Scaling and chiral extrapolation of pion mass and decay constant with maximally twisted mass QCD

TL;DR

The paper tackles the determination of the pion mass $m_\mathrm{PS}$ and decay constant $f_\mathrm{PS}$ in $n_f=2$ QCD using maximally twisted mass fermions, focusing on controlled extrapolations to the continuum, infinite volume, and physical quark masses. It employs large-scale ETMC lattice simulations at $\beta=3.90$ and $4.05$, performing joint fits of $m_\mathrm{PS}$, $f_\mathrm{PS}$, $r_0/a$, and $Z_P$ within ($\chi$PT) at NLO and, where possible, NNLO, including finite-size corrections via CDH and assessing lattice artifacts. The study delivers precise determinations of low-energy constants $\bar{\ell}_3$ and $\bar{\ell}_4$, the chiral condensate $\Sigma^{\overline{MS}}(2\,\mathrm{GeV})$, and the ratio $f_\pi/f_0$, while establishing that lattice artifacts are small and flavour breaking is consistent with zero in the continuum. These results validate maximally twisted mass QCD for reliable chiral and continuum extrapolations and provide important inputs for phenomenology and quark mass determinations.

Abstract

We present an update of the results for pion mass and pion decay constant as obtained by the ETM collaboration in large scale simulations with maximally twisted mass fermions and two mass degenerate flavours of light quarks. We discuss the continuum, chiral and infinite volume extrapolation of these quantities as well as the extraction of low energy constants, and investigate possible systematic uncertainties.

Figures (2)

• Figure 1: (a) Mass splitting $r_0^2((m_\mathrm{PS}^\pm)^2-(m_\mathrm{PS}^0)^2)$ as a function of $(a/r_0)^2$. (b) Data for $r_0f_\mathrm{PS}$ as a function of $r_0\mu_R$ for $\beta=3.90$ and $\beta=4.05$ and Fits A and C.
• Figure 2: (a) Data for $(r_0m_\mathrm{PS})^2/r_0\mu_R$ as a function of $r_0\mu_r$ and Fits A and C. (b) Data for $r_0f_\mathrm{PS}$ as a function of $r_0\mu_R$ and resulting curves of Fit B. The vertical lines indicate the fit range.