Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · hep-lat/9802038

Tadpole renormalization and relativistic corrections in lattice NRQCD

Norman H. Shakespeare·Howard D. Trottier
View original source ↗Read source document ↗Export metadata ↓

Abstract

We make a comparison of two tadpole renormalization schemes in the context of the quarkonium hyperfine splittings in lattice NRQCD. Improved gauge-field and NRQCD actions are analyzed using the mean-link $u_{0,L}$ in Landau gauge, and using the fourth root of the average plaquette $u_{0,P}$. Simulations are done for $c\bar c$, $b\bar c$, and $b\bar b$ systems. The hyperfine splittings are computed both at leading and at next-to-leading order in the relativistic expansion. Results are obtained at lattice spacings in the range of about 0.14~fm to 0.38~fm. A number of features emerge, all of which favor tadpole renormalization using $u_{0,L}$. This includes much better scaling behavior of the hyperfine splittings in the three quarkonium systems when $u_{0,L}$ is used. We also find that relativistic corrections to the spin splittings are smaller when $u_{0,L}$ is used, particularly for the $c\bar c$ and $b\bar c$ systems. We also see signs of a breakdown in the NRQCD expansion when the bare quark mass falls below about one in lattice units. Simulations with $u_{0,L}$ also appear to be better behaved in this context: the bare quark masses turn out to be larger when $u_{0,L}$ is used, compared to when $u_{0,P}$ is used on lattices with comparable spacings. These results also demonstrate the need to go beyond tree-level tadpole improvement for precision simulations.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Norman H. Shakespeare, Howard D. Trottier. 1998-03-09. Tadpole renormalization and relativistic corrections in lattice NRQCD. https://doi.org/10.1103/physrevd.58.034502

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Can multi-level Monte-Carlo address the sign problem in a finite-density Bose gas?

Numerical simulation of field theories with complex actions is frustrated by the sign problem, which causes an exponential growth in statistical sampling noise. A key example of such a theory is QCD at finite baryon chemical potential, which has important applications to the structure of atomic nuclei and neutron stars. Until now, the sign problem has precluded the possibility of first-principles numerical calculations that could provide key insight into these important physical systems. In this work, we propose an approach to avoiding this limitation by applying a reweighting procedure coupled with a multi-level Monte-Carlo sampling algorithm that offers an exponential enhancement of statistics to counteract the sign problem. We test the approach on a simpler model that displays the same sign problem at finite chemical potential. Our results demonstrate the promise of the proposed approach, significantly increasing the range over which precise calculations are possible, and providing improvements all the way up to the phase transition.

hep-lat↗
arXiv2026

A Note On Lattice Definition of Gauge Theories With Chiral Fermions

Because of the fermion doubling problem, it has been a longstanding challenge to describe a lattice algorithm for studying four-dimensional gauge theories coupled to chiral fermions. Recently, an algorithm to do so has been described by Craig, extending partial results in the previous literature. Here we describe a variant of this algorithm, based on interpolating a lattice gauge field over the continuum (as in Craig's work) and coupling the interpolated gauge field to continuum chiral fermions. The same variant was also proposed recently by Hsu. In any dimension and for any anomaly-free representation, this approach can be implemented on a computer in principle, but not in practice by Monte Carlo methods because the chiral fermion path integral is not positive.

hep-lat↗
arXiv2026

2+1 flavor light hadron spectrum with PACS10 configurations

We present the results for the hadron spectrum, the pseudoscalar meson decay constants, and the quark mass ratio in the continuum limit using the ``PACS10'' gauge configurations generated with the $O(a)$-improved Wilson quark action and the Iwasaki gauge action. Numerical simulations are carried out at three lattice spacings keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. We calculate physical quantities with two choices of conventions to define pseudoexperimental values expected in the isosymmetric QCD. In order to investigate the finite size effects on the physical quantities we have additionally generated the (5.4 fm$)^4$ lattice at the coarsest lattice spacing of $a=0.08487(14)$~fm, which is a hypercube with half the length in each direction compared to the PACS10 configurations. While the finite size effect is hardly observed in comparison of the hadron effective masses on the (10.9 fm$)^4$ and (5.4 fm$)^4$ lattices, the results for the pseudoscalar meson decay constants show discrepancies beyond the error bars. The (5.4 fm$)^4$ lattice also serves for determining the expansion parameters of the pseudoscalar meson masses and decay constants, and the octet baryon masses in terms of the quark masses around the physical point with the aid of the mass reweighting technique. The expansion parameters are used for the fine-tuning of the physical point employing the pseudoexperimental masses of the $π$ meson, $K$ meson, and the $Ξ$ baryon as physical inputs in each convention. We compare the results for the octet baryon masses and the pseudoscalar decay constants in the continuum limit with the corresponding pseudoexperimental values in both conventions. We also discuss the deviation between two results with different conventions. As for the quark mass ratio the result is compared with the recent FLAG summary.

hep-lat↗