# Improving the Kinetic Couplings in Lattice Non-Relativistic QCD

## TL;DR

This paper enhances lattice NRQCD by calculating higher-order kinetic corrections, determining one-loop matching coefficients, and testing the impact on bottomonium mass calculations using multiple lattice spacings.

## Contribution

The work introduces improved kinetic operators in lattice NRQCD with one-loop corrections and assesses their effects on bottomonium mass determinations.

## Key findings

- Improved dispersion relation accuracy up to (p^6)
- One-loop matching coefficients for kinetic operators determined
- Enhanced bottomonium mass precision with new corrections

## Abstract

We improve the non-relativistic QCD (NRQCD) action by comparing the dispersion relation to that of the continuum through $\mathcal{O}(p^6)$ in perturbation theory. The one-loop matching coefficients of the $\mathcal{O}(p^4)$ kinetic operators are determined, as well as the scale at which to evaluate $\alpha_s$ in the $V$-scheme for each quantity. We utilise automated lattice perturbation theory using twisted boundary conditions as an infrared regulator. The one-loop radiative corrections to the mass renormalisation, zero-point energy and overall energy-shift of an NRQCD $b$-quark are also found. We also explore how a Fat$3$-smeared NRQCD action and changes of the stability parameter $n$ affect the coefficients. Finally, we use gluon field ensembles at multiple lattice spacing values, all of which include $u$, $d$, $s$ and $c$ quark vacuum polarisation, to test how the improvements affect the non-perturbatively determined $\Upsilon(1S)$ and $\eta_b(1S)$ kinetic masses, and the tuning of the $b$ quark mass.