Improving the Kinetic Couplings in Lattice Non-Relativistic QCD

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 ${\rm Y}(1S)$ and ${\eta }_b(1S)$ kinetic masses, and the tuning of the $b$ quark mass.

arXiv comment19 pages, 14 figures, 9 tables

References in corpus (42)

• Heavy quarkonium: progress, puzzles, and opportunities
• On the Viability of Lattice Perturbation Theory
• Improved Nonrelativistic QCD for Heavy Quark Physics
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• The static potential in QCD to two loops
• High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• Variants of fattening and flavor symmetry restoration
• Constrained Curve Fitting
• Scaling studies of QCD with the dynamical HISQ action
• Radiative Transitions in Charmonium from Lattice QCD
• High-precision quark masses and QCD coupling from $n_f=4$ lattice QCD
• $|V_{ub}|$ from $B\to \pi \ell \nu$ decays and (2+1)-flavor lattice QCD
• B-meson decay constants from improved lattice NRQCD and physical u, d, s and c sea quarks
• Heavy meson masses and decay constants from relativistic heavy quarks in full lattice QCD
• Precise heavy-light meson masses and hyperfine splittings from lattice QCD including charm quarks in the sea
• The Upsilon spectrum and the determination of the lattice spacing from lattice QCD including charm quarks in the sea
• $B_s\to K\ell \nu$ form factors from lattice QCD
• Helicity operators for mesons in flight on the lattice
• The ${\rm Y}$ and ${{\rm Y}}^{\prime }$ Leptonic Widths, $a_{\mu }^b$ and $m_b$ from full lattice QCD
• The Search for Beauty-fully Bound Tetraquarks Using Lattice Non-Relativistic QCD
• Bottomonium spectrum at order v^6 from domain-wall lattice QCD: precise results for hyperfine splittings
• New methods for B meson decay constants and form factors from lattice NRQCD
• Gradient flow and scale setting on MILC HISQ ensembles
• Angular Momentum on the Lattice: The Case of Non-Zero Linear Momentum
• Radiative corrections to the lattice gluon action for highly improved staggered quarks (HISQ) and the effect of such corrections on the static potential
• Prediction of the bottomonium D-wave spectrum from full lattice QCD
• Radiative Corrections to the Kinetic Couplings in Nonrelativistic Lattice QCD
• Tests of Improved Kogut-Susskind Fermion Actions
• One-Loop Matching of the Heavy-Light A_0 and V_0 Currents with NRQCD Heavy and Improved Naive Light Quarks
• Scale setting for alpha_s beyond leading order
• Automated generation of lattice QCD Feynman rules
• Automatically generating Feynman rules for improved lattice field theories
• The mass of the b-quark from lattice NRQCD and lattice perturbation theory
• Bottomonium hyperfine splittings from lattice NRQCD including radiative and relativistic corrections
• Moving NRQCD for heavy-to-light form factors on the lattice
• Excited Upsilon Radiative Decays
• Second Order Perturbation Theory for Improved Gluon and Staggered Quark Actions
• Radiative improvement of the lattice NRQCD action using the background field method with applications to quarkonium spectroscopy
• Fast Fits for Lattice QCD Correlators
• Hindered M1 Radiative Decay of ${\rm Y}(2S)$ from Lattice NRQCD
• Perturbation theory vs. simulation for tadpole improvement factors in pure gauge theories
• TaylUR 3, a multivariate arbitrary-order automatic differentiation package for Fortran 95

Cited by in corpus (1)

• Heavy Quarkonium in Extreme Conditions