Lattice QCD and the two-photon decay of the neutral pion

  • Harvey B. Meyer
Regular Article - Theoretical Physics
Part of the following topical collections:
  1. Topical issue on lattice field theory methods in hadron and nuclear physics


Two-photon decays probe the structure of mesons and represent an important contribution to hadronic light-by-light scattering. For the neutral pion, the decay amplitude tests the effects of the chiral anomaly; for a heavy quarkonium state, it measures the magnitude of its wave function at the origin. We rederive the expression of the decay amplitude in terms of a Euclidean correlation function starting from the theory defined on the torus. The derivation shows that for timelike photons the approach to the infinite-volume decay amplitude is exponential in the periodic box size.


Matrix Element Vector Boson Decay Amplitude Neutral Pion Chiral Anomaly 
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  1. 1.
    R. Hofstadter, R.W. McAllister, Phys. Rev. 98, 217 (1955).ADSCrossRefGoogle Scholar
  2. 2.
    E.D. Bloom, D.H. Coward, H. DeStaebler, J. Drees, G. Miller, L.W. Mo, R.E. Taylor, M. Breidenbach, J.I. Friedman, G.C. Hartmann, H.W. Kendall, Phys. Rev. Lett. 23, 930 (1969).CrossRefADSGoogle Scholar
  3. 3.
    M. Breidenbach, J.I. Friedman, H.W. Kendall, E.D. Bloom, D.H. Coward, H. DeStaebler, J. Drees, L.W. Mo, R.E. Taylor, Phys. Rev. Lett. 23, 935 (1969).CrossRefADSGoogle Scholar
  4. 4.
    S.L. Adler, Phys. Rev. 177, 2426 (1969).CrossRefADSGoogle Scholar
  5. 5.
    J. Bell, R. Jackiw, Nuovo Cimento A 60, 47 (1969).CrossRefADSGoogle Scholar
  6. 6.
    X. Feng, S. Aoki, H. Fukaya, S. Hashimoto, T. Kaneko et al., Phys. Rev. Lett. 109, 182001 (2012) arXiv:1206.1375.ADSCrossRefGoogle Scholar
  7. 7.
    H.-W. Lin, S.D. Cohen, PoS (ConfinementX), 113 (2012) arXiv:1302.0874.Google Scholar
  8. 8.
    X. Feng, S. Aoki, H. Fukaya, S. Hashimoto, T. Kaneko et al., PoS LATTICE2012, 180 (2012) arXiv:1211.2504.Google Scholar
  9. 9.
    M. Luscher, Commun. Math. Phys. 105, 153 (1986).MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    M. Luscher, Nucl. Phys. B 354, 531 (1991).MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    S. Weinberg, The Quantum Theory of Fields, Vol. 1, Foundations (Cambridge University Press, Cambridge, 1995) pp. 609.Google Scholar
  12. 12.
    L. Lellouch, M. Luscher, Commun. Math. Phys. 219, 31 (2001) hep-lat/0003023.MathSciNetADSCrossRefMATHGoogle Scholar
  13. 13.
    M.E. Peskin, D.V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, USA, 1995) pp. 842.Google Scholar
  14. 14.
    F. Jegerlehner, A. Nyffeler, Phys. Rep. 477, 1 (2009) arXiv:0902.3360.ADSCrossRefGoogle Scholar
  15. 15.
    M. Luscher, Commun. Math. Phys. 104, 177 (1986).MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    L. Landau, E. Lifshitz, Course of Theoretical Physics III: Quantum Mechanics (Butterworth-Heinemann, 1981) pp. 689.Google Scholar
  17. 17.
    H.B. Meyer, Phys. Rev. Lett. 107, 072002 (2011) arXiv:1105.1892.ADSCrossRefGoogle Scholar
  18. 18.
    X.-d. Ji, C.-w. Jung, Phys. Rev. Lett. 86, 208 (2001) hep-lat/0101014.ADSCrossRefGoogle Scholar
  19. 19.
    J.J. Dudek, R.G. Edwards, Phys. Rev. Lett. 97, 172001 (2006) hep-ph/0607140.ADSCrossRefGoogle Scholar
  20. 20.
    S. Weinberg, The Quantum Theory of Fields, Vol. 2, Modern Applications (Cambridge University Press, Cambridge, 1996) pp. 489.Google Scholar
  21. 21.
    S.L. Adler, W.A. Bardeen, Phys. Rev. 182, 1517 (1969).CrossRefADSGoogle Scholar
  22. 22.
    C. Kim, C. Sachrajda, S.R. Sharpe, Nucl. Phys. B 727, 218 (2005) hep-lat/0507006.ADSCrossRefGoogle Scholar
  23. 23.
    M.T. Hansen, S.R. Sharpe, Phys. Rev. D 86, 016007 (2012) arXiv:1204.0826.ADSCrossRefGoogle Scholar
  24. 24.
    J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 539 (1985).ADSCrossRefGoogle Scholar
  25. 25.
    K. Polejaeva, A. Rusetsky, Eur. Phys. J. A 48, 67 (2012) arXiv:1203.1241.ADSCrossRefGoogle Scholar
  26. 26.
    R.A. Briceno, Z. Davoudi, Phys. Rev. D 87, 094507 (2013) arXiv:1212.3398.ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.PRISMA Cluster of Excellence, Institut für Kernphysik and Helmholtz Institute MainzJohannes Gutenberg-Universität MainzMainzGermany

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