A Muon g-2 Recap

Ref. [8] is R. Aliberti et al., The anomalous magnetic moment of the muon in the Standard Model: an update, Phys. Rept. 1143 (2025) 1 [arXiv:2505.21476].

A paper on the latest developments of calculating muon g-2 (the anomalous magnetic moment of the muon which can be calculated in the Standard Model from first principles) in the latest BMW group calculation not only updates their calculation to be more precise (and consistent with the high precision experimental results), but also provide excellent background for the entire enterprise of calculating muon g-2 and comparing it to the experimental results.

The overview of the paper is as follows:

Almost twenty years ago, physicists at Brookhaven National Laboratory measured the magnetic moment of the muon with a remarkable precision of 0.54 parts per million (ppm) [20]. Since that time, the reference Standard Model prediction forth is quantity has exhibited a persistent discrepancy with experiment of more than three sigma [9]. This raises the tantalising possibility of undiscovered forces or elementary particles. The attention of the world was drawn to this discrepancy when Fermilab presented a brilliant confirmation of Brookhaven’s measurement, which brought the discrepancy to 4.2 sigma [21]. In the meantime a very large-scale lattice QCD calculation of a key theoretical contribution was performed by the Budapest-Marseille-Wuppertal (BMW) collaboration [3], as seen in Fig. 1. This result significantly reduces the difference between theory and experiment, suggesting that new physics may not be needed to explain the experimental results. However, it simultaneously introduces a new discrepancy with the existing data-driven determination of this contribution. 

Since then, the experimental [2] results have been updated with significantly improved precision, and the lattice result has been independently confirmed by other lattice collaborations. At the same time, new developments in the data-driven inputs that the lattice calculations replace [17–19] lead to a significant spread in the results depending on what inputs are taken. This has culminated in an updated theory prediction based on the lattice results instead of the data-driven determinations, as seen in Fig. 1. 

In these proceedings, I present a new hybrid calculation that combines an update to the most precise lattice results with data-driven inputs in a low-energy region where the observed discrepancies are not present. This new result leads to aprediction that differs from the experimental measurement by only 0.5𝜎, providing a remarkable validation of the Standard Model to 0.31 ppm.

As Table 1 shows, the main problem is how to more precisely measure the Hadronic Vacuum Polarization (HVP) component more precisely.

According to the abstract: 

The latest results from the Budapest-Marseille-Wuppertal (BMW) and DMZ collaborations, . . . [make] a determination of the hadronic vacuum polarisation contribution to a precision of 0.45%. [i.e. from ± 6.1 to ± 3.2.]

This new calculation is about twice as precise as the previous HVP calculation. 

The conclusion of the paper states that:

Recent lattice QCD results have surpassed the precision of all other theoretical predictions of the hadronic vacuum polarisation contribution to the muon magnetic moment. When taken together with the latest theory consensus for the other contributions [8], these results show excellent agreement with the latest experimental measurements [2]. This a remarkable success for quantum field theory, bringing together diverse computational tools to include all aspects of the Standard Model in a single calculation that validates the Standard Model to 0.31 ppm.

As a practical matter, this further tightens global constrains on low to medium energy deviations from the Standard Model. 

Mirror Universes And Dark Energy?

An interesting idea, coupled to one of the most plausible explanations for baryon asymmetry and what came before the Big Bang, even if it may not actually be provable.

We investigate a possible resolution of the dark energy problem within a pair-universe framework, in which the Universe emerges as an entangled pair of time-reversed sectors. 

In this setting, a global zero-energy condition allows vacuum energy contributions from the two sectors to cancel, alleviating the need for extreme fine-tuning. We propose that the observed dark energy does not originate from vacuum fluctuations but instead arises as an effective entanglement energy between the visible universe and its mirror counterpart. 

Treating the cosmological constant as an integration constant fixed by boundary conditions rather than a fundamental parameter, we show that the cosmological equations can be formulated without explicitly introducing vacuum energy. By imposing physically motivated boundary conditions at the cosmological event horizon, we obtain an integration constant consistent with the observed dark energy density. The parallel mirror world scenario thus provides a unified framework that may simultaneously explain the origins of dark energy and dark matter.

Merab Gogberashvili, Tinatin Tsiskaridze, "Dark Energy from Entanglements with Mirror Universe" arXiv:2603.03385 (March 3, 2026) (published at 8 Physics 29 (2026)).

MOND-like Behavior Within The Milky Way In Milky Way Subsystems

The radial acceleration relation and baryonic Tully-Fischer relation, while not perfect, work far too well to be consistent with almost any dark matter particle theories (ultra-light bosonic dark matter still might be possible to make work).

We test whether parsec-scale stellar systems in the Milky Way follow the galactic radial acceleration relation (RAR) or the baryonic TullyFisher relation (BTFR). 

We analyse 5646 Gaia DR3 open clusters from the Hunt & Reffert catalogue. Observed accelerations are derived from velocity dispersions and characteristic radii, and baryonic accelerations from stellar masses and characterisitc radii. The clusters are placed on the RAR and BTFR planes and compared with Newtonian and MOND expectations. Approximately 90 per cent of open clusters (those with N⋆≤250) lie close to the RAR, albeit with significant scatter. In a first-of-its-kind test, a smaller fiducial sample is consistent with a best-fitting acceleration scale g†≈1.2×10−10 ms−2±0.5 dex, compatible with canonical MOND values. 

More massive clusters approach the Newtonian virial expectation. No correlations are found between RAR residuals and galactocentric radii, distance to the Galactic disk midplane, age, or morphology. Tidal effects and unresolved binaries are insufficient to reproduce the observations without fine-tuning. 

Interpreted within a MOND framework, the alignment of most open clusters with the RAR and BTFR suggests that low-acceleration dynamics operate on parsec scales within the Milky Way. This implies that the Galactic gravitational field is not smooth on these scales and may include regions where the total gravitational acceleration falls below a0, partially mitigating the external field effect, thereby motivating higher-resolution modelling of the Galactic potential and informing other small-scale gravity tests within the Galaxy.

Mark D. Huisjes, X. Hernandez, "Most open clusters follow the radial acceleration relation (RAR) and the baryonic Tully-Fisher relation (BTFR)" arXiv:2603.03522 (March 3, 2026).

The Wide Binary Wars Continue

Neither the astrophysicists who say that there is evidence of MOND in wide binaries, nor those who say there is not, are relenting, and I currently rate the debate as inconclusive.

If this paper is right, it is bad for MOND, but good for Deur, who reproduces MOND behavior in galaxies by another formula and mechanism.

Wide binaries (WBs) offer a unique opportunity to test gravity in the low-acceleration regime, where modifications such as Milgromian dynamics (MOND) predict measurable deviations from Newtonian gravity. 

We construct a rigorous framework for conducting the wide binary test (WBT), emphasizing high quality sample selection, filtering of poor astrometric solutions, contamination mitigation, and uncertainty propagation. We show that undetected close binaries, chance alignments, and improper treatment of projection effects can mimic MOND-like signals. We introduce a checklist of best practices to identify and avoid these pitfalls. Applying this framework to Gaia DR3 data, we compile a high-purity sample of WBs within 130 pc with projected separations of 1 - 30 kAU, spanning the transition between the Newtonian and MOND regimes. 

We find that the scaled relative velocity distribution of wide binaries does not exhibit the 20% enhancement expected from MOND and is consistent with Newtonian gravity across all separations. A meta-analysis of previous WBTs shows that apparent MOND signals diminish as methodological rigour improves. We conclude that when stringent quality controls are applied, there is no observational evidence for MOND-induced velocity boosts in wide binaries. 

Our results place strong empirical constraints on modified gravity theories operating between a0/10 and 200 a0, where a0 is the MOND acceleration scale. Across this range of internal accelerations, Newtonian gravity is up to 1500x more likely than MOND for our cleanest sample.

Stephen A. Cookson, Indranil Banik, Kareem El-Badry, Will Sutherland, Zephyr Penoyre, Charalambos Pittordis, Cathie J. Clarke, "A Quality Framework for Testing Gravity with Wide Binaries: No Evidence for MOND" arXiv:2602.24035 (February 27, 2026) (published in MNRAS).