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).

Hadron Physics To Do

One of my long-standing to dos for a blog post, which keeps getting put off because it is a pretty big project, is to survey the current state of the literature regarding hadron and/or hadron molecule resonances that aren't simple pseudo-scalar valance quark-antiquark, and simple three valance quark baryons, with u, d, s, c, and b valance quarks.

These include scalar mesons, axial-vector mesons, tetraquarks, pentaquarks, hexaquarks (if any), quarkonia, toponium, glueballs, mixed/blended meson resonances, glueball-quark hybrids, hadron molecules, excited hadron resonances, and other XYZ resonances. 

There are also "leptonic atoms" which substitute positively charged leptons for protons in an atomic nucleus and are bound by quantum electrodynamics (i.e. by electromagnetism) rather than by the strong force, that probably belong in the same discussion (and generally have a mass of less than 4 GeV).

As a prelude, the big bottom line is that there is not a global solution, really, even to any large group of unclassified resonances. Each resonance has to be figured out on its own. It is sometimes quite an epic effort to discriminate between plausible explanations of their structure. 

But there is also no BSM physics. QCD can explain it, but you have to be open to more involved hadron and hadron molecule structures than the vanilla mesons and baryons display. Thus, we are slowly and painfully, but inexorably, reaching a point where essentially all resonances have a Standard Model explanation.

Also, except for toponium, this highly sophisticated analysis and classification of hadron resonances, while it requires lots of data points, doesn't require the extreme high energies of the 13-14 TeV LHC (Large Hadron Collider). 

Generally speaking, all hadron resonances are somewhere between 135 MeV (the lightest pion) and about 30 GeV (a hypothetical six b quark hexaquark), and the lower middle part of this range is very crowded with all sorts of resonances. This is comfortably below the energy scale of even a W or Z or Higgs boson, and is also below the energy scale of a top quark-antitop quark pair. 

Maybe a post just spelling out the possibilities would be a good prelude to a post putting forth the leading theories about which resonances are most likely matches to which possibilities.

The SM Expectation For Higgs Boson Pair Production

A new study makes a state of the art prediction of the Higgs boson pair production rate from gluon fusion in the Standard Model. 

Some day when Higgs boson pair production experiments are about 1000 times more precise than they are today, this prediction can be compared to the experimental data, which is one way to determine is the Higgs boson self-coupling is consistent with the Standard Model prediction or if it instead has a value more consistent with a beyond the Standard Model value. 

Gluon fusion is one of the main mechanisms by which Higgs bosons and Higgs boson pairs are created, and combined with Standard Model predictions for the other possible mechanisms, can be compared to the actual experimentally observed rates of Higgs boson pair production at particle collider experiments.

Despite the lengths of many authors go to in order to make the calculation that considers all sorts of higher order corrections, however, the uncertainties are still large. 

But the experimental measurements currently aren't any better. They show that the actual rate of Higgs boson pair production is merely less than 2.4 times the Standard Model expectation (i.e. less than about 87.3 fb) with a 95% confidence interval. Higgs boson pair production rates are 0.06% of the overall Higgs boson production. In the Standard Model, Higgs boson pair production predominantly (90%) comes from the gluon fusion mechanism that the new study calculates considering all feasible to calculate factors.

Total Higgs boson production at 13 TeV is about 55.6 pb (+6% -8% uncertainties at one sigma) of which 48.4 (87% of the total) comes from gluon fusion with the remaining 7.2 pb coming from six other main production mechanisms. Higgs boson pair production at 13 TeV using a gluon fusion rate of 33 fb is 36.36 fb, of which 3.36 fb come from five other main non-gluon fusion production mechanisms. And, 1 picobarn (pb) = 1,000 femtobarns (fb).

This study (see below) concludes that double Higgs boson pair production at 13 TeV from gluon fusion is actually 30.4 fb (but subject to a roughly + 10% -23% uncertainty, so its is consistent with the earlier less exhaustively calculated result quoted in the Particle Data Group review below the fold which has roughly the same uncertainty on a percentage basis; the new result has a central value which is about 8% smaller than the old one). A ± 0.2 GeV change in the Higgs boson mass from 125.0 GeV shifts the predicted value by only about + 0.3% (if it is lighter) - 0.4% (if it is heavier), so the gluon fusion Higgs boson pair production rate isn't very sensitive to tweaks to the Higgs boson mass within the current range of uncertainty, but is probably a little bit less than 30.4 fb.

The paper and its abstract are as follows:

In this contribution, the higher-order QCD and electroweak corrections to Standard Model Higgs boson pair production via the gluon-fusion mechanism, gg→hh, are summarized and the different sources of theoretical uncertainty are assessed. The discussion includes finite top quark mass effects, matching to parton showers, approximate NNLO and N3LO QCD corrections, NLO electroweak effects, and uncertainties associated with the top quark mass scheme and perturbative scale choices. In addition, we provide an updated state-of-the-art recommendation for the inclusive gluon-fusion Higgs boson pair production cross section and the corresponding Higgs boson pair invariant-mass distribution.

Ajjath A H, et al., "Higgs Boson Pair Production via Gluon Fusion: Higher-Order Corrections and Theoretical Uncertainties" arXiv:2609.04868 (September 4, 2026) (Contribution to CERN Report 5 approved by LHC Higgs Working Group, Working Group 4 Report number LHCHWG-2026-010).

It concludes that:

Notably, while this prediction is sensitive to the Higgs boson mass, it is not sensitive enough to meaningfully distinguish Higgs boson masses experimentally because the differences due to the Higgs boson mass are smaller than the uncertainty in the prediction.

The conclusion explains:

This report has summarized the current status of precision predictions for Standard Model Higgs boson pair production via gluon fusion. The discussion brings together NLO QCD calculations with full top quark mass dependence, approximate NNLO QCD predictions, N3LO QCD corrections and soft-gluon resummation, NLO electroweak corrections, and details the main sources of theoretical uncertainty entering the theoretical prediction. 

The final recommendations provide state-of-the-art SM reference predictions for phenomenological studies and LHC analyses. They combine higher-order QCD (exact NLO, approximate NNLO and N3LO + N3LL) and EW (NLO) corrections, together with a full uncertainty budget. The combined inclusive cross sections, including the dominant uncertainty associated with the top-quark mass scheme, are collected in Table 12, while their dependence on the Higgs-boson mass is given in Table 13. Additionally we provide differential distributions in m(hh) (Section 7.5), along with corresponding K-factors from the higher-order calculations. These numbers should be used as the definitive predictions of this report, superseding the intermediate results shown in the preceding sections where different input parameters or PDF choices are used. It is worth noting that while the present work does not reduce the overall uncertainty with respect to the previous recommendation, its central prediction includes N3LO+N3LL QCD corrections in the HTL, NLO electroweak effects and updated PDF sets, and should therefore provide a more accurate reference value. 

Further improvements in the SM prediction will come from reducing uncertainties associated with finite top quark mass effects and mass-scheme choice, extending fully differential predictions with consistently combined higher-order QCD and electroweak effects, and updating the recommendations as parton distributions and input parameters evolve.

Background from the Particle Data Group (with somewhat icky formatting) appears below the fold. 

Handedness

 

From here.

A Single Possible Direct Dark Matter Detection

The Lux-Zepplin direct dark matter experiment has detected a single event that could be a dark matter particle (see also here). But given the immense amount of searching which drives up look elsewhere effects and the myriad other possible explanations for a single outlier data point, it is not a definitive dark matter detection yet.

From my posts on this at the link:

With this detector does that mean that the dark matter candidate would interact with the weak nuclear force?

Or some novel fifth force that has a cross-section of interaction much weaker (by factors of millions or billions or so) than the SM weak force.

The DM cross-section of interaction of atomic nuclei (and hence the weak force charge of DM particles) would have to be profoundly weaker than that of neutrinos if it is a weak force interaction, which would be surprising since every SM particle with weak force interactions has the same weak force charge.

What would even be a standard for credible detection here? 3 events? 10? When would they start calling Stockholm?

Not sure, does the paper say what statistical significance this event has?

The paper estimates the global statistical significance at 2.6 sigma, with a local statistical significance of up to 3.4 sigma. But the number of events probably isn't sufficient to determine the significance. It also depends, in part, about the details of each event and how far those details are from the expected background events on the chart in the OP. 

But given the amount of searching that has been done with multiple direct dark matter detection experiments that are all roughly similar to each other, the significance after the look elsewhere effect should be much lower than the local statistical significance.

You'd probably need a local significance of something like 10 sigma to get a global significance that meets the 5 sigma discovery threshold. Also, it isn't just 5 sigma, you also need a theoretical framework to attach the result to and replication, to be a true discovery.

So, you'd need (1) to do a lot of analysis with outside peer reviewers to rule out extremely faint backgrounds that weren't considered in the original analysis or other possible non-DM sources of this outlier data point, and (2) you'd need another experiment in addition to LZ to see it.

But, this makes funding direct dark matter detection experiments similar to LZ for the purpose of replicating this result and tuned to the parameters space where this was seen a no brainer.

Another issue is that even if the event is some non-SM particle, it doesn't necessarily follow that it is a significant component of DM.

Direct DM experiments are based upon the assumptions that the total DM mass flux and DM particle momentum can be pretty well determined from Milky Way dynamics, so you are looking at a parameter space in which DM particle mass and DM particle cross-section of interaction with nucleons trade off against each other for any given result.

This outlier data point, if it is real, points to a fairly high DM particle mass (some arXiv phenomenology papers are speculating in the 1 TeV order of magnitude). But anything much above 10 keV of mass presents real problems as a major component of DM since inferred DM distributions which are "cored" rather than "cuspy" suggest that you need much smaller DM masses to reduce the core-cusp problem, and plausible self-interaction strengths of heavy DM particles still don't solve that problem in simulations.

So, even if it is DM, it might be a type of DM particle that makes up, for example, only 1% of DM, as a DM analog to something like carbon atoms in interstellar space, while the predominant component of particle DM, as a DM analog of something like hydrogen atoms, might be too light for LZ to detect significantly due to neutrino backgrounds.

Analysis of this result in other preprints include:
https://arxiv.org/abs/2609.01475
https://arxiv.org/abs/2609.01504
https://arxiv.org/abs/2609.01592
https://arxiv.org/abs/2609.02608
https://arxiv.org/abs/2609.02775
https://arxiv.org/abs/2609.02868
https://arxiv.org/abs/2609.02823
https://arxiv.org/abs/2609.02807

If there are multiple kinds of DM particles and this is only a rare and heavy member of that set, this implies that the cross-section of interaction can be much higher (and thus, much closer to the neutrino-nucleon cross section of interaction). This is because the cross-section of interaction calculations assume that there is only one kind of DM particle, so that the actual events recorded comes from interactions with 100% of the DM flux through LZ. But if this assumption is wrong and only, for example, 1% of DM particles are massive enough for LZ to detect, then the actual cross-section of interaction implied by a given number of events is 100 times greater in that example.

If DM particles of this mass are extremely rare (the DM analog to uranium or lead, perhaps, making up only one in a million or billion DM particles) within the universe of DM particles, then perhaps the cross-section of interaction could be equivalent to the strength of the weak force interaction of SM particles.

The effective lower bound of DM particle mass that LZ can detect is about 0.2-0.5 GeV, and the signal to noise ratio starts to degrade meaningfully for DM particle masses below 10 GeV. And, there are, to repeat, strong suggestions from the inferred shape of DM distributions, that the predominant share of DM particles (assuming that they exist) should be about 10 keV or less, which is about 20,000 times less massive than DM particles that can give rise to events detected by LZ which are distinguishable from background events, and about 1,000,000 times less massive than DM particles that LZ can detect with maximum efficiency.

My suspicions

I think that this result is either a fluke in the background events (which at 2.6 sigma global significance, a global significance that I suspect is actually overstated, is entirely plausible), or a methodological error.

Even if it is, however, a genuine BSM particle, the one observed seems unlikely to be a DM particle, and particularly unlikely to be a Higgsino, which is what many of the linked papers suggest. A Higgsino is fairly tightly constrained in supersymmetry theories to have properties that this particle is unlikely to have, and might even be possible to rule out with further analysis of this particular data point.

Further, supersymmetry theories are simply not credible as theoretical frameworks in the broader sense for a variety of reasons, even though a Higgsino mass of 1.1 TeV was predicted in 2012 as the mass of a Higgsino that was the sole component of dark matter according to Hall, Lawrence J.; Nomura, Yasunori (2012). "Spread Supersymmetry". Journal of High Energy Physics. 2012: 82. arXiv:1111.4519 doi:10.1007/JHEP01(2012)082

The non-detection of any hint of a Higgsino at the LHC also casts doubt on this hypothesis, although the formal exclusions from the LHC (which is always a bit dicey because it depends on the Higgsino model used and the mass splitting between it and certain other supersymmetric particles) only go up to about 1.025 TeV.

There are also lots of strong reasons from astronomy, as I just scratched the surface of above, to think that either gravity (modified, non-perturbative, otherwise) or a fifth force, rather than dark matter particles make more sense, and that heavy dark matter particles (1 TeV or more particles that are at the fringe of what LZ and other direct detection experiments can be sensitive to), at least as a primary source of dark matter, are among the least observationally favored dark matter particle hypotheses.

This doesn't inherently rule out the possibility of a new fundamental particle, and the spectrum of composite bound quark and gluon structures, except toponium (which has a very distinct signature and set of conditions in which it can be formed) pretty much top out in the low tens of GeV, far below the 1 TeV scale. Toponium is 344-347 GeV, which is still below the TeV scale. The most massive observed atom, Oganesson (element 118), specifically its isotope Oganesson-294, has a mass of only about 274 GeV, which is still well below 1 TeV. A mass of 1 TeV would require a rather large and complex molecule (not hadron molecule, but a normal molecule made up of ordinary chemical elements), so an event like this, if being properly interpreted is not a good fit for any known fundamental particle, any known or possible hadron, any known or plausible future atom or atomic element. So, if there is a real detection of a 1 TeV mass particle, it is very much beyond the Standard Model and new physics. But even if it is real, that doesn't mean that it is an important contributor to dark matter. It could be a BSM particle with nothing meaningful to do with dark matter phenomena.

Indeed, the lack of well-motivated candidates for a 1 TeV particle with a very low cross-section of interaction with nucleons (at least no larger than the weak force coupling), makes this extraordinary claim require extraordinary proof and compels a very hard look for other explanations, especially given its only modest statistical significance so far.

The External Field Effect In MOND

Stacy McGaugh explains at his blog, Triton Station, how important it is to consider the external field effect (in which external gravitational fields prevent MOND effects from arising) when using astronomy data to determine if MOND is a good description of reality. Because, when the external field effect is strong enough, MOND reduces to Newtonian gravity.

Indirect Experimental Constraints On The X17 Hypothesis

A new analysis constrains the properties of a hypothetical X17 particle using experimental measurements of muon g-2 and electron g-2. It does not rule out the X17 particle hypothesis, although it does meaningfully constrain the properties it can have if it does exist.

We combine the current experimental muon g−2 world average, which incorporates the final Fermilab result, with the latest electron g−2 determinations based on cesium and rubidium measurements to set 95% CL exclusion contours for a pure vector mediator coupled to leptons. We explicitly test the assumption that the electron and muon coupling magnitudes are equal by comparing this restricted case with the case of independent electron and muon couplings and quantify the impact on the allowed parameter space. 

In the minimal visible dark-photon model, both leptons constrain the same kinetic mixing and are analyzed through a combined χ2 analysis. We compare the resulting g−2 bounds with existing accelerator direct-search exclusions and model-dependent astrophysical and cosmological constraints. From the accelerator comparison, we identify a region in the (mA′,|ϵ|) parameter space near 17~MeV, close to the reported X17 mass, that remains allowed by the direct-search contours displayed here but is excluded by the cesium-based electron g−2 constraint. The rubidium-based fit does not exclude this interval. 

For an X17 boson with independent lepton couplings, we constrain the electron and muon couplings separately. Electron-only direct searches leave two disconnected allowed regions near the reported X17 mass: a newly reopened low-coupling interval and a higher-coupling region above the NA64 excluded band. The cesium-based electron g−2 constraint closes the higher-coupling region, while the rubidium-based constraint reduces its extent; neither affects the newly reopened low-coupling interval. 

Using the current experimental muon g−2 world average, we obtain a new g−2-based exclusion region for the muon coupling, with no significant preference for a nonzero coupling.

Raoul Serao, Antonio Capolupo, "Electron and Muon g−2 Constraints on Light Vector Bosons: Dark Photons and the X17 Boson" arXiv:2608.24677 (August 25, 2026).

Replicating MOND In A Spin-Foam Model

Spin-foam is a quantum gravity approach that quantizes space-time, rather than treating gravity as a separate force with a carrier boson comparable to a photon or a gluon.

We argue that effects of the quantum spin-connection foam, which describes quantum gravity according to the precanonical quantization of General Relativity, may already be observed in the form of the small cosmological constant and a modification of Newtonian dynamics at small accelerations, manifested in the flat rotation curves of galaxies. 

We obtain a modification of the Newtonian potential that takes into account the existence of a fundamental small acceleration scale, a∗ = 8πGℏϰ, where ϰ is a parameter with the dimensions of inverse spatial volume that appears on dimensional grounds. The connection between ϰ and the hadronic scale of the mass gap in the pure Yang-Mills sector of the Standard Model leads to an estimated value of a∗ compatible with the Milgromian acceleration scale in MOND. The connection between a*^2 and the cosmological constant leads to a realistic value of the latter. Milgromian MOND, together with a theoretically distinct interpolating function, is derived under the assumption that classical dynamics is modified by the mean-field acceleration calculated from the simplest solution of precanonical quantum gravity in the nonrelativistic approximation. 

We also indicate that the effects of Newtonian dynamics modified by the spin-connection foam may be observable in the Solar System and even in laboratory experiments.

Igor V. Kanatchikov, Valery A. Kholodnyi, "Effects of Quantum Spin-Connection Foam in the Solar System, Galaxies, and the Universe" arXiv:2608.12404 (August 11, 2026) (The Seventeenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories, Pescara 7-12 July 2024, edited by G. Vereshchagin and R. Ruffini, this https URL, October 2026).

Hadronic B Decay Anomalies

The anomaly of the day is an anomaly in a certain kind of B meson decay. I'm very skeptical and think it will go away and is probably due to poor modeling of the Standard Model prediction, but I'll note its existence in this post for further analysis.

The decays B→PP, where the pseudoscalar P is a π or K, have been studied under the assumption of flavour SU(3) symmetry [SU(3)F]. The global fit shows a 3.6σ discrepancy with the Standard Model (SM). 

Separate fits for ΔS=0 and ΔS=1 decays find parameter sets that differ by a factor of 10, suggesting 1000% SU(3)F breaking, significantly larger than the ∼ 30% breaking expected in the SM. This study has been extended to include final states with η and η′ mesons. The resulting global fit, once again under the assumption of SU(3)F symmetry, is worse, with a 4.1σ deviation from the SM. When theoretical constraints |C˜/T˜| = 0.2 or A˜ = 0 are imposed, the fits worsen, with the discrepancy approaching 5σ. These results hint at new-physics contributions to these decays.

Marianne Bouchard, David London, "Anomalies in Hadronic B Decays" arXiv:2608.11298 (August 11, 2026) (Contribution to the Proceedings of the XVI International Conference on Beauty, Charm, Hyperons in Hadronic Interactions (BEACH 2026), 7-12 June 2026, Firenze, Italy).

Another Alternative To Particle Dark Matter

A Covarying Coupling Constant theory performs similarly to, but not better than MOND. Both are much better at explaining galaxy rotation dynamics than a Cold Dark Matter theory using an NFW dark matter distribution (which is theoretically necessary for truly sterile dark matter particles).

The Covarying Coupling Constants (CCC) framework, developed to account for high-redshift JWST observations, contains a mechanism -- a covarying-constant effective mass field keyed to local density -- that modifies galactic dynamics without particle dark matter. 

We test it against the full Spitzer Photometry and Accurate Rotation Curves (SPARC) sample of 175 disc galaxies, extending an earlier study of a few objects. Working in an inverse formulation, in which each model predicts the baryonic rotation curve from the observed one, we compare CCC against Modified Newtonian Dynamics (MOND) and one- and two-parameter Navarro-Frenk-White (NFW) haloes on identical footing, using the reduced χ2ν. We show that the published sharp density turn-off in the earlier study is unphysical and replace it with a smooth transition -- the density-space analogue of the MOND interpolating function, introducing no new parameter. One-parameter smooth-CCC then performs comparably to galaxy-by-galaxy fitted MOND (the lower χ(ν)^2 in 56 per cent of galaxies, mean χ(ν)^2 of 2.58 versus 2.65; the paired difference is not significant), while two-parameter NFW shows a substantially broader fit-quality distribution and a larger tail of poor or boundary-limited fits (mean χ(ν)^2≈7). The CCC turn-off density is not universal (scatter 0.82 dex) and correlates with galaxy size, qualitatively consistent with a spherical reconstruction applied to flattened disc systems. Recast as an acceleration, however, a(t) = V(flat)^2/R(t) has scatter 0.33 dex (on the 91-galaxy resolved subset) -- matching the MOND scale a0 (0.34 dex) -- and comparable magnitude of order 2×10^−10 m/s^2, with its size correlation removed. Though not designed for galactic dynamics, CCC describes rotation curves as well as galaxy-by-galaxy fitted MOND.

Rajendra P. Gupta, Nikolaos Samaras "Testing Covarying Coupling Constants (CCC) against the full SPARC rotation-curve sample: a like-for-like comparison with MOND and NFW" arXiv:2608.11575 (August 12, 2026).

Systemic Deviations From The Radial Acceleration Relation?

There is weak evidence that the radial acceleration relation, which is implied by Milgrom's toy-model MOND theory of weak field gravity, requires a single parameter correction is correlated with the compactness of the galaxies measured, primarily in dwarf galaxies.

Query if this could be due to the external field effect or due to gravitationally bound systems that are not in equilibrium? It could also be due to underestimated systemic error in estimating gas fractions, which is much harder to determine that stellar mass.

We ask whether any one-parameter structural correction to the radial acceleration relation (RAR) can be uniquely recovered from SPARC rotation curves, and answer with an identifiability audit: each candidate is benchmarked against per-galaxy nuisance freedom, with predictive scoring against mass-only and data-quality baselines. 

In the full sample (N = 126) the answer is no: a hybrid compactness term improves the fit, but zero-point freedom absorbs the gain, and in cross-validation the model fails to out-predict a mass-only baseline and loses to a quality-flag baseline. 

One regime retains structural information: in gas-dominated, low-acceleration disks -- where MOND's strict locality and ΛCDM feedback models diverge most sharply -- the RAR residual correlates with compactness (r = 0.46, p = 1.3×10^−4), remains significant under hierarchical partial pooling (β = 0.23, p = 1.7×10^−5; N = 63), and survives canonical joint control for quality, sampling, mass, inclination error, and first-order pressure support (r = 0.30, p = 0.02). All significant results pass a Benjamini-Hochberg correction over the declared 27-test family. 

Three limits temper that survival: it is not significant under rank-based control over the widest proxy set; it resides in faint dwarfs independent surveys do not reach; and after mass control it is shared across the mass-size manifold. Pressure support brackets the interpretation -- isotropic drift correction absorbs a quarter of the amplitude, while a Jeans treatment overcorrects resolved cases -- leaving the physical origin undetermined. The audit's product is the extraction limit: claimed corrections must clear the 0.106 dex per-galaxy nuisance floor, a mass-only baseline, and data-quality stratification.

Lukas A. Sosna, "An Identifiability Audit of One-Parameter Structural Corrections to the Radial Acceleration Relation in SPARC" arXiv:2608.08945 (August 9, 2026).

Is Milgrom's Constant Really Constant?

Reductionist physicists always like to derive physical constants, rather than than simply measure them. This paper proposes a way to do so for modified gravity in a MOND-like theory, expanding the theory's domain of applicability to galaxy clusters while sacrificing the universality of Milgrom's constant, a(0). 

It also hints, as Deur explicitly concludes, that MOND-like effects may be influenced by the extent to which a matter distribution is (or is not) spherically symmetric, and provides a mechanism to explain why MOND-like effects arise.

Modified Newtonian Dynamics (MOND) generally resolves the need for dark matter in galaxy rotation curves introducing a single new constant of acceleration a(0). It is well known that increasing a(0) by a factor of a few can alleviate the residual mass discrepancies that MOND leaves in galaxy clusters. 

Within a parameter-free Machian interpretation of MOND, in which a(0) ∼ GM(u)/R(u)^2 arises from the scalar sum of inverse-square distance gravitational mass contributions in the universe, we promote a(0) to a variable influenced by mass external to a locally enclosed region in the spherically symmetric case. 

Instead of a boost of a(0) in terms of gravitational potentials as in EMOND, we show that a boost in terms of this directionless inverse-square field roughly amounts to the boost needed to accommodate the mass discrepancies of MOND in galaxy clusters. We conclude by beginning to generalize the proposed formulation beyond spherical symmetry.

Manuel Uruena Palomo, Juan David Santander, "Machian MOND: a variable a0 in galaxy clusters" arXiv:2608.04894 (August 5, 2026) (published version in International Journal of Modern Physics D).

Cloud-9

A hydrogen gas cloud, called Cloud-9, that has been observed in deep space in the radio wave frequency, which cannot be seen in the visible light spectrum provides a way to distinguish between different dark matter hypotheses and while the paper below doesn't consider it, between modified gravity theories and dark matter hypotheses.

Starless gas clouds provide a new way to test gravitational dynamics and this is just the first examination of many to come.

Between cold dark matter and self-interacting dark matter, the observations strongly favor self-interacting dark matter, although neither hypothesis is a great fit.

Recently, the Five-hundred-meter Aperture Spherical Telescope discovered a gas-rich hydrogen cloud near M94 in the 21cm band. Lacking an optical counterpart, this object, dubbed Cloud-9, has been identified as a compelling Reionization Limited H Cloud (RELHIC). RELHICs provide exceptionally clean laboratories for probing dark matter, free from the baryonic complexities associated with star formation and feedback. 

We show that the observed hydrogen column density profile of Cloud-9 is consistent with a gas cloud embedded in either a cuspy halo predicted by the standard cold dark matter (CDM) model or a cored halo produced by self-interacting dark matter (SIDM). 

In both cases, the halo must have an unusually diffuse central density. The best-fitting CDM halo lies around 7σ below the cosmological concentration--mass relation, whereas SIDM core-forming halos reduce the tension to only around 3σ. 

We further identify Cloud-9 analogs in the Concerto suite of cosmological zoom-in simulations with velocity-dependent SIDM, demonstrating that RELHICs provide a promising new probe of dark matter self-interactions.

Morgan Ohana, Xingyu Zhang, Hai-Bo Yu, "Cold Dark Matter and Self-Interacting Dark Matter Interpretations of Cloud-9" arXiv:2608.04362 (August 5, 2026).

Meanwhile, another new paper finds that the tight relationship between the distribution of baryonic matter and galactic rotation curves has held true for as far back as at least z=0.42 (i.e. 4.4 billion years ago) with astronomy data.

The Baryonic Tully-Fisher relation (BTFR) is one of the tightest scaling relations for disk galaxies in the local Universe, and therefore is an important tool for studying the fomation and evolution of galaxies. . . . 

A random forest classifier is used to investigate the origin of the outlier component. We find that low signal significance and inaccurate inclinations are the key factors that contribute to the outlier population, indicating that observational effects are the dominant origin. 

Evolutionary trends are examined in three different redshift bins. Both the slope and zero point show consistency within 1-σ uncertainty in the two low redshift bins, indicating no significant evolution.

A Possible Glueball Resonance

A glueball is a strong force bound system without any valence quarks that binds gluons, the carrier bosons of the strong force instead of quarks. A well-established resonance seen in experiments at discovery level significance since 2011, whose internal structure is unclear, is shown in a new preprint to be consistent with a nearly pure pseudoscalar glueball state (i.e. a spin-0, electromagnetically neutral boson with odd parity and no valence quarks).

The properties of glueballs (which depend primarily on a single experimentally measured physical constant, the strong force coupling constant), have been calculated from the very early days of quantum chromodynamics (QCD), which is the Standard Model theory of the strong force. And, there are only a modest number of theoretically possible glueballs. This resonance is on the low end of, but consistent with, the mass predicted for a pseudoscalar glueball.

But distinguishing a glueball resonance from a non-glueball resonance is difficult, and because glueballs are always bosons and share quantum numbers with bosons that include valence quarks, they have a natural tendency to blend with similar bosons making a mere glueball component in a resonance rather than a pure glueball, something that is probably common in reality.

There have only been a few resonances that have been convincingly interpreted as a near pure glueball, and this is one of them. But the fact that this is an analysis of a lone author which has not yet been published in a peer reviewed journal bodes caution in accepting this conclusion as definitive. But to the extent that this analysis holds up, it confirms an important qualitative prediction of QCD (i.e. the existence of glueballs with various quantum numbers that have their predicted masses).

In this work, we take the X(2370) with J^PC = 0−+ as a glueball consists of three valence gluons, and construct a six-quark current based on rigorous current-field duality to obtain the glueball-quark Lagrangian. Then we perform Fierz transformation to bosonize the quark current into a series of three pseudoscalar mesons. At last, we obtain ratios among the partial decay widths of the glueball to three pseudoscalar mesons in a model-independent way, which are compatible with the experimental data from the BESIII Collaboration and support assigning the X(2370) as a glueball.

Zhi-Gang Wang, "Analysis of the X(2370) as a glueball based on rigorous current-field duality" arXiv:2608.03362 (August 4, 2026).

In other physics news, the Higgs boson continues to be consistent with Standard Model expectations in newly observed ways.

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).

A New Higgs Boson Mass Measurement

Every new precision measurement of the Higgs boson mass is golden, and it is increasingly being pinned down to some precision.

A measurement of the Higgs boson mass in the diphoton decay channel is performed using proton-proton collision data at a center-of-mass energy of 13 TeV. The data set recorded with the CMS detector between 2016 and 2018 is used, corresponding to an integrated luminosity of 138 fb−1. A refined detector calibration and new analysis techniques are employed to improve the precision of the results compared to earlier measurements. The Higgs boson mass is measured to be mH = 125.13 ± 0.15 GeV = 125.13 ± 0.10 (stat) ± 0.12 (syst) GeV. 

In addition, a combination with the mass measurement at center-of-mass energies of 7 and 8 TeV in the diphoton final state is performed resulting in mH = 125.06 ± 0.14 GeV = 125.06 ± 0.09 (stat) ± 0.11 (syst) GeV.

CMS Collaboration, "A measurement of the Higgs boson mass in the diphoton decay channel in proton-proton collisions at s√ = 13TeV" arXiv:2607.28396 (July 30, 2026) (Submitted to Physics Letters B.).

This result compares to a Particle Data Group global average of 125.13 ± 0.11 GeV (S = 1.5).

LambdaCMD Still Broken

No matter how much you fuss with the LambdaCDM based simulations, they generically predict the wrong number and type of satellite galaxies (related study here) producing a 2.4 sigma tension:

The kinematic approach yields a larger diversity in central dark matter densities than expected from the CDM population, as inferred from the stellar-to-halo mass relation, with compact ultra-faints appearing overdense and larger systems appearing underdense. For the ultra-faint dwarfs with at least 10 stars with spectroscopic measurements, this discrepancy persists at the ~2.4σ level across all considered systematic variations on the semi-analytic modeling.

The Hubble tension remains unresolved, which implies that the cosmological constant, Lamba, of the LambdaCDM model, isn't actually constant. And at galaxy scales, CDM has lots of problems:

Small-scale cosmic structure provides a powerful test of the fundamental nature of dark matter (DM). A wide range of DM models impact matter clustering on small scales, including warm, fuzzy, and (self-)interacting DM. In these scenarios, DM physics such as free-streaming, wave interference, and self/Standard Model interactions alter the abundance and internal structure of DM halos. Cosmological and astrophysical probes of nonlinear structure---including dwarf galaxies, strong lensing, the Lyman-α forest, stellar streams, and high-redshift galaxies---are therefore sensitive to these effects. 

Here, we review DM constraints provided by small-scale structure, focusing on observables that probe scales smaller than ∼1 Mpc, which define the frontier of current measurements. We summarize how these constraints have been translated to limits on microphysical DM models, and we discuss key modeling uncertainties and observational systematics. Finally, we highlight the growing importance of probe combination and simulation-based inference for this field, and we overview upcoming observational facilities that will sharpen small-scale structure tests of DM physics.

Ethan O. Nadler, Keir K. Rogers, Alex Drlica-Wagner, "Dark Matter Constraints from Small-Scale Cosmic Structure" arXiv:2607.28564 (July 30, 2026) (73 pages, submitted to Reviews of Modern Physics). The conclusion of this article states:

Over the past two decades, measurements of small scale structure have evolved from potential challenges to the CDM paradigm into a powerful probe of the fundamental nature of DM. For example, the combination of increasingly complete observations of faint galaxies and stellar streams, advances in strong lensing, and the development of flexible, empirically-grounded modeling frameworks has enabled robust inference that connects DM microphysics to data at the small-scale frontier. As a result, these probes now provide among the most stringent constraints on many DM properties, complementing LSS analyses and terrestrial experiments. At the same time, our understanding of small-scale cosmology remains incomplete, and new tensions have emerged on highly nonlinear scales, many of which are related to the inner densities of low-mass subhalos. 

Small-scale structure will likely play a central role in an eventual DM discovery. In the presence of a terrestrial detection, cosmological confirmation will be essential to show that newly-detected particles are the cosmological DM, and small-scale structure provides a uniquely sensitive avenue to achieve this goal. Conversely, evidence for departures from collisionless CDM inferred from nonlinear structure would offer critical guidance for direct detection and collider experiments by narrowing the viable particle DM parameter space. Thus, small-scale structure acts as a bridge between astrophysics and particle physics, creating interdisciplinary opportunities at the interface of astrophysical data and particle theory. 

A key milestone in the coming years will be the detection (or robust exclusion) of DM halos with masses below the galaxy formation threshold. Establishing the existence of completely dark halos would open a new observational window into structure formation and enable the most incisive small-scale structure tests of DM physics to date. On the other hand, an absence of such systems would constitute strong evidence against CDM and for DM physics beyond gravity. Either outcome will mark an important transition in our understanding of DM. 

Realizing the potential of upcoming small-scale structure data will require both observational and theoretical advances. On the observational side, next-generation facilities will dramatically increase the statistical power of current probes while enabling the first DM constraints from new data. On the theoretical side, progress will depend on accurately modeling nonlinear structure across DM scenarios, robustly marginalizing over the impact of baryonic physics on small-scale structure, and combining data from multiple probes in a unified framework. Together, these developments point toward a future in which small-scale structure enables precision tests—and perhaps discovery—of fundamental DM physics.

This article, however, is far too tentative and unwilling to drawn any conclusions from an already abundant supply of observations in its exceptionally long review of the literature and prospects for future study.

While the Hubble tension has received more widespread mainstream attention, the galaxy and galaxy cluster scale issues with cold dark matter particles is, IMHO, the far greater challenge to the LambdaCDM model. In measure after measure, it fails irremediably. 

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).

New Combined Standard Model Constant Measurements

A new study tries to extract several Standard Model Constant measurements from the same data set and obtains results generally consistent with prior efforts to measure the same constants, but with greater uncertainty than the state of the art measurements of these quantities.

X17 Hypothesis Less Constrained Following Reanalysis of Data

The conclusion of a new reanalysis of X17 relevant experimental data loosens the constraints greatly. But, I remain deeply skeptical of its existence.

Also, why use units of 10^-3 GeV instead of MeV in your key chart?

[T]he revised exclusion limits no longer extend to the X17 mass of 16.88 MeV, leaving a sizeable region of parameter space for the vector-boson interpretation of the anomaly, bounded by the NA64 and Orsay constraints. Interestingly, the remaining allowed interval, 6.5 × 10^−5 ≲ εe ≲ 1.1 × 10^−4, is compatible with the recent preliminary measurement of the X17 lifetime. We further observe that, for these coupling values, the X17 decay length for a 100 GeV/c e− beam-dump experiment is of the order of few meters, resulting to an invisible signature for a missing-energy setup such as NA64-e [51]. The X17 parameters space not any longer constrained by E141 could thus be explored in the near future by NA64 through the invisible-mode dataset accumulated so far by the experiment.

Since its first observation by the ATOMKI experiment in 2018, the ∗Be anomaly has attracted considerable interest within the dark sector community as it may indicate the existence of a new fundamental particle with a mass of about 16.9 MeV, the X17. However, the minimal model describing X17 as a new vector boson is severely constrained by null results from legacy beam-dump experiments. Among these, the E141 experiment at SLAC places stringent limits on the X17 coupling to electrons εe in the 5.1 × 10^−5 ≲ εe ≲ 1.7 × 10^−4 region. 

This excludes the possibility of a long-lived X17, potentially in contrast with the preliminary estimate of the particle lifetime recently reported by the ATOMKI collaboration. The E141 limits commonly adopted in the literature rely on reinterpretations of the original analysis under solid but simplifying assumptions. While these studies provide a reliable estimate of the experiment's reach, they rely on approximations that were well justified when the boson mass was largely unconstrained. With the X17 mass now confined to a narrow region by recent experimental observations, a more refined treatment of the E141 sensitivity becomes necessary. 

In this work, we revisit the E141 exclusion limits in the X17 scenario by performing a dedicated reanalysis that incorporates a more accurate treatment of the experimental setup and signal prediction. We quantify the impact of these refinements on the excluded parameter space and discuss their implications for the compatibility between the E141 constraints and the vector boson interpretation of the ATOMKI anomalies.

A. Celentano, A. Marini, L. Marsicano, "Updated E141 constraints on a long-lived X17 vector boson" arXiv:2607.22102 (July 24, 2026).

Another recent X17 paper highlighted by @neo is as follows:

The X17 particle has been proposed to explain the invariant mass anomalies observed in electron-positron pairs during nuclear transitions at the Atomki experiment. Motivated by recent observations of 8B solar neutrinos induced coherent elastic neutrino-nucleus scattering (CEνNS), we present the first comprehensive analysis of the hypothetical boson using data from multi-ton dark matter direct detection facilities. 

We consider the new particle as a light Z′ mediator arising from a spontaneously broken U(1)′ symmetry, featuring both vector and axial-vector couplings to leptons. By evaluating the latest datasets from XENONnT, PandaX-4T, and LUX-ZEPLIN, we derive stringent limits on the effective vector coupling utilizing marginalization procedures. Our global analysis provides competitive constraints that meaningfully narrow the allowed parameter space of the model, while exhibiting a clear sensitivity to the tau-flavor coupling.

M. F. Mustamin, M. Demirci, M. Deniz, "Signatures of X17 through Coherent Elastic Solar Neutrino-Nucleus Scattering in Direct Detection Searches"arXiv:2607.12691 (July 14, 2026).

The conclusion of this article states:

Motivated by the first observation of coherent elastic neutrino-nucleus scattering induced by 8B solar neutrinos, we have derived robust constraints on the effective couplings of a light Z′ gauge boson, interpreted here as the X17 particle. Initially conjectured to explain the invariant mass anomalies observed by the Atomki experiment, this hypothetical mediator can be handled within a U(1)′ gauge symmetry framework. Crucially, we have explicitly accounted for the flavor-dependent nature of the couplings, which naturally arise from solar neutrino flavor transitions during their propagation to Earth. 

Our analysis utilized the latest datasets from direct detection searches at XENONnT, PandaX-4T, and LUX-ZEPLIN experiments. While these multi-ton direct detection facilities were fundamentally designed to search for weakly interacting massive dark matter particles, their recent milestone in detecting solar neutrino-induced nuclear recoils offers a novel and powerful avenue for probing BSM physics. We systematically evaluated the flavor-dependent effective couplings—Cνe eff, Cνµ eff, and Cντ eff—that quantify the X17 interactions with the xenon target. By rigorously marginalizing over the relevant effective neutrino couplings, we have derived comprehensive 1 dof and 2 dof limits of the effective vector couplings using each dataset released by the experiments. Our global analysis reveals that PandaX-4T and LUXZEPLIN provide relatively similar behavior, while the combined datasets effectively break individual experimental degeneracies. Most importantly, we have found that the SM hypothesis remains completely protected and consistent within the 90% CL allowed regions across all flavor combinations. Overall, our derived bounds are highly competitive with the allowed parameter spaces previously mapped by IceCube and COHERENT+reactor studies. We also highlight the sensitivity of these detectors to the tau-flavor coupling, a direct consequence of the oscillated solar neutrino flux.

A non-lepton universal coupling seems particularly dubious.