Wilson Chiral Perturbation Theory for twisted mass QCD at NLO

Abstract

We investigate the quark mass dependence of pion sectors in the twisted mass lattice QCD, using the Wilson Chiral Perturbation Theory (WChPT). In order to consider the small quark mass regime such that m q ∼ a 2 Λ 3 , we include O(a 2 , am) terms at the leading order (LO), which induce a non-trivial phase structure at the tree level. At the next leading order (NLO), due to the presence of the twisted mass, not only pion masses but also a vacuum expectation of the neutral pion have divergences, which must be removed by local counter terms at the NLO. We demonstrate that cancellations of these divergences can be consistently performed within a framework of the WChPT. As an interesting application of the NLO calculation, we derive the twisted quark mass dependence of the pion mass at the maximal twist where the PCAC quark mass vanishes.

Determination of low-energy constants of Wilson chiral perturbation theory

“…Before closing this section, we mention that WχPT calculations at NLO have been carried out for the pion mass and decay constant with N f = 2 [52][53][54] and N f = 2+1+1 [55] flavours of twisted mass fermions.…”