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arXiv · 1812.11639

Improving the Kinetic Couplings in Lattice Non-Relativistic QCD

Christine T. H. Davies·Judd Harrison·Ciaran Hughes·Ronald R. Horgan·Georg M. von Hippel·Matthew Wingate
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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.

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Christine T. H. Davies, Judd Harrison, Ciaran Hughes, Ronald R. Horgan, Georg M. von Hippel, Matthew Wingate. 2018-12-30. Improving the Kinetic Couplings in Lattice Non-Relativistic QCD. https://doi.org/10.1103/physrevd.99.054502

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