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 Non-Perturbative QCD Have A Cosmological Constant Analog?

A new paper explores a potential parallel between non-perturbative quantum chromodynamics (the physics of the strong force that binds quarks into hadronic structures) and gravity. This isn't entirely surprising, as both are non-abelian gauge theories. And, it suggests that features like the cosmological constant may have a natural source in a non-abelian quantum gravity theory.

Einsteins gravity with a cosmological constant Λ in four dimensions can be reformulated as a λϕ^4 theory characterized solely by the dimensionless coupling λ∝G(N)Λ (G(N) being Newton's constant). The quantum triviality of this theory drives λ → 0, and a deviation from this behavior could be generated by matter couplings. Here, we study the significance of this conformal symmetry and its breaking in modeling non-perturbative QCD. The hadron spectra and correlation functions are studied holographically in an AdS(5) geometry with induced cosmological constants on four-dimensional hypersurface. 

Our analysis shows that the experimentally measured spectra of the ρ and a(1) mesons, including their excitations and decay constants, favour a non-vanishing induced cosmological constant in both hard-wall and soft-wall models. Although this behavior is not as sharp in the soft-wall model as in the hard-wall model, it remains consistent. Furthermore, we show that the correction to the Gell-Mann-Oakes-Renner relation has an inverse dependence on the induced cosmological constant, underscoring its significance in holographic descriptions of low-energy QCD.

Mathew Thomas Arun, Nabeel Thahirm, "On the role of cosmological constant in modeling hadrons" arXiv:2510.06380 (October 7, 2025).

A New Paper Argues For Dark Matter Over MOND

This paper argues for dark matter particles rather than modified gravity based upon observations of very low mass dwarf galaxies, although it has a very small sample size of just twelve galaxies.

A tight correlation between the baryonic and observed acceleration of galaxies has been reported over a wide range of mass (10^8 < Mbar/M⊙ < 10^11) - the Radial Acceleration Relation (RAR). This has been interpreted as evidence that dark matter is actually a manifestation of some modified weak-field gravity theory. 

In this paper, we study the radially resolved RAR of 12 nearby dwarf galaxies, with baryonic masses in the range 10^4 < Mbar/M⊙ < 10^7.5, using a combination of literature data and data from the MUSE-Faint survey. We use stellar line-of-sight velocities and the Jeans modelling code GravSphere to infer the mass distributions of these galaxies, allowing us to compute the RAR. We compare the results with the EDGE simulations of isolated dwarf galaxies with similar stellar masses in a ΛCDM cosmology. 

We find that most of the observed dwarf galaxies lie systematically above the low-mass extrapolation of the RAR. Each galaxy traces a locus in the RAR space that can have a multi-valued observed acceleration for a given baryonic acceleration, while there is significant scatter from galaxy to galaxy. 

Our results indicate that the RAR does not apply to low-mass dwarf galaxies and that the inferred baryonic acceleration of these dwarfs does not contain enough information, on its own, to derive the observed acceleration. 

The simulated EDGE dwarfs behave similarly to the real data, lying systematically above the extrapolated RAR. We show that, in the context of modified weak-field gravity theories, these results cannot be explained by differential tidal forces from the Milky Way, nor by the galaxies being far from dynamical equilibrium, since none of the galaxies in our sample seems to experience strong tides. As such, our results provide further evidence for the need for invisible dark matter in the smallest dwarf galaxies.

Mariana P. Júlio, et al., "The radial acceleration relation at the EDGE of galaxy formation: testing its universality in low-mass dwarf galaxies" arXiv:2510.06905 (October 8, 2025) (Accepted for publication in A&A).

How Flat Is The Universe?

The planet Earth is, to a good approximation, a perfect sphere. But, it isn't perfectly spherical.

Space-time in the universe as a whole is, to a good approximation, perfectly Euclidian. But, it has some curvature.

The magnitude by which the Earth differs from being a perfect sphere (in relative terms) is roughly similar to the magnitude by which the universe differs from being perfectly Euclidian. And, both on average and at the greatest extremes, Earth differs less from being perfectly spherical in relative terms, than the space-time of the universe differs from being perfectly Euclidean.