Lattice QCD with two light Wilson quarks and maximally twisted mass

TL;DR

The paper reports on the European Twisted Mass Collaboration's two-flavour lattice QCD program using maximally twisted mass fermions, achieving automatic $O(a)$ improvement at lattice spacings down to $a\approx 0.07$ fm and pseudoscalar masses near $300$ MeV. It demonstrates small lattice artifacts in charged observables, describes finite-size effects via continuum CHPT, and performs combined CHPT fits to extract low-energy constants, quark masses, and the lattice scale, cross-validating with nucleon masses. It also quantifies flavor-breaking effects that primarily affect the neutral pseudoscalar sector, and presents broader results for strange and charm masses, decay constants, and epsilon-regime condensates, with plans to extend to $2+1+1$ flavours. Overall, the work shows that maximally twisted mass QCD provides controlled discretisation errors and a solid path toward precise hadronic phenomenology from lattice simulations.

Abstract

We summarise status and recent results of the European Twisted Mass collaboration (ETMC). The collaboration has generated gauge configurations for three different values of the lattice spacing smaller or equal 0.1 fm and values of the charged pseudo scalar mass as low as 300 MeV with two flavours of maximally twisted mass quarks. We provide evidence that O(a) improvement works very well with maximally twisted mass fermions and that also higher order lattice artifacts appear to be small. The currently only quantity in the light meson and baryon sector where cut-off effects are visible is the neutral pseudo scalar meson mass and we present an attempt to understand this from a theoretical point of view. We describe finite size effects and quark mass dependence of the mass and decay constant of the (charged) pseudo scalar meson with chiral perturbation theory formulae and our current estimate for the low energy constants l_{3,4} is l_3=3.44(8)(35) and l_4=4.61(4)(11). Results for the average up-down, the strange and the charm quark mass and the chiral condensate are also presented.

Figures (7)

• Figure 1: (a) $f_\mathrm{PS}\ [\mathrm{MeV}]$ as a function of $a^2[\mathrm{fm}^2]$ in the quenched approximation Jansen:2005kk. (b) Monte Carlo history of $P-\langle P\rangle$ and $\Delta H$ for ensemble $C_1$.
• Figure 2: (a) Comparison of the cost estimate we measure for the mtmHMC (data points) to the DD-HMC (lines). For the DD-HMC we used Eq.(3.1). The upper (lower) line compares to the $\beta=4.05$ ($\beta=3.9$) data points. (b) $r_0/a$ as a function of $(a\mu)^2$ for $\beta=3.9$. The line represents a linear extrapolation in $(a\mu)^2$ to the chiral limit.
• Figure 3: (a) renormalised PCAC quark mass against renormalised twisted mass for $\beta=3.9$ and $\beta=4.05$. The statistical uncertainty on $Z_\mathrm{P}$ is not included. (b) Effective mass plot for the charged pseudo scalar mass for ensemble $B_1$, $B_3$ and $B_5$. The lines represent the fitted value for $am_\mathrm{PS}$.
• Figure 4: (a) $r_0f_\mathrm{PS}$ as a function of $(r_0m_\mathrm{PS})^2$ for $\beta=3.9$ ($B_1$ to $B_5$) and $\beta=4.05$ ($C_1$ to $C_4$). (b) Continuum extrapolation of $f_\mathrm{PS}$ at fixed volume for three reference values of $r_0m_\mathrm{PS}$. The data points at $\beta=3.8$ are not used.
• Figure 5: (a) Relative finite size effects for ensembles $C_2$, $C_5$ and $C_6$. The line represents a fit with formula (\ref{['eq:fit']}) to our data. (b) $f_\mathrm{PS}/f_0$ as a function of $\chi_\mu/f_0^2$ as obtained from a combined fit to $\chi$PT formulae. The dashed line is the fitted function Eq. (\ref{['eq:chirfo2']}), and the data points are FS corrected.