Lattice QCD results for the topological up-quark mass contribution: too small to rescue the $m_u=0$ solution to the strong CP problem

TL;DR

This study uses lattice QCD to compute the topological contribution to the up-quark mass, finding it too small to resolve the strong CP problem via a massless up-quark hypothesis.

Contribution

First direct lattice calculation of the topological up-quark mass contribution, providing quantitative evidence against the massless up-quark solution to the strong CP problem.

Findings

Topological mass contribution is an order of magnitude too small.

Rules out the massless up-quark solution to the strong CP problem.

Supports previous phenomenological and lattice results.

Abstract

A vanishing Yukawa coupling of the up quark could in principle solve the strong CP problem. To render this solution consistent with current algebra results, the up quark must receive an alternative mass contribution that conserves CP symmetry. Such a contribution could be provided by QCD through non-perturbative topological effects, including instantons. In this talk, we present the first direct lattice computation of this topological mass contribution, using gauge configurations generated by the Extended Twisted Mass collaboration. We use the Iwasaki gauge action, Wilson twisted mass fermions at maximal twist, and dynamical up, down, strange and charm quarks. Our result for the topological mass contribution is an order of magnitude too small to account for the phenomenologically required up-quark mass. This rules out the "massless" up-quark solution to the strong CP problem, in accordance with previous results relying on $\chi$PT fits to lattice data. The talk is based on [Alexandrou et al., PRL 125, 232001 (2020)], where more details can be found.