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).
Robert Wilson, a group theorist mathematician blogger who has taken aim at physics, has written some interesting speculations about the impact of gravity on measurements of the masses of subatomic particles. For example, see
ReplyDeletehttps://robwilson1.wordpress.com/2025/07/23/a-dynamic-dirac-equation/
where he discusses modifying the standard model's Dirac equation to reflect the gravitational background.
There is no doubt that gravity has some effect. But, the strength of the gravitational field at the fundamental particle and individual hadron scale is so tiny that any gravitational effect is likely to be far smaller than the uncertainty in those measurements from other causes. Also, the strong equivalence principle, to the extent that it holds, should prevent that from mattering in most cases.
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