The Upsilon spectrum and the determination of the lattice spacing from lattice QCD including charm quarks in the sea

TL;DR

This paper presents lattice QCD calculations of the Upsilon spectrum including charm sea quarks, achieving precise determinations of splittings and quark mass ratios, and providing improved methods for setting the lattice spacing.

Contribution

It introduces an improved NRQCD action with radiative corrections and includes charm sea quarks, enhancing the accuracy of Upsilon spectrum predictions in lattice QCD.

Findings

Upsilon 2S-1S splitting used to determine lattice spacing with high precision

Predicted mass difference between Upsilon and eta_b is 70(9) MeV

Calculated strange quark mass ratio mb/ms = 54.7(2.5)

Abstract

We give results for the Upsilon spectrum from lattice QCD using an improved version of the NRQCD action for b quarks which includes radiative corrections to kinetic terms at O(v^4) in the velocity expansion. We also include for the first time the effect of up, down, strange and charm quarks in the sea using 'second generation' gluon field configurations from the MILC collaboration. Using the {\Upsilon} 2S - 1S splitting to determine the lattice spacing, we are able to obtain the 1P - 1S splitting to 1.4% and the 3S - 1S splitting to 2.4%. Our improved result for M (Upsilon) - M (eta_b) is 70(9) MeV and we predict M(Upsilon) - M(eta_b') = 35(3) MeV. We also calculate pi, K and eta_s correlators using the Highly Improved Staggered Quark action and perform a chiral and continuum extrapolation to give values for M(eta_s) (0.6893(12) GeV) and f_{eta_s} (0.1819(5) GeV) that allow us to tune the strange quark mass as well as providing an independent and consistent determination of the lattice spacing. Combining the NRQCD and HISQ analyses gives mb/ms = 54.7(2.5) and a value for the heavy quark potential parameter of r_1 = 0.3209(26) fm.