Topological susceptibility with a single light quark flavour

TL;DR

This paper investigates whether the topological susceptibility vanishes when the up quark mass approaches zero, using lattice QCD simulations with Wilson-like fermions, to address a key aspect of the strong CP problem.

Contribution

It provides empirical progress on testing the vanishing of topological susceptibility at zero up quark mass with $N_f=1+2$ clover fermions, considering scheme dependence and non-perturbative effects.

Findings

Preliminary results suggest the topological susceptibility behavior near zero up quark mass.

Simulations across multiple $eta$ values indicate possible trends towards the continuum limit.

Amplification of non-perturbative effects due to mass differences is observed.

Abstract

One of the historical suggestions to tackle the strong CP problem is to take the up quark mass to zero while keeping $m_d$ finite. The $\theta$ angle is then supposed to become irrelevant, i.e. the topological susceptibility vanishes. However, the definition of the quark mass is scheme-dependent and identifying the $m_u=0$ point is not trivial, in particular with Wilson-like fermions. More specifically, up to our knowledge there is no theoretical argument guaranteeing that the topological susceptibility exactly vanishes when the PCAC mass does. We will present our recent progresses on the empirical check of this property using $N_f=1+2$ flavours of clover fermions, where the lightest fermion is tuned very close to $m^{PCAC}_u$=0 and the mass of the other two is kept of the order of magnitude of the physical $m_s$. This choice is indeed expected to amplify any unknown non-perturbative effect caused by $m_u\not=m_d$. The simulation is repeated for several $\beta$s and those results, although preliminary, give a hint about what happens in the continuum limit.