A first look at maximally twisted mass lattice QCD calculations at the physical point

TL;DR

This paper reports a first-principles exploration of maximally twisted mass lattice QCD calculations at the physical point using an Iwasaki gauge action plus a clover term for a mass-degenerate quark doublet. It demonstrates that simulations at the physical pion mass are feasible with moderate lattice spacing (~0.1 fm), showing stable dynamics, linear PCAC behavior, and preliminary agreement of light- and heavy-light pseudoscalar observables with phenomenology. A staged plan to reach $N_f=2+1+1$ flavors is outlined, including stability checks with $N_f=2+2$, a strategy for tuning $c_{sw}$ via a tadpole-improved estimate, and the use of $N_f=4$ runs to inform the heavy sector. The results suggest reduced isospin-breaking artefacts and promising heavy-flavor decay constants, supporting future simulations at multiple lattice spacings and larger volumes.

Abstract

In this contribution, a first look at simulations using maximally twisted mass Wilson fermions at the physical point is presented. A lattice action including clover and twisted mass terms is presented and the Monte Carlo histories of one run with two mass-degenerate flavours at a single lattice spacing are shown. Measurements from the light and heavy-light pseudoscalar sectors are compared to previous $N_f = 2$ results and their phenomenological values. Finally, the strategy for extending simulations to $N_f = 2 + 1 + 1$ is outlined.

Figures (6)

• Figure 1: Monte Carlo histories of the plaquette and the PCAC quark mass.
• Figure 2: Behaviour of the PCAC quark mass as a function of $1/2\kappa$ at the physical point.
• Figure 3: Measurements from the pion sector compared to old results. All errors are statistical only.
• Figure 4: Measurements from the heavy-light pseudoscalar sector as indicated. The blue points correspond to old ETMC $N_f=2$ simulation results while the values from the physical point simulation are shown in red. The experimental value is indicated by the black filled circle. For $f_{D_s}/f_D$, the value of the chiral extrapolation of the old results is given by the filled square. The horizontal axis is given by the pion mass squared on the lattice in physical units, normalized by the physical value of the pion decay constant. All errors are statistical only with auto-correlations taken into account.
• Figure 5: Pictorial representation of the information flow in the $N_f=2+2$, $N_f=4$ and $N_f=2+1+1$ simulation effort. $N_f=2+2$ runs demonstrate stability and extrapolations in a small number of pion masses give $\kappa_c$ at the physical point. The $N_f=4$ simulations at a number of quark mass values provide renormalization constants which are necessary for tuning the heavy sector in the $N_f=2+1+1$ simulations.