Leptonic widths of heavy quarkonia:S-wave QCD/NRQCD matching coefficients for the electromagnetic vector annihilation current atO(αsv2)

2006/05/31 by A. Hart, Georg von Hippel, G. M. von Hippel +1 · 1 citation
Physics and Astronomy · #Annihilation #Gluon #High-Energy Particle Collisions Research #Lattice (music) #Lattice QCD #Lattice field theory #Mathematical physics #Meson #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quark #hep-lat

paper · pdf · doi:10.1103/physrevd.75.014008

published as Phys.Rev.D75:014008,2007 · Corrections to section VA

arxiv created 2007/01/04 · openalex publication_date 2007/01/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We construct the S-wave part of the electromagnetic vector annihilation current to O(\ensuremathα_sv²) on the lattice for heavy quarks whose dynamics are described by the NRQCD action, and v is the nonrelativistic quark velocity inside the meson. The lattice vector current for QQ annihilation is expressed as a linear combination of lattice operators with quantum numbers L=0, J^P=1^\ensuremath-, and the coefficients are determined by matching this lattice current to the corresponding continuum current in QCD to O(v²) at one-loop. The annihilation channel gives a complex amplitude and a proper choice for the contours of integration is needed; a simple Wick rotation is not possible. In this way, and with a careful choice of subtraction functions in the numerical integration, the Coulomb-exchange and infrared singularities appearing in the amplitudes are successfully treated. The matching coefficients are given as a function of the heavy quark mass Ma in lattice units. An automated vertex generation program written in Python is employed, allowing us to use a realistic NRQCD action and an improved gluon lattice action. A change in the definition of either action is easily accommodated in this procedure. The final result, when combined with lattice simulation results, describes the electromagnetic decays of heavy quarkonia, notably the \ensuremathΥ meson.

Citations

• Discovery of a Narrow Resonance ine+e−Annihilation
• Υspectrum andmbfrom full lattice QCD
• Experimental Observation of a Heavy ParticleJ
• Heavy-quark self-energy in nonrelativistic lattice QCD
• Observation of a Dimuon Resonance at 9.5 GeV in 400-GeV Proton-Nucleus Collisions
• Perturbation theory versus simulation for tadpole improvement factors in pure gauge theories
• Improved nonrelativistic QCD for heavy-quark physics
• The mass-centre in the restricted theory of relativity and its connexion with the quantum theory of elementary particles
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• Automated generation of lattice QCD Feynman rules