Twisted mass lattice QCD: Recent developments and results
Andrea Shindler
TL;DR
Twisted mass QCD (tmQCD) is evaluated as a viable discretization for $N_f=2$ light quarks, enabling access to $m_<300$ MeV and potential matching to chiral perturbation theory when coupled with efficient solvers and sufficient volume. The framework yields automatic $O(a)$ improvement for parity-even, multiplicatively renormalizable observables in the fully twisted limit when the untwisted mass is tuned to the critical value $m_0 = m_c$, yielding a renormalized twisted mass $\mu_R$ without additional $O(a)$ terms. The work identifies infrared divergent cutoff effects from mis-tuning the critical mass, and shows that determining $m_c$ from vanishing PCAC mass at fixed $\mu$ and extrapolating to $\mu=0$ removes these artifacts for generic $\mu$, provided $\mu > a\Lambda^2$. It also discusses incorporating lattice artifacts into tm$\chi$PT via different power-counting schemes, guiding interpretation of data near the chiral limit and finite lattice spacing. Overall, tmQCD with proper critical-mass tuning and improved algorithms provides a scalable, renormalization-friendly approach for large-scale lattice QCD with light pions and reliable matching to continuum QCD.
Abstract
I review recent theoretical developments and numerical results of twisted mass QCD. I argue that, combined with an efficient algorithm, twisted mass QCD can be an attractive QCD lattice action, to perform large scale simulations at small pion masses, where a matching with chiral perturbation theory can be performed. Open issues like flavour breaking effects are also addressed.