.

The Standard Model separately conserves B and L in all interactions except sphaleron interactions, which have been never observed and are theoretically confined to extremely high energy scales and mass-energy densities, which the Large Hadron Collider (LHC) (the most powerful particle collider of all time), cannot reach.

The conservation of baryon number and lepton number is established remarkably robustly in experiments.

Some of the main experimental searches that have not detected B and L non-conservation are the searches for neutrinoless double beta decay, the search for tree-level flavor changing neutral currents, and the search for proton decay. These non-detections have ruled out or tightly constrained many theories in physics including Majorana neutrino mass and most of the simpler grand unified theories (GUTs), such as SU(5).

Baryon number (B) conservation underlies the apparent stability of ordinary matter by forbidding the decay of nucleons, while lepton number (L) conservation plays a central role in the structure of lepton interactions and the possible origin of neutrino mass. 

In the Standard Model, B and L are accidental global symmetries rather than imposed fundamental principles. However, they are expected to be violated in many extensions of the theory, including frameworks of unification and processes in the early Universe. 

This review summarizes the status of experimental tests of B and L conservation and discusses them within a unified framework for interpreting current and future searches across different processes and experimental approaches, outlining historical and theoretical motivation, key physical processes, as well as their broader connections and complementarity to other searches.

Volodymyr Takhistov, "Experimental Tests of Baryon and Lepton Number Conservation" arXiv:2602.09097 (February 9, 2026).

Cosmology Evidence For A Normal Neutrino Hierarchy

Cosmology data increasingly favors, even under dynamical dark energy models, a normal neutrino mass hierarchy over an inverted neutrino mass hierarchy, although still not at the five sigma "discovery" level.

Constraints from direct measurements of the neutrino's absolute masses are much less constraining, although neutrino oscillation data also favors a normal neutrino mass hierarchy, in a completely independent measurement, to a similar degree.

We present cosmological parameters measurements from the full combination of DESI DR1 galaxy clustering data described with large-scale structure effective field theory. By incorporating additional datasets (photometric galaxies and CMB lensing cross-correlations) and extending the bispectrum likelihood to smaller scales using a consistent one-loop theory computation, we achieve substantial gains in constraining power relative to previous analyses. 

Combining with the latest DESI baryon acoustic oscillation data and using cosmic microwave background (CMB) priors on the power spectrum tilt and baryon density, we obtain tight constraints on the ΛCDM model, finding the Hubble constant H0=69.08±0.37 kms−1Mpc−1, the matter density fraction Ωm=0.2973±0.0050, and the mass fluctuation amplitude σ8=0.815±0.016 (or the lensing parameter S8≡σ8Ωm/0.3‾‾‾‾‾‾‾√=0.811±0.016), corresponding to 0.6%, 1.7%, and 2% precision respectively. Adding the Pantheon+ supernova sample (SNe), we find a preference of 2.6σ for the w0wa dynamical dark energy model from low-redshift data alone, which increases to 2.8σ when exchanging the SNe with Planck CMB data. 

Combining full-shape data with BAO, CMB, and SNe likelihoods, we improve the dark energy figure-of-merit by 18% and bound the sum of the neutrino masses to Mν<0.057 eV in ΛCDM and Mν<0.095 eV in the w0wa dynamical dark energy model (both at 95\% CL). 

This represents an improvement of 25% over the background expansion constraints and the strongest bound on neutrino masses in w0waCDM to date. Our results suggest that the preference for the normal ordering of neutrino mass states holds regardless of the cosmological background model, and is robust in light of tensions between cosmological datasets.

Mikhail M. Ivanov, et al., "Reanalyzing DESI DR1: 4. Percent-Level Cosmological Constraints from Combined Probes and Robust Evidence for the Normal Neutrino Mass Hierarchy" arXiv:2601.16165 (January 22, 2026).

Neutrino Oscillations Disfavor Dark Dimensions And Right Handed Neutrinos

Two moderately popular beyond the Standard Model neutrino physics models are strongly disfavored by empirical data.

Right-handed neutrinos are naturally induced by dark extra dimension models and play an essential role in neutrino oscillations. The model parameters can be examined by the long-baseline neutrino oscillation experiments. In this work, we compute the predicted neutrino oscillation spectra within/without extra dimension models and compare them with the experimental data. We find that the neutrino data in the T2K and NOvA experiments are compatible with the standard neutrino oscillation hypothesis. The results set the stringent exclusion limit on the extra dimension model parameters at a high confidence level. The derived constraints on dark dimension right-handed neutrinos are complementary to those results from the collider experiments and cosmological observations.

Ai-Yu Bai, Auttakit Chatrabhuti, Yin-Yuan Huang, Hiroshi Isono, Jian Tang, "Dark Dimension Right-handed Neutrinos Confronted with Long-Baseline Oscillation Experiments" arXiv:2601.00790 (January 2, 2026).

JUNO Hype And Reality

A new neutrino physics experiment published a preprint with new measurements of neutrino oscillation constants. The new equipment works to high precision and will help fine tune the exact values of some the least precisely known experimentally measured parameters in the Standard Model of Particle Physics. 

This is interesting to people who follow particle physics closely. It is also scientifically important. But honestly, it isn't that interesting to the average person with only a general interest in science.

But, Rory Harris at Live Science in a fit a yellow journalism in the science world, writes a story containing all sorts of nonsense about JUNO revealing beyond the Standard Model physics, as well as the usual, misleading blather about CP violation experimentation answering questions about the baryon asymmetry of the universe (which this experiment does not do).

Why Does Cosmology Give Us A Negative Neutrino Mass As A Best Fit Value?

The apparent preference for a best fit value of the neutrino masses from cosmology measurements is probably a matter of some fine methodological adjustments that weren't made for gravitational lensing.

Recent analyses combining cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) challenge particle physics constraints on the total neutrino mass, pointing to values smaller than the lower limit from neutrino oscillation experiments. To examine the impact of different CMB likelihoods from Planck, lensing potential measurements from Planck and ACT, and BAO data from DESI, we introduce an effective neutrino mass parameter (∑m̃ ν) which is allowed to take negative values. 

We investigate its correlation with two extra parameters capturing the impact of gravitational lensing on the CMB: one controlling the smoothing of the peaks of the temperature and polarization power spectra; one rescaling the lensing potential amplitude. In this configuration, we infer ∑m̃ ν=−0.018+0.085−0.089 eV (68% C.L.), which is fully consistent with the minimal value required by neutrino oscillation experiments. 

We attribute the apparent preference for negative neutrino masses to an excess of gravitational lensing detected by late-time cosmological probes compared to that inferred from Planck CMB angular power spectra. We discuss implications in light of the DESI BAO measurements and the CMB lensing anomaly.

Andrea Cozzumbo, et al., "A short blanket for cosmology: the CMB lensing anomaly behind the preference for a negative neutrino mass" arXiv:2511.01967 (November 3, 2025).

The Latest Neutrino Oscillation Parameters

Background

Data from W and Z boson decays and from cosmology measurements, strongly favor a model with exactly three active neutrino flavors, as do requirements for mathematical consistent in the Standard Model of Particle Physics, which requires that each generation of Standard Model fermions (i.e. an up-like quark, a down-like quark, an electron-like charged lepton, and a neutrino) must be complete with four members. The lower bound on a fourth active neutrino mass is on the order of 45,000,000,000,000 meV, while we know that none of the other three active neutrino masses are more than about 900 meV, and we have strong indications that the largest of the three active neutrino masses is no more than about 70 meV.

When the Standard Model was first formulated in the 1970s, neutrinos were assumed to be massless fermions. Experiments proved that this couldn't be the case in 1998, and that neutrinos change flavors and oscillate between their three mass eigenstates. Since then, scientists have worked to determine their mass and additional properties arising from the fact that they have mass, which has culminated in a basic three favor, Dirac neutrino model of neutrino oscillation to which the data has been fit.

This neutrino oscillation behavior is characterized by two mass differences Δm(21) and Δm(32), whether the masses are in a "normal" or "inverted" hierarchy, and four parameters of the PMNS matrix: three of which describe the probability of each of the possible transitions between the three neutrino flavors, and one of which δCP describes charge parity violation (i.e. how those transition probabilities differ between neutrinos and antineutrinos).  

The two mass differences have been measured to decent precision. A normal mass hierarchy is favored by the experimental data, but not to terribly great statistical significance (the preference is close to two sigma). The three main mixing angles of the PMNS matrix have been measured to reasonable but modest precision, although it isn't entirely established if one of them is a bit less than 45º or a bit more than 45º (the data increasing favors a value that is a bit more than 45º). Attempts to measure δCP are very imprecise and generally can't entirely rule out the possibility that there is no CP violation in neutrino oscillation, the best fit values of measurements of δCP consistently favor near maximum CP violation in neutrino oscillations.

The world average measured value of those parameters are as follows (according to the Particle Data Group):

In addition, to fully characterize the properties of neutrinos in the basic three flavor, Dirac neutrino model to which experimental data is fitted, one needs to know the absolute rest mass of at least one of the neutrino mass eigenstates. The experimental upper bound on the mass of the lightest absolute neutrino mass eigenstate is about 800 meV. The experimental lower bound on the sum of the three neutrino mass eigenstates is on the order of 58 meV for a "normal" hierarchy of neutrino masses, and 110 meV. for an "inverted" hierarchy of neutrino masses Reasonably robust upper bounds on the sum of the three neutrino masses from cosmology models and astronomy measurements favor an upper bound for the sum of the three neutrino masses to around 130 meV, with some measurements putting it below the 110 meV cap allowed for an inverted hierarchy for neutrino masses with some more aggressive theoretical assumptions.

The New Paper

A new paper combines the latest data from two major neutrino physics collaborations (NOvA and T2K) to tighten up the precision of measurements of the Δm(32) and δCP parameters of neutrino oscillations, which is hard to do with a single collaboration's data, because the observables in each experiment depend upon more than one parameter, and it is hard to tell with just a single experiment's data, which parameter is driving those observables. But, since the mix of parameters that drive the observables in each experiment is different (in part, by design to allow for just this kind of combined data analysis), when the two collaborations' data are combined, these degeneracies in each individual collaboration's data can be minimized.

The new paper below improves the precision of the measurement of Δm(32) a bit, and also makes for a still very imprecise, but improved, measurement of δCP. 

The new combined measurement for Δm(32) is at the very low end of the current the world average plus or minus two sigma range.

The new paper rules out the possibility of zero CP violation in neutrino mixing at the 3 sigma level for an inverted neutrino mass hierarchy assumption, and at a roughly 2.4 sigma level of significance for a normal neutrino mass hierarchy assumption.

The landmark discovery that neutrinos have mass and can change type (or "flavor") as they propagate -- a process called neutrino oscillation -- has opened up a rich array of theoretical and experimental questions being actively pursued today. 

Neutrino oscillation remains the most powerful experimental tool for addressing many of these questions, including whether neutrinos violate charge-parity (CP) symmetry, which has possible connections to the unexplained preponderance of matter over antimatter in the universe. Oscillation measurements also probe the mass-squared differences between the different neutrino mass states (Δm^2), whether there are two light states and a heavier one (normal ordering) or vice versa (inverted ordering), and the structure of neutrino mass and flavor mixing. 

Here, we carry out the first joint analysis of data sets from NOvA and T2K, the two currently operating long-baseline neutrino oscillation experiments (hundreds of kilometers of neutrino travel distance), taking advantage of our complementary experimental designs and setting new constraints on several neutrino sector parameters. 

This analysis provides new precision on the Δm(32)^2 mass difference, finding 2.43+0.04−0.03 (−2.48+0.03−0.04) × 10^−3 eV^2 in the normal (inverted) ordering, as well as a 3σ interval on δCP of [−1.38π, 0.30π] ([−0.92π, −0.04π]) in the normal (inverted) ordering. The data show no strong preference for either mass ordering, but notably if inverted ordering were assumed true within the three-flavor mixing paradigm, then our results would provide evidence of CP symmetry violation in the lepton sector.

NOvA, T2K Collaborations, "Joint neutrino oscillation analysis from the T2K and NOvA experiments" arXiv:2510.19888 (October 22, 2025).

Further Neutrino Property Issues 

Additional parameters are needed if neutrinos are actually Majorana particles (i.e. if they are their own antiparticles), or if they oscillate with a "sterile" right handed neutrino which only interacts via neutrino oscillation (and not via the electromagnetic, weak, or strong forces of the Standard Model) which is often proposed as a way for Dirac neutrinos to acquire mass in what is called a see-saw mechanism. 

Most physicists believe that one of these two possibilities should be possible to give rise to a mechanism for mass generation in neutrinos. Mass generation via the Higgs mechanism is not a good fit for neutrinos since all neutrinos are "left handed" in parity, and all antineutrinos are "right handed" in parity, unlike all other Standard Model fermions which have both left and right parity versions of both their particles and their antiparticles, making four states possible.

The most definitive phenomenological parameter of Majorana neutrinos would be neutrinoless double beta decay, which has not been observed to high precision. But neutrinoless double beta decays involving Majorana neutrinos is a function of their absolute mass scale. It is more rare to the extent that neutrinos are less massive. And, current bounds on neutrinoless double beta decay are not so strong that this can be ruled out for reasonable neutrino mass scales, although it's getting close to that point. Majorana neutrinos would also have a more complicated oscillation behavior involving more mixing parameters than the Dirac neutrino model.

A Dirac neutrino model with a see-saw mechanism involving oscillation with a sterile neutrino would imply that the transition probabilities of the PMNS matrix parameters wouldn't be unitary. In other words, the probabilities of all the three flavor model transitions wouldn't add up to 100%, because some small percentage of neutrino oscillations would be to one or more sterile neutrino flavors. So far, the observed PMNS matrix parameters are consistent with unitarity. But since the measured parameters each have uncertainties, there is room within those uncertainties for transitions to an additional sterile neutrino flavor (or even to multiple sterile neutrino flavors). The upper bound on missing neutrino transition probabilities is quite low, however, and to make a see-saw mechanism work with such small experimentally allowed transition probabilities, the mass of a hypothetical sterile neutrino would have to be very high.

For the record, I don't like either solution and think that we need to find a "third way" mechanism for generating neutrino mass, although I don't know what it would be.

A Proposal To Explain The Neutrino Mixing Angles

Many papers try to explain fundamental constants in the Standard Model in terms of deeper relationships. This attempt to gain insight into the neutrino oscillation parameters is more thought provoking than most. 

We propose a geometric hypothesis for neutrino mixing: twice the sum of the three mixing angles equals 180∘, forming a Euclidean triangle. This condition leads to a predictive relation among the mixing angles and, through trigonometric constraints, enables reconstruction of the mass-squared splittings. 

The hypothesis offers a phenomenological resolution to the θ23 octant ambiguity, reproduces the known mass hierarchy patterns, and suggests a normalized geometric structure underlying the PMNS mixing. 

We show that while an order-of-magnitude scale mismatch remains (the absolute splittings are underestimated by ∼10×), the triangle reproduces mixing ratios with notable accuracy, hinting at deeper structural or symmetry-based origins. 

We emphasize that the triangle relation is advanced as an empirical, phenomenological organizing principle rather than a result derived from a specific underlying symmetry or dynamics. 

It is testable and falsifiable: current global-fit values already lie close to satisfying the condition, and improved precision will confirm or refute it. We also outline and implement a simple χ2 consistency check against global-fit inputs to quantify agreement within present uncertainties.

Mohammad Ful Hossain Seikh, "A geometrical approach to neutrino oscillation parameters" arXiv:2510.06526 (October 7, 2025).

Does The Weak Mixing Angle Minimize Magic?

"Magic" is a quantum mechanical property that roughly speaking quantifies the extent to which a quantum computer is more powerful than a conventional computer. 

The "weak mixing angle" is a physically measured quantity in electroweak unification theory, which treats the weak force and electromagnetism as having a common, unified origin and functional relationships to each other, in which three weak isospin fields and a weak hypercharge field are transformed into the photon and the W+, W-, and Z bosons. It quantifies what transformation from an idealized state in the theory is necessary to produce the world that we actually see.

It turns out that quantum magic appears to be minimized at very close to the weak mixing angle at the Z boson mass energy scale. Since the amount of magic at the Z boson mass energy scale can be calculated in the Standard Model, rather than merely measured experimentally, this potentially makes the weak mixing angle a derived constant rather than an experimentally measured fundamental constant. It is also suggestive of how the weak mixing angle arises at a fundamental level.

Qiaofeng Liu, Ian Low, Zhewei Yin, "A Quantum Computational Determination of the Weak Mixing Angle in the Standard Model" arXiv:2509.18251 (September 22, 2025) (abstract presented as an image rather than cut and pasted, to preserve mathematical equation formatting).

In other news, we are about a decade away from fully describing the properties of the neutrino.

More Neutrino Oscillation Physical Constant Measurements

Almost all of the experimental data favors a normal mass ordering for neutrinos over an inverted mass ordering, but given the limitations of current experiments, the preference is almost always a weak one.

The Particle Data Group value for delta m(32) squared in normal ordering is as follows:

Taking the square root, the PDG value is a gap of 49.5 meV.

A new paper's results are consistent with the world average. The paper, its abstract, and the chart below from its supplementary materials are as follows:

This Letter reports measurements of muon-neutrino disappearance and electron-neutrino appearance and the corresponding antineutrino processes between the two NOvA detectors in the NuMI neutrino beam. These measurements use a dataset with double the neutrino mode beam exposure that was previously analyzed, along with improved simulation and analysis techniques. 

A joint fit to these samples in the three-flavor paradigm results in the most precise single-experiment constraint on the atmospheric neutrino mass-splitting, Δm^2(32) = 2.431 +0.036 −0.034 (−2.479 +0.036 −0.036) × 10^−3 ~eV^2 if the mass ordering is Normal (Inverted). In both orderings, a region close to maximal mixing with sin^2(θ23) = 0.55 +0.06 −0.02 is preferred. 

The NOvA data show a mild preference for the Normal mass ordering with a Bayes factor of 2.4 (corresponding to 70% of the posterior probability), indicating that the Normal ordering is 2.4 times more probable than the Inverted ordering. When incorporating a 2D Δm^2(32) --sin^2(2*θ13) constraint based on Daya Bay data, this preference strengthens to a Bayes factor of 6.6 (87%).

NOvA Collaboration, "Precision measurement of neutrino oscillation parameters with 10 years of data from the NOvA experiment" arXiv:2509.04361 (September 4, 2025).

An Electroweak Centric Model For Standard Model Mass Generation

The basic intuitive gist of the proposal of this paper is one that I've entertained myself, although I don't have the theoretical physics chops to spell it out at this level of formality and technical detail (and I'm really not qualified to evaluate the merits to this proposal at that level). I've seen one or two other papers (not recent ones) that take a similar approach.

The ratio of the electron mass to the lightest neutrino mass eigenstate is roughly the same as the ratio of the electromagnetic coupling constant to the weak force coupling constant, and both are masses are similar to what would be expected from the self-interactions of electrons and neutrinos via the electromagnetic and weak forces with themselves. Electrons interact via both of these forces, while neutrinos interact only via the weak force.

The down quark mass is about twice as much as the up quark mass, just as the absolute value of the down quark electromagnetic charge is twice the absolute value of the up quark electromagnetic charge. All quarks have the same magnitude of strong force color charge. And all of the fundamental fermions of the Standard Model have the same magnitude of weak force charge. Quarks interact via the strong force, the electromagnetic, and the weak force, so their self-interactions might be expected to be larger than for the electron which doesn't interact via the strong force.

Figuring out how this can work in concert with the three fundamental fermion generations is particularly challenging. I'm inclined to associate it with a W boson mediated dynamic process that sets the relative values of the Higgs Yukawas. This paper doesn't attempt to look beyond the first generation of fundamental fermions in implementing its model.

I'm not thrilled with the "leptoquark" component of this theory, but the fact that it gives rise to neutrino mass without either Majorana mass or a see-saw mechanism is very encouraging.

In the Standard Model of elementary particles the fermions are assumed to be intrinsically massless. Here we propose a new theoretical idea of fermion mass generation (other than by the Higgs mechanism) through the coupling with the vector gauge fields of the unified SU(2) ⊗ SU(4) gauge symmetry, especially with the Z boson of the weak interaction that affects all elementary fermions. The resulting small masses are suggested to be proportional to the self-energy of the Z field as described by a Yukawa potential. Thereby the electrically neutral neutrino just gets a tiny mass through its Z-field coupling. In contrast, the electrically charged electron and quarks can become more massive by the inertia induced through the Coulomb energy of the electrostatic fields surrounding them in their rest frames.

Eckart Marsch, Yasuhito Narita, "On the Lagrangian and fermion mass of the unified SU(2) ⊗ SU(4) gauge field theory" arXiv:2508.15332 (August 21, 2025) (13 pages).

The introduction of the paper is as follows:

According to the common wisdom of the Standard Model (SM) of elementary particle physics, the fermions are intrinsically massless, but they gain their masses via phase transition from the vacuum of the Higgs field. However, this notion introduces many free parameters (the Yukawa coupling constants) that are to be determined through measurements. These have been made at the LHC only for some members of the second and third family of heavy leptons and quarks, yet not for the important first family of fermions, of which the stable and long-lived hadrons form according to the gluon forces of quantum chromodynamics (QCD). 

Here we just consider the first fermion family of the SM and propose a new idea of the fermion mass generation. The key assumption is that their masses may be equal to the relevant gauge-field energy in the rest frames of these charged fermions carrying electroweak or strong charges. Their masses are suggested to originate from jointly breaking the chiral SU(2) symmetry combined with the hadronic isospin SU(4) symmetry, as described in the recent model by Marsch and Narita, following early ideas of Pati and Salam and their own work. Unlike in the SM, in their model both symmetries are considered as being unified to yield the SU(2) ⊗ SU(4) symmetry, which then is broken by the same procedures that are applied successfully in the electroweak sector of the SM. 

The outline of the paper is as follows. We briefly discuss the extended Dirac equation and its Lagrangian including the Higgs, gauge-field and fermion sectors. Especially, the covariant derivative is discussed and the various gauge-field interactions are described. Also the different charge operators (weak and strong) are presented. Then the CPT theorem is derived for the extended Dirac equation including the gauge field terms. The remainder of the paper addresses the idea of mass generation from gauge field energy in the fermion rest frame. Finally we present the conclusions.

The paper's conclusion states:

In this letter, we have considered a new intuitive idea of how the elementary fermions might acquire their finite empirical masses. We obtained diagonal mass matrices as Kronecker products within the framework of the unified gauge-field model of Marsch and Narita. The mass matrices still commute with the five Gamma matrices of the extended free Dirac equation without gauge fields. However, when including them the chiral SU(2) and the hadronic SU(4) symmetries both are broken by the mass term. Thus, the breaking of the initial unified SU(2) ⊗ SU(4) symmetry by the Higgs-like mechanism gives the fermions their different charges as well as specific masses. 

In the SM the initial common mass m is assumed to be zero, and then the Dirac spinor splits into two independent two-component Weyl spinors. But when the gauge fields are switched on, their self-energy gives inertia and thus mass to the fermions in their rest frame. The breaking of gauge symmetry yields the electromagnetic massless photon field E(µ) and the weak boson field Z(µ), which becomes very massive via the Higgs mechanism. It also induces inertia for all eight fermions, yet the resulting masses are rather small owing to the very small Compton wavelength of the Z boson. The neutrino and electron can acquire masses in this way, which yet differ by six orders of magnitude. The hadronic charge of the leptons is zero, and thus they decouple entirely from QCD. It is responsible by confinement through the gluons for the mass of the various resulting composite fermions, in particular for the proton mass. 

The masses of the light fermions are thus argued to originate physically from the major self-energy of the electrostatic field as well as from the minor self-energy of the Z-boson field, which is proportional to the Higgs vacuum that determines the Z-boson mass. It is clear, however, that the masses of heavy composite hadrons, in particular of the proton and neutron, involve dominant contributions from the energy of the binding gluon fields, as the QCD lattice simulations have clearly shown. 

In conclusion, the extended Dirac equation contains a physically well motivated mass term. It remedies the shortcoming of the SM that assumes massless fermions at the outset, whereas the empirical reality indicates that they are all massive. Therefore, the neutrino cannot be a Majorana particle, as it has often been suggested in the literature. This notion is in obvious contradiction to the observed neutrino oscillation, implying clearly finite masses. Chiral symmetry is broken in our theory, yet the parity remains intact. 

Finally, we like to mention the masses of the heavy gauge bosons involved in the above covariant derivative and related matrix. In the reference of the particle data group we find in units of MeV/c^2 the values: M(Z) = 91.2 and M(W) = 80.4. For the “leptoquark" boson V we obtain M(V) = 35.4. For the sum of these masses we find the following surprising results: M(V) + M(Z) = 126.6, which equals within less than a one-percent margin the measured mass of the Higgs boson, M(H) = 125.3. Also, M(W) + M(Z) = 171.6, which again equals within less than a one-percent margin the measured mass of the top quark, M(T) = 172.7. Whether this is just a fortuitous coincidence or indicates a physical connection has to remain open.