Minimal Gravitational Fields

Gravity is an infinite range force. In isolated circumstances, gravitational pulls from opposite directions can cancel out. But, the vast majority of the time, there is at least some small net gravitational pull in one direction or another.

Stacy McGaugh at Triton Station digs into this observation, in both a Newtonian approximation and MOND, to determine that the minimum gravitational acceleration in deep space in MOND (in light of new data about the percentage of baryons that are in deep space) is about 2% of Milgrom's constant a(0).

This is important in MOND in a way that it isn't in conventional general relativity, because "MOND breaks the strong equivalence principle (but not the weak or Einstein equivalence principle)" with its external field effect.

Can Gravity Help Explain Some Standard Model Constants?

An interesting short paper (five pages) argues that the difference between the CKM matrix parameters and those of the PMNS matrix can be explained with an asymptotically safe gravity extension of the Standard Model.

The quark mixing (CKM) matrix is near-diagonal, whereas the lepton mixing (PMNS) matrix is not. We learn that both observations can generically be explained within an ultraviolet completion of the Standard Model with gravity. 

We find that certain relations between CKM matrix elements should hold approximately because of asymptotically safe regimes, including |Vud|2+|Vus|2≈1 and |Vcd|2+|Vcs|2≈1. Theoretically, the accuracies of these relations determine the length of the asymptotically safe regimes. Experimental data confirms these relations with an accuracy of 10−5 and 10−3, respectively. This difference in accuracies is also expected, because the ultraviolet completion consists in a fixed-point cascade during which one relation is established already much deeper in the ultraviolet. This results in |Vub|2<|Vcb|2 and translates into measurable properties of B-mesons. 

Similar results would hold for the PMNS matrix, if neutrino Yukawa couplings were large. The ultraviolet complete theory therefore must -- and in fact can -- avoid such an outcome. It contains a mechanism that dynamically limits the size of neutrino Yukawa couplings. Below an upper bound on the sum of Dirac neutrino masses, this allows the PMNS matrix to avoid a near-diagonal structure like the CKM matrix. Thus, large neutrino mixing is intimately tied to small Dirac neutrino masses, ∑mν≲(1)eV and a mass gap in the Standard Model fermion masses.

Astrid Eichhorn, Zois Gyftopoulos, Aaron Held, "Quark and lepton mixing in the asymptotically safe Standard Model" arXiv:2507.18304 (July 24, 2025).

Unsolved Physics Problems

 

I would add at least a couple more. 

There are false problems that ask "why doesn't the universe act like I think (for no good reason) that it should?" This includes the hierarchy problem, the strong CP problem, the baryon asymmetry of the universe, and all research invoking the concept of "naturalness."

And, there are contradictory data problems, where one asks why multiple measurements of the same thing (in your current theory) are producing irreconcilable results. These have included the proton radius puzzle, the data based calculation of muon g-2, the measurement of the mean lifetime of unbound neutrons, the reanalysis of CDF data to determine the W boson mass that produced an anomalous result, and the Hubble tension. Usually, in these cases, the answer is that somebody screwed up in one or both of the experiments (at a minimum by overstating the uncertainty in the result), or the theoretical analysis involved, but sometimes, the theory that said the measurements should be the same was wrong.

BSM Physics Constraints In Light Of Muon g-2

The confirmation that the Standard Model prediction for muon g-2 matches the experimental result greatly constrains beyond the Standard Model physics. But how much? 

A new preprint engages with that question.

We review the role of the anomalous magnetic moment of the muon a_mu as a powerful probe of physics beyond the Standard Model (BSM), taking advantage of the final result of the Fermilab g-2 experiment and the recently updated Standard Model value. This review provides both a comprehensive summary of the current status, as well as an accessible entry point for phenomenologists with interests in dark matter, Higgs and electroweak or neutrino and flavour physics in the context of a wide range of BSM scenarios. It begins with a qualitative overview of the field and a collection of key properties and typical results. It then focuses on model-independent, generic formulas and classifies types of BSM scenarios with or without chiral enhancements. A strong emphasis of the review are the connections to a large number of other observables -- ranging from the muon mass and the muon--Higgs coupling and related dipole observables to dark matter, neutrino masses and high-energy collider observables. Finally, we survey a number of well-motivated BSM scenarios such as dark photons, axion-like particles, the two-Higgs doublet model, supersymmetric models and models with leptoquarks, vector-like leptons or neutrino mass models. We discuss the impact of the updated Standard Model value for a_mu and of complementary constraints, exploring the phenomenology and identifying excluded and viable parameter regions.

Peter Athron, Kilian Möhling, Dominik Stöckinger, Hyejung Stöckinger-Kim, "The Muon Magnetic Moment and Physics Beyond the Standard Model" arXiv:2507.09289 (July 12, 2025) (Invited review for Progress in Particle and Nuclear Physics; 274 pages, 50 figures).