Quark mass dependence of hadron masses from lattice QCD

TL;DR

This paper develops a sum-rule framework in lattice QCD to compute derivatives of hadron (meson) masses with respect to sea and valence quark masses, using connected and disconnected three-point functions evaluated on a single gauge ensemble via stochastic propagators and Z2 noise. The authors derive exact identities relating dM/dm_v and dM/dm_s to C_3/C and D_3/C, and implement variational methods to extract ground-state contributions while mitigating excited-state contamination. By applying these techniques to quenched and two-flavor dynamical configurations, they find significant differences in the sea-quark derivative, particularly in the disconnected sector, and discuss how to relate bare lattice parameters to physical quantities through scale-setting with R_0 and implications for J and M_V/M_P. The work provides a practical, efficient route to quantify sea-quark effects in dynamical simulations, with careful consideration of lattice-spacing changes and the interpretation of sea-quark dependence in hadron masses.

Abstract

We discuss lattice methods to obtain the derivatives of a lattice meson mass with respect to the bare sea and valence quark masses. Applications are made to quenched and dynamical fermion configurations. We find evidence for significant differences between quenched and dynamical fermion configurations. We discuss how to relate dependence on the bare lattice parameters to more phenomenologically useful quantities.

Figures (5)

• Figure 1:
• Figure 2: The connected correlation $C_3/C$ versus time $t=t_1+t_2$ in lattice units. The data are for the variational combination that reduces the excited state contribution and are from quenched lattices with $\kappa=0.14077$ with $|t_1-t_2| < 2$. We expect the ground state contribution to be dominant when $t_1 > 2$ and $t_2 > 2$, that is for $t \ge 6$.
• Figure 3: The disconnected correlation $-N_f D_3/C$ with $N_f=2$ versus time $t=t_1+t_2$ in lattice units. The upper data are from dynamical fermions with $\kappa_{\rm sea}=0.139$, while the lower data from quenched lattices with $\kappa=0.13843$. The curves show the two-state fits to these data with $|t_1-t_2|=0$ or 1 as described in the text. The additional points (crosses and octagons) have $|t_1-t_2| =2$ or 3 and are fitted by the dotted curve.
• Figure 4: The lattice evaluation of $R_0$ for dynamical fermion configurations with sea quarks of hopping parameter $\kappa$ from refukqcddf. We define $m_s \equiv 1/\kappa$.
• Figure 5: An illustration of the bare valence ($v$) and sea ($s$) quark mass dependence of pseudoscalar ($P$) and vector ($V$) meson masses in units of $R_0$.