Is the Unitarity Triangle Right?

TL;DR

This paper explores whether the near-right angle of the CKM unitarity triangle is coincidental or indicative of new physics, proposing a flavor symmetry model linking quark and lepton mixing properties.

Contribution

It introduces a flavor permutation symmetry framework that connects quark and lepton mixing parameters, predicting a nearly right unitarity triangle angle consistent with experimental data.

Findings

Predicted alpha=89.0±0.2 degrees, matching observations.

Linked smallness of V_ub and U_e3 to mu-tau symmetry.

Forecasted large Dirac CP phase in both sectors.

Abstract

The latest fits to the CKM matrix indicate that alpha=(90.7+4.5-2.9) degrees. The proximity of alpha to a right-angle raises the question: is it merely accidental or is it due to some physics beyond the Standard Model? In the framework of our recently-proposed flavour permutation symmetry, we consider the similarities between the quark and lepton mixing matrices, V and U, arguing that the relative smallness of one element in each suggests common constraints. These constraints link the smallness of V_ub and U_e3 with each other, and with the approximate mu-tau symmetry observed in leptonic mixing, together with a prediction of a large Dirac CP phase in both the quark and lepton sectors. In the quark case, we predict alpha=(89.0\pm 0.2) degrees, in agreement with data and suggesting that the unitarity triangle is in fact very nearly, but not exactly right.