Leptonic widths of heavy quarkonia: Swave QCD/NRQCD matching coefficients for the electromagnetic vector annihilation current at O({alpha}{sub s}v{sup 2})
Abstract
We construct the Swave part of the electromagnetic vector annihilation current to O({alpha}{sub s}v{sup 2}) 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{sup P}=1{sup }, and the coefficients are determined by matching this lattice current to the corresponding continuum current in QCD to O(v{sup 2}) at oneloop. 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 Coulombexchange 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,more »
 Authors:
 SUPA, School of Physics, University of Edinburgh, Edinburgh EH9 3JZ (United Kingdom)
 Department of Physics, University of Regina, Regina, Saskatchewan S4S 0A2 (Canada)
 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Cambridge CB3 0WA (United Kingdom)
 Publication Date:
 OSTI Identifier:
 20933223
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevD.75.014008; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANNIHILATION; B QUARKS; C QUARKS; COMPUTERIZED SIMULATION; GLUONS; LATTICE FIELD THEORY; MASS; MESONS; PARTICLE DECAY; PARTICLE WIDTHS; QUANTUM CHROMODYNAMICS; QUANTUM NUMBERS; QUARKQUARK INTERACTIONS; QUARKONIUM; S WAVES; SINGULARITY; T QUARKS; VECTOR CURRENTS
Citation Formats
Hart, A., Hippel, G. M. von, and Horgan, R. R. Leptonic widths of heavy quarkonia: Swave QCD/NRQCD matching coefficients for the electromagnetic vector annihilation current at O({alpha}{sub s}v{sup 2}). United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.014008.
Hart, A., Hippel, G. M. von, & Horgan, R. R. Leptonic widths of heavy quarkonia: Swave QCD/NRQCD matching coefficients for the electromagnetic vector annihilation current at O({alpha}{sub s}v{sup 2}). United States. doi:10.1103/PHYSREVD.75.014008.
Hart, A., Hippel, G. M. von, and Horgan, R. R. Mon .
"Leptonic widths of heavy quarkonia: Swave QCD/NRQCD matching coefficients for the electromagnetic vector annihilation current at O({alpha}{sub s}v{sup 2})". United States.
doi:10.1103/PHYSREVD.75.014008.
@article{osti_20933223,
title = {Leptonic widths of heavy quarkonia: Swave QCD/NRQCD matching coefficients for the electromagnetic vector annihilation current at O({alpha}{sub s}v{sup 2})},
author = {Hart, A. and Hippel, G. M. von and Horgan, R. R.},
abstractNote = {We construct the Swave part of the electromagnetic vector annihilation current to O({alpha}{sub s}v{sup 2}) 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{sup P}=1{sup }, and the coefficients are determined by matching this lattice current to the corresponding continuum current in QCD to O(v{sup 2}) at oneloop. 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 Coulombexchange 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 {upsilon} meson.},
doi = {10.1103/PHYSREVD.75.014008},
journal = {Physical Review. D, Particles Fields},
number = 1,
volume = 75,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}

QCD predictions for annihilation decays of {ital P}wave quarkonia to nexttoleading order in {alpha}{sub {ital s}}
The decay rates of {ital P}wave heavy quarkonia to light hadrons are presented to leading order in {ital v}{sup 2} and nexttoleading order in {alpha}{sub {ital s}}. They include contributions from both the colorsinglet component and the coloroctet component of quarkonia. Applying these results to charmonium and using measured decay rates for the {chi}{sub {ital c}1} and {chi}{sub {ital c}2} by E760, we determine the two nonperturbative decay matrix elements, and then predict the hadronic decay rates of {chi}{sub {ital c}0} and {ital h}{sub {ital c}}, and the electromagnetic decay rates of {chi}{sub {ital c}0} and {chi}{sub {ital c}2}. Themore » 
Gluonic and leptonic decays of heavy quarkonia and the determination of {alpha}{sub {ital s}}({ital m}{sub {ital c}}) and {alpha}{sub {ital s}}({ital m}{sub {ital b}})
The determination of the QCD running coupling constants {alpha}{sub {ital s}}({ital m}{sub {ital c}}) and {alpha}{sub {ital s}}({ital m}{sub {ital b}}) is studied with heavy quarkonia {ital cc{vert_bar}} and {ital bb{vert_bar}} decays. The decay rates of {ital V}{implies}3{ital g} and {ital V}{implies}{ital e}{sup +}{ital e}{sup } for {ital V}={ital J}/{psi} and {upsilon} are given in terms of the BetheSalpeter amplitudes. To the firstorder relativistic correction of onshell quarks, for the leptonic decay, we have {gamma}({ital V}{implies}{ital e}{sup +}{ital e}{sup }) =(4{pi}{alpha}{sup 2}{ital e}{sub {ital Q}}{sup 2}/{ital m}{sub {ital Q}}{sup 2}){vert_bar}F{ital d}{sup 3}{ital q} [1(2{ital q}{searrow}{sup 2}/3{ital m}{sub {ital Q}}{sup 2})]{psi}{submore » 
Nonrelativistic QCD predictions of Dwave quarkonia {sup 3}D{sub J}(J=1,2,3) decay into light hadrons at order {alpha}{sub s}{sup 3}
In this paper, in the framework of nonrelativistic QCD we study the light hadron (LH) decays of the spintriplet (S=1) Dwave heavy quarkonia. The shortdistance coefficients of all Fock states in the {sup 3}D{sub J} (J=1, 2, 3) quarkonia including the Dwave color singlet, Pwave color octet, and Swave color singlet and color octet are calculated perturbatively at {alpha}{sub s}{sup 3} order. The operator evolution equations of the fourfermion operators are also derived and are used to estimate the numerical values of the longdistance matrix elements. We find that for the cc system, the LH decay widths of {psi}(1{sup 3}D{submore »