Strange quarks in quenched twisted mass lattice QCD

TL;DR

This work extends twisted mass lattice QCD to a two-doublet SU(4) framework to study strange hadrons in quenched QCD, deriving the corresponding tm$ ext{ChPT}$ and applying it to kaon spectra and decay constants. It demonstrates $O(a)$ improvement at maximal twist and provides explicit NLO expressions for kaon masses and $f_K$, including flavor breaking and lattice discretization effects. Numerical simulations at three lattice spacings reveal linear dependence of $m_K^2$ on the summed twisted masses, a small but nonzero $m_{K^0}-m_{K^±}$ that scales with $a^2$, and decay constants consistent with tm$ ext{ChPT}$ expectations, along with notable parity- and flavor-breaking effects intrinsic to twisted formulations. The study also contrasts twisted vs untwisted strange quark implementations, highlights scalar–pseudoscalar mixing in the neutral sector, and discusses implications for future dynamical simulations and mixed-action strategies to reach realistic three-flavor QCD phenomenology.

Abstract

Two twisted doublets, one containing the up and down quarks and the other containing the strange quark with an SU(2)-flavor partner, are used for studies in the meson sector. The relevant chiral perturbation theory is presented, and quenched QCD simulations (where the partner of the strange quark is not active) are performed. Pseudoscalar meson masses and decay constants are computed; the vector and scalar mesons are also discussed. A comparison is made to the case of an untwisted strange quark, and some effects due to quenching, discretization, and the definition of maximal twist are explored.

Figures (12)

• Figure 1: Pseudoscalar meson mass squared as a function of the sum of quark and antiquark twisted mass parameters. Subscripts $l$ and $h$ indicate the light and heavy doublets. Results labelled by method (i) are from the present work; results labelled by method (ii) are from Ref. flavorbreaking and have equal masses for the quark and anti-quark. Straight lines are linear fits to the data from method (i).
• Figure 2: The difference between charged and neutral squared pseudoscalar meson masses as a function of the sum of quark and antiquark twisted masses. Subscripts $l$ and $h$ indicate the light and heavy doublets.
• Figure 3: The difference between charged and neutral squared pseudoscalar meson masses as a function of squared lattice spacing, for selected values of the charged meson mass.
• Figure 4: The pseudoscalar meson decay constant as a function of the squared charged pseudoscalar meson mass. Results labelled by method (i) are from the present work; results labelled by method (ii) are from Ref. scaling. Straight lines are linear fits to the data from method (i).
• Figure 5: Scaling of the pseudoscalar decay constant for four choices of the quark mass.