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).