skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks

Abstract

We present a lattice calculation of the hadronic vacuum polarization and the lowest order hadronic contribution (HLO) to the muon anomalous magnetic moment, a{sub {mu}}=(g-2)/2, using 2+1 flavors of improved staggered fermions. A precise fit to the low-q{sup 2} region of the vacuum polarization is necessary to accurately extract the muon g-2. To obtain this fit, we use staggered chiral perturbation theory, including a model to incorporate the vector particles as resonances, and compare these to polynomial fits to the lattice data. We discuss the fit results and associated systematic uncertainties, paying particular attention to the relative contributions of the pions and vector mesons. Using a single lattice spacing ensemble generated by the MILC Collaboration (a=0.086 fm), light quark masses as small as roughly one-tenth the strange quark mass, and volumes as large as (3.4 fm){sup 3}, we find a{sub {mu}}{sup HLO}=(713{+-}15)x10{sup -10} and (748{+-}21)x10{sup -10} where the error is statistical only and the two values correspond to linear and quadratic extrapolations in the light quark mass, respectively. Considering various systematic uncertainties not eliminated in this study (including a model of vector resonances used to fit the lattice data and the omission of disconnected quark contractions in the vector-vector correlationmore » function), we view this as agreement with the current best calculations using the experimental cross section for e{sup +}e{sup -} annihilation to hadrons (692.4{+-}5.9{+-}2.4)x10{sup -10}, and including the experimental decay rate of the tau lepton to hadrons (711.0{+-}5.0{+-}0.8{+-}2.8)x10{sup -10}. We discuss several ways to improve the current lattice calculation.« less

Authors:
;  [1];  [2]
  1. Physics Department, Columbia University, New York, New York 10027 (United States)
  2. (United States) and RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York, 11973-5000 (United States)
Publication Date:
OSTI Identifier:
20929559
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 11; Other Information: DOI: 10.1103/PhysRevD.75.114502; (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; CHIRALITY; CORRELATION FUNCTIONS; CROSS SECTIONS; D QUARKS; ELECTRON-POSITRON INTERACTIONS; ELECTRONS; FLAVOR MODEL; MAGNETIC MOMENTS; MASS; MUONS; PARTICLE DECAY; PERTURBATION THEORY; PIONS; POSITRONS; S QUARKS; TAU PARTICLES; U QUARKS; VACUUM POLARIZATION; VECTOR MESONS

Citation Formats

Aubin, C., Blum, T., and Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046. Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.114502.
Aubin, C., Blum, T., & Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046. Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks. United States. doi:10.1103/PHYSREVD.75.114502.
Aubin, C., Blum, T., and Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046. Fri . "Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks". United States. doi:10.1103/PHYSREVD.75.114502.
@article{osti_20929559,
title = {Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon anomalous magnetic moment with improved staggered quarks},
author = {Aubin, C. and Blum, T. and Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046},
abstractNote = {We present a lattice calculation of the hadronic vacuum polarization and the lowest order hadronic contribution (HLO) to the muon anomalous magnetic moment, a{sub {mu}}=(g-2)/2, using 2+1 flavors of improved staggered fermions. A precise fit to the low-q{sup 2} region of the vacuum polarization is necessary to accurately extract the muon g-2. To obtain this fit, we use staggered chiral perturbation theory, including a model to incorporate the vector particles as resonances, and compare these to polynomial fits to the lattice data. We discuss the fit results and associated systematic uncertainties, paying particular attention to the relative contributions of the pions and vector mesons. Using a single lattice spacing ensemble generated by the MILC Collaboration (a=0.086 fm), light quark masses as small as roughly one-tenth the strange quark mass, and volumes as large as (3.4 fm){sup 3}, we find a{sub {mu}}{sup HLO}=(713{+-}15)x10{sup -10} and (748{+-}21)x10{sup -10} where the error is statistical only and the two values correspond to linear and quadratic extrapolations in the light quark mass, respectively. Considering various systematic uncertainties not eliminated in this study (including a model of vector resonances used to fit the lattice data and the omission of disconnected quark contractions in the vector-vector correlation function), we view this as agreement with the current best calculations using the experimental cross section for e{sup +}e{sup -} annihilation to hadrons (692.4{+-}5.9{+-}2.4)x10{sup -10}, and including the experimental decay rate of the tau lepton to hadrons (711.0{+-}5.0{+-}0.8{+-}2.8)x10{sup -10}. We discuss several ways to improve the current lattice calculation.},
doi = {10.1103/PHYSREVD.75.114502},
journal = {Physical Review. D, Particles Fields},
number = 11,
volume = 75,
place = {United States},
year = {Fri Jun 01 00:00:00 EDT 2007},
month = {Fri Jun 01 00:00:00 EDT 2007}
}
  • Cited by 12
  • Here we report the first lattice QCD calculation of the hadronic vacuum polarization (HVP) disconnected contribution to the muon anomalous magnetic moment at physical pion mass. The calculation uses a refined noise-reduction technique that enables the control of statistical uncertainties at the desired level with modest computational effort. Measurements were performed on the 48 3×96 physical-pion-mass lattice generated by the RBC and UKQCD Collaborations. In conclusion, we find the leading-order hadronic vacuum polarization amore » $$HVP(LO)disc\atop{μ}$$=-9.6(3.3)(2.3)×10 -10, where the first error is statistical and the second systematic.« less
  • Here we report the first lattice QCD calculation of the hadronic vacuum polarization (HVP) disconnected contribution to the muon anomalous magnetic moment at physical pion mass. The calculation uses a refined noise-reduction technique that enables the control of statistical uncertainties at the desired level with modest computational effort. Measurements were performed on the 48 3×96 physical-pion-mass lattice generated by the RBC and UKQCD Collaborations. In conclusion, we find the leading-order hadronic vacuum polarization amore » $$HVP(LO)disc\atop{μ}$$=-9.6(3.3)(2.3)×10 -10, where the first error is statistical and the second systematic.« less
  • The contribution of the eight-order vertices containing sixth-order one-electron-loop vacuum-polarization subdiagrams to the muon anomalous magnetic moment, which was evaluated previously using the integration routine riwiad on a CDC 7600 computer, is reevaluated using the integration routine vegas on an IBM ES/9000 computer. The previous calculation was found to suffer from a severe underestimation of errors. The new result, [minus]0.241 5(19), is close to the asymptotic analytic result obtained recently by Broadhurst [ital et] [ital al]. using a renormalization group technique. The difference between the numerical and analytic results may be written as 10.23(39)([ital m][sub [ital e]]/[ital m][sub [mu]]).
  • We present a four-flavour lattice calculation of the leading-order hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, aμ hvp, arising from quark-connected Feynman graphs. It is based on ensembles featuring N f=2+1+1 dynamical twisted mass fermions generated by the European Twisted Mass Collaboration (ETMC). Several light quark masses are used in order to yield a controlled extrapolation to the physical pion mass. We employ three lattice spacings to examine lattice artefacts and several different volumes to check for finite-size effects. Including the complete first two generations of quarks allows for a direct comparison with phenomenological determinationsmore » of a μ hvp. The final result involving an estimate of the systematic uncertainty a μ hvp=6.74 (21)(18) 10 -8 shows a good overall agreement with these computations.« less