Quark mixing sum rules and the right unitarity triangle

TL;DR

This paper derives quark mixing sum rules for hierarchical mass matrices with texture zeros, explaining the right-angled unitarity triangle and predicting the reactor angle within grand unified theories.

Contribution

It introduces new quark mixing sum rules for specific mass matrix textures and links them to the right-angled unitarity triangle and lepton mixing predictions.

Findings

Right-angled unitarity triangle explained by real mass matrices with a single imaginary element.

Sum rules show phenomenological viability of textures with up to four zeros.

Framework predicts the reactor angle accurately in grand unified theories.

Abstract

In analogy with the recently proposed lepton mixing sum rules, we derive quark mixing sum rules for the case of hierarchical quark mass matrices with 1-3 texture zeros, in which the separate up and down type 1-3 mixing angles are approximately zero, and $V_{ub}$ is generated from $V_{cb}$ as a result of 1-2 up type quark mixing. Using the sum rules, we discuss the phenomenological viability of such textures, including up to four texture zeros, and show how the right-angled unitarity triangle, i.e., $\alpha \approx 90^\circ$, can be accounted for by a remarkably simple scheme involving real mass matrices apart from a single element being purely imaginary. In the framework of grand unified theories we show how the quark and lepton mixing sum rules may combine to yield an accurate prediction for the reactor angle.