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

Abstract

We compute the low lying eigenvalues of the Hermitian Dirac operator in lattice QCD with $N_{\mathrm{f}}=2+1+1$ twisted mass fermions. We discuss whether these eigenvalues are in the $ϵ$-regime or the $p$-regime of Wilson chiral perturbation theory ($\chi$PT) for twisted mass fermions. Reaching the deep $ϵ$-regime is practically unfeasible with presently typical simulation parameters, but still the few lowest eigenvalues of the employed ensemble evince some characteristic $ϵ$-regime features. With this conclusion in mind, we develop a fitting strategy to extract two low energy constants from analytical $ϵ$-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.

Comments: 28 pages, 7 figures, substantial revision, version accepted for publication in Computer Physics Communications