Topological susceptibility with a single light quark flavour

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan

^* Speaker, e-mail: jfrison@post.kek.jp

Published online: 26 March 2018

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 θ 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 $m_u^{PCAC}=0$ 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 ≠ m_d. The simulation is repeated for several βs and those results, although preliminary, give a hint about what happens in the continuum limit.