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.
Highlights
The Standard Model (SM) of particle physics has been incredibly successful at describing experimental data to date [1,2]
In many ways, this success has been a double-edged sword; while SM predictions have overwhelmingly agreed with experimental measurements within errors, this has left little room for large new-physics effects to be observed
The authors of Ref. [12] show that using Lie group elements when constructing the lattice field theory introduces unphysical tadpole diagrams which do not contribute to continuum schemes
Summary
The Standard Model (SM) of particle physics has been incredibly successful at describing experimental data to date [1,2]. The kinetic couplings can be found perturbatively by matching the NRQCD on shell energy (which corresponds to the location of the pole of the quark propagator in the interacting theory) to the continuum QCD dispersion relation. The aim of this study is to determine the one-loop coefficients cð11Þ, cð51Þ, δC (and Zðm1Þ and W0) for different improved NRQCD actions to find the best way forward for increasingly accurate nonperturbative calculations in the future. Before these coefficients can be used, it is first necessary to remove unphysical contributions from tadpole diagrams which can cause the coefficients to be rather large [12]
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call