Quark and lepton mixing in the asymptotically safe Standard Model

TL;DR

This paper proposes that the observed patterns of quark and lepton mixing matrices can be explained by an ultraviolet complete Standard Model with gravity, predicting specific relations and constraints on mixing parameters and neutrino masses.

Contribution

It introduces a framework where asymptotically safe gravity influences flavor mixing, deriving testable relations and mechanisms for neutrino mass and mixing behavior.

Findings

Relations between CKM matrix elements are approximately valid and experimentally confirmed.

Differences in relation accuracies reflect the ultraviolet regime structure.

Large neutrino mixing is compatible with small neutrino masses and a fermion mass gap.

Abstract

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 $|V_{ud}|^2+|V_{us}|^2 \approx 1$ and $|V_{cd}|^2+|V_{cs}|^2\approx 1$. 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 $|V_{ub}|^2 < |V_{cb}|^2$ 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, $\sum m_{\nu} \lesssim {\mathcal{O}} (1)\, \rm eV$ and a mass gap in the Standard Model fermion masses.