Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data - a case study

TL;DR

This study analyzes the low eigenvalues of the Hermitian Dirac operator in lattice QCD with twisted mass fermions, using chiral perturbation theory to extract low energy constants and compare theoretical predictions with lattice data.

Contribution

It develops a fitting strategy to extract low energy constants from eigenvalues in the $oldsymbol{ ext{epsilon}}$-regime, linking lattice data with chiral perturbation theory predictions.

Findings

Eigenvalues show features of the $oldsymbol{ ext{epsilon}}$-regime.

Extracted the chiral condensate and $oldsymbol{W_8}$ constant.

Proposed improvements for theoretical and lattice computations.

Abstract

We compute the low lying eigenvalues of the Hermitian Dirac operator in lattice QCD with $N_{\rm f} = 2+1+1$ twisted mass fermions. We discuss whether these eigenvalues are in the $\epsilon$-regime or the $p$-regime of Wilson chiral perturbation theory ($\chi$PT) for twisted mass fermions. Reaching the deep $\epsilon$-regime is practically unfeasible with presently typical simulation parameters, but still the few lowest eigenvalues of the employed ensemble evince some characteristic $\epsilon$-regime features. With this conclusion in mind, we develop a fitting strategy to extract two low energy constants from analytical $\epsilon$-regime predictions at a fixed index. Thus, we obtain results for the chiral condensate and the low energy constant $W_8$. We also discuss how to improve both the theoretical calculation and the lattice computation.