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Vector correlators in lattice QCD: Methods and applications

  • David Bernecker
  • Harvey B. MeyerEmail author
Regular Article - Theoretical Physics

Abstract

We discuss the calculation of the leading hadronic vacuum polarization in lattice QCD. Exploiting the excellent quality of the compiled experimental data for the e + e → hadrons cross-section, we predict the outcome of large-volume lattice calculations at the physical pion mass, and design computational strategies for the lattice to have an impact on important phenomenological quantities such as the leading hadronic contribution to (g − 2) μ and the running of the electromagnetic coupling constant. First, the R(s) ratio can be calculated directly on the lattice in the threshold region, and we provide the formulae to do so with twisted boundary conditions. Second, the current correlator projected onto zero spatial momentum, in a Euclidean time interval where it can be calculated accurately, provides a potentially critical test of the experimental R(s) ratio in the region that is most relevant for (g − 2) μ . This observation can also be turned around: the vector correlator at intermediate distances can be used to determine the lattice spacing in fm, and we make a concrete proposal in this direction. Finally, we quantify the finite-size effects on the current correlator coming from low-energy two-pion states and provide a general parametrization of the vacuum polarization on the torus.

Keywords

Spectral Function Ward Identity Helmholtz Equation Polarization Tensor Vector Correlator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    F. Jegerlehner, J. Phys. G 29, 101 (2003) arXiv:hep-ph/0104304.ADSCrossRefGoogle Scholar
  2. 2.
    F. Jegerlehner, A. Nyffeler, Phys. Rep. 477, 1 (2009) arXiv:0902.3360.ADSCrossRefGoogle Scholar
  3. 3.
    T. Blum, Phys. Rev. Lett. 91, 052001 (2003) arXiv:hep-lat/0212018.ADSCrossRefGoogle Scholar
  4. 4.
    C. Aubin, T. Blum, Phys. Rev. D 75, 114502 (2007) arXiv:hep-lat/0608011.ADSCrossRefGoogle Scholar
  5. 5.
    X. Feng, K. Jansen, M. Petschlies, D.B. Renner, Two-flavor QCD correction to lepton magnetic moments at leading-order in the electromagnetic coupling, arXiv:1103.4818.
  6. 6.
    M. Della Morte, B. Jager, A. Juttner, H. Wittig, The leading hadronic vacuum polarisation on the lattice, arXiv:1011.5793.
  7. 7.
    HPQCD Collaboration (I. Allison et al.), Phys. Rev. D 78, 054513 (2008) arXiv:0805.2999.ADSCrossRefGoogle Scholar
  8. 8.
    B. Lautrup, A. Peterman, E. de Rafael, Phys. Rep. 3, 193 (1972).ADSCrossRefGoogle Scholar
  9. 9.
    B. Lautrup, E. de Rafael, Nuovo Cimento A 64, 322 (1969).CrossRefADSGoogle Scholar
  10. 10.
    G.M. de Divitiis, N. Tantalo, Non leptonic two-body decay amplitudes from finite volume calculations, arXiv:hep-lat/0409154.
  11. 11.
    C. Kim, C. Sachrajda, Phys. Rev. D 81, 114506 (2010) arXiv:1003.3191.ADSCrossRefGoogle Scholar
  12. 12.
    H.B. Meyer, Phys. Rev. Lett. 107, 072002 (2011) arXiv:1105.1892.ADSCrossRefGoogle Scholar
  13. 13.
    M. Luscher, Nucl. Phys. B 364, 237 (1991).MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    X. Feng, K. Jansen, D.B. Renner, Phys. Rev. D 83, 094505 (2011) arXiv:1011.5288.ADSCrossRefGoogle Scholar
  15. 15.
    CP-PACS Collaboration (S. Aoki et al.), Phys. Rev. D 76, 094506 (2007) arXiv:0708.3705.ADSCrossRefGoogle Scholar
  16. 16.
    M. Luscher, Nucl. Phys. B 354, 531 (1991).MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    Particle Data Group Collaboration (C. Amsler et al.), Phys. Lett. B 667, 1 (2008).ADSCrossRefGoogle Scholar
  18. 18.
    B.B. Brandt, S. Capitani, D. Djukanovic, G. von Hippel, B. Jager, Wilson fermions at fine lattice spacings: scale setting, pion form factors and (g − 2)μ, PoS LAT2010, 164 (2010), arXiv:1010.2390.
  19. 19.
    F. Jegerlehner, Nucl. Phys. Proc. Suppl. 181-182, 26 (2008).ADSCrossRefGoogle Scholar
  20. 20.
    M. Davier, A. Hoecker, B. Malaescu, Z. Zhang, Eur. Phys. J. C 71, 1515 (2011) arXiv:1010.4180.ADSCrossRefGoogle Scholar
  21. 21.
    K. Hagiwara, R. Liao, A. Martin, D. Nomura, T. Teubner, (g − 2)μ and (α 22) re-evaluated using new precise data, arXiv:1105.3149.
  22. 22.
    M. Davier, S. Eidelman, A. Hocker, Z. Zhang, Eur. Phys. J. C 27, 497 (2003) arXiv:hep-ph/0208177.ADSCrossRefGoogle Scholar
  23. 23.
    G. Amelino-Camelia, F. Archilli, D. Babusci, D. Badoni, G. Bencivenni, et al., Eur. Phys. J. C 68, 619 (2010) arXiv:1003.3868.ADSCrossRefGoogle Scholar
  24. 24.
    KLOE Collaboration (S.E. Muller et al.), Chin. Phys. C 34, 686 (2010) arXiv:0912.2205.CrossRefGoogle Scholar
  25. 25.
    KLOE Collaboration (F. Ambrosino et al.), Phys. Lett. B 700, 102 (2011) arXiv:1006.5313.ADSCrossRefGoogle Scholar
  26. 26.
    BABAR Collaboration (B. Aubert et al.), Phys. Rev. Lett. 103, 231801 (2009) arXiv:0908.3589.ADSCrossRefGoogle Scholar
  27. 27.
    M. Passera, W. Marciano, A. Sirlin, Phys. Rev. D 78, 013009 (2008) arXiv:0804.1142.ADSCrossRefGoogle Scholar
  28. 28.
    M. Della Morte, A. Juttner, JHEP 11, 154 (2010) arXiv:1009.3783.ADSCrossRefGoogle Scholar
  29. 29.
    M. Goeckeler et al., Phys. Rev. D 54, 5705 (1996) arXiv:hep-lat/9602029.ADSCrossRefGoogle Scholar
  30. 30.
    H.B. Meyer, Transport Properties of the Quark-Gluon Plasma -- A Lattice QCD Perspective, arXiv:1104.3708.
  31. 31.
    R. Baier, R-charge thermodynamical spectral sum rule in N=4 Yang-Mills theory, arXiv:0910.3862.
  32. 32.
    E-989 Collaboration, http://gm2.fnal.gov/.
  33. 33.
    E.V. Shuryak, J. Verbaarschot, Nucl. Phys. B 410, 55 (1993) arXiv:hep-ph/9302239.ADSCrossRefGoogle Scholar
  34. 34.
    T. Schaefer, Phys. Rev. D 77, 126010 (2008) arXiv:0711.0236.ADSCrossRefGoogle Scholar
  35. 35.
    R. Sommer, Nucl. Phys. B 411, 839 (1994) arXiv:hep-lat/9310022.ADSCrossRefGoogle Scholar
  36. 36.
    K. Rummukainen, S.A. Gottlieb, Nucl. Phys. B 450, 397 (1995) arXiv:hep-lat/9503028.ADSCrossRefGoogle Scholar
  37. 37.
    M. Luescher, S. Sint, R. Sommer, P. Weisz, Nucl. Phys. B 478, 365 (1996) arXiv:hep-lat/9605038.ADSCrossRefGoogle Scholar
  38. 38.
    C. Lin, G. Martinelli, C.T. Sachrajda, M. Testa, Nucl. Phys. B 619, 467 (2001) arXiv:hep-lat/0104006.ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Institut für KernphysikJohannes Gutenberg Universität MainzMainzGermany

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