Heavy Dynamical Fermions in Lattice QCD

TL;DR

This paper derives a simple formula for how heavy dynamical fermions affect the gauge coupling in lattice QCD and compares it with numerical simulations, revealing both agreement and complex effects at different quark masses.

Contribution

It provides a new analytical expression for the gauge coupling shift due to heavy fermions and compares it with numerical results, highlighting limitations at high flavor numbers.

Findings

Analytical formula matches simulations for light quarks

Heavy flavors cause additional effects beyond coupling shift

Confinement-deconfinement transitions observed at zero coupling with many heavy quarks

Abstract

It is expected that the only effect of heavy dynamical fermions in QCD is to renormalize the gauge coupling. We derive a simple expression for the shift in the gauge coupling induced by $N_f$ flavors of heavy fermions. We compare this formula to the shift in the gauge coupling at which the confinement-deconfinement phase transition occurs (at fixed lattice size) from numerical simulations as a function of quark mass and $N_f$. We find remarkable agreement with our expression down to a fairly light quark mass. However, simulations with eight heavy flavors and two light flavors show that the eight flavors do more than just shift the gauge coupling. We observe confinement-deconfinement transitions at $\beta=0$ induced by a large number of heavy quarks. We comment on the relevance of our results to contemporary simulations of QCD which include dynamical fermions.