Flavour Breaking Effects of Wilson twisted mass fermions

Abstract

We study the flavour breaking effects appearing in the Wilson twisted mass formulation of lattice QCD. In this quenched study, we focus on the mass splitting between the neutral and the charged pion, determining the neutral pion mass with a stochastic noise method to evaluate the disconnected contributions. We find that these disconnected contributions are significant. Using the Osterwalder-Seiler interpretation of the connected piece of the neutral pion correlator, we compute the corresponding neutral pion mass to study with more precision the scaling behaviour of the mass splitting.

Figures (2)

• Figure 1: Correlation function ratios (for local operators only) of the neutral to the charged pion correlation functions for both the full correlation functions in eq. (\ref{['correlations']}) and taking only the connected part of the neutral pion correlation function. The solid lines are the corresponding ratios from the fits to these correlation functions. We also indicate the values of mass splitting $\Delta m=m_{\pi^0}-m_{\pi^+} >0$, see also table \ref{['table:datastochastic']}.
• Figure 2: Relative pion mass difference as function of $(a/r_0)^2$ at two fixed values of the charged pion mass employing the pion and the PCAC definitions of the critical point.