Hadronic Matrix Elements and Weak Decays in Lattice QCD

  • Guido Martinelli
Part of the NATO ASI Series book series (NSSB, volume 223)


Many important progresses have been done in lattice QCD since the first pioneering numerical calculations were started about 10 years ago. Since then substantial advances have been possible thanks to a great theoretical effort in understanding the lattice quantum field theory and to the extraordinary increase in the available conputer power. Almost all aspects of particle physics are currently studied on the lattice, already with phenomenologically relevant results. Although we are not yet at the point to be able to predict with sufficient accuracy the mass of the proton, many steps forward have been done in the calculation of the hadronic matrix elements. Lattice QCD offers in fact the unique possibility, of computing with the same method many different matrix elements which are of interest in the phenomenology of the Standard Model. Among the other quantities I will report the most recent results obtained for the pion and proton structure functions and electromagnetic form factors, the nucleon G-term, the meson decay constants and the weak hamiltonian matrix elements, including the semileptonic decays of D mesons. These lectures have been conceived to serve as an elementary introduction to this fascinating field and to offer to nonexperts a survey of the most relevant results.


Matrix Element Form Factor Ward Identity Vector Current Pseudoscalar Meson 
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.


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  1. 1.
    C.N. Yang, R.L. Mills, Phys.Rev. 96 (1954) 191.MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    H.D. Politzer, Phys.Rev.Lett.30 (1973) 1346;ADSCrossRefGoogle Scholar
  3. 2a.
    D.J. Gross and F. Wilczek, Phys.Rev.Lett. 30 (1973) 1343ADSCrossRefGoogle Scholar
  4. 2b.
    D.J. Gross and F. Wilczek, Phys.Rev. D8 (1973) 3633. For a detailed introduction to QCD see E.S.Abers, B.W.Lee, Phys.Rep. 9 (1973) 1.ADSGoogle Scholar
  5. 3.
    K.G. Wilson, Phys.Rev. D10 (1974) 2445; “New Phenomena in Subnuclear Physics”, A.Zichichi ed, Plenum Press, New York (1977).ADSGoogle Scholar
  6. 4.
    G.C. Wick, Phys.Rev. 96 (1954) 1124.MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 5.
    L.H. Karsten and J. Smit, Nucl.Phys. B183 (1981) 103.ADSCrossRefGoogle Scholar
  8. 6.
    H.B. Nielsen and N. Ninomiya, Nucl.Phys. B185 (1981) 20MathSciNetADSCrossRefGoogle Scholar
  9. 6a.
    H.B. Nielsen and N. Ninomiya, Nucl.Phys. B193 (1981) 173.MathSciNetADSCrossRefGoogle Scholar
  10. 7.
    M. Bochicchio, L. Maiani, G. Martinelli, G.C. Rossi and M. Testa, Nucl.Phys. B262 (1985) 331.ADSCrossRefGoogle Scholar
  11. 8.
    G. Curci, Phys.Lett. B167 (1986) 425.ADSGoogle Scholar
  12. 9.
    L. Maiani and G. Martinelli, Phys.Lett. 168B (1986) 265.ADSGoogle Scholar
  13. 10.
    L. Maiani, G. Martinelli, G.C. Rossi and M. Testa, Phys.Lett. 176B (1986) 445ADSGoogle Scholar
  14. 10a.
    L. Maiani, G. Martinelli, G.C. Rossi and M. Testa, Nucl.Phys. B289 (1987) 505.ADSCrossRefGoogle Scholar
  15. 11.
    G. Martinelli and C.T. Sachrajda, Phys.Lett. B190 (1987) 151.ADSGoogle Scholar
  16. 12.
    G. Martinelli and C.T. Sachrajda, Phys.Lett. B196 (1987) 184;ADSGoogle Scholar
  17. 12a.
    G. Martinelli and C.T. Sachrajda, Nucl.Phys. B306 (1988) 865.ADSCrossRefGoogle Scholar
  18. 13.
    M.B. Gavela, L. Maiani, G. Martinelli, S. Petrarca, F. Rapuano and C.T. Sachrajda, Nucl.Phys. B306 (1988) 677ADSCrossRefGoogle Scholar
  19. 13a.
    M.B. Gavela, L. Maiani, O. Pène and S. Petrarca, Phys.Lett. B206 (1988) 113.ADSGoogle Scholar
  20. 14.
    T.A .De Grand and R.D. Loft, Preprint COLO-HEP-165 (nov. 1987) to appear in Phys.Rev. D38(1988) 954.Google Scholar
  21. 15.
    C. Bernard et al., Nucl.Phys. (Proc.Suppl.) B9 (1989) 155 and refs. therein.ADSCrossRefGoogle Scholar
  22. 16.
    S. Narison, Phys.Lett. B198 (1987) 104.ADSGoogle Scholar
  23. 17.
    C.A. Dominguez and N. Paver, Phys.Lett. B197 (1987) 423.ADSGoogle Scholar
  24. 18.
    For the exponentiation method see: F. Fucito, G. Parisi, S. Petrarca, Phys.Lett. 115B (1982) 148ADSGoogle Scholar
  25. 18a.
    G. Martinelli, G. Parisi, R. Petronzio, F. Rapuano 116B (1982) 432Google Scholar
  26. 18b.
    C. Bernard et al., Phys.Rev.Lett. 49 (1982) 1076ADSCrossRefGoogle Scholar
  27. 18c.
    S. Gottlieb, P.B. Mackenzie, H.B. Thacker, D. Weintgarten, Nucl.Phys. B263 (1986) 704.ADSCrossRefGoogle Scholar
  28. 19.
    For the source method see: C. Bernard in “Gauge Theories on a lattice”, 1984 eds. Zachos et al., Nat.Tech. Information Service, Springfield, VA (1984)Google Scholar
  29. 19a.
    R. Gupta et al., Phys.Lett. 164B (1985) 347.ADSGoogle Scholar
  30. 20.
    G. Martinelli and C.T. Sachrajda, Nuch.Phys. B316 (1989) 305.ADSGoogle Scholar
  31. 21.
    J. Ashman et al. (EMC Collaboration), Phys.Lett. B206 (1988) 364.ADSGoogle Scholar
  32. 22.
    B. Meyer and C. Smith, Phys.Lett. 123B (1983) 62.ADSGoogle Scholar
  33. 23.
    G. Martinelli and Y.C. Zhang, Phys.Lett. 123B (1983) 77.ADSGoogle Scholar
  34. 24.
    R. Groot, J. Hoek and J. Smit, Nucl.Phys. B237 (1984) 111.ADSCrossRefGoogle Scholar
  35. 25.
    J. Mandula, G. Zweig and J. Govaerts, Nucl.Phys. B228 (1983) 9.Google Scholar
  36. 26.
    G. Martinelli and Zhang Yi Cheng, Phys.Lett. B125 (1983) 7.Google Scholar
  37. 27.
    S.R. Amendolia et al., Nucl.Phys. B277 (1986) 168.ADSCrossRefGoogle Scholar
  38. 28.
    C.J. Bebek et al., Phys.Rev. D17 (1987) 1693 and refs. therein.ADSGoogle Scholar
  39. 29.
    C. Newman et al., Phys.Rev.Lett. 42 (1979) 951.ADSCrossRefGoogle Scholar
  40. 30.
    J. Badier et al., Proc. EPS Conference on HEP, Geneva (1979) p.751.Google Scholar
  41. 31.
    R. Barate et al., Phys.Rev.Lett. 43 (1979) 1541.ADSCrossRefGoogle Scholar
  42. 32.
    B. Betev et al., Z.Phys. C28 (1985) 15.ADSGoogle Scholar
  43. 33.
    J.D. Bjorken and S.D. Drell, “Relativistic Quantum Mechanics” (Mc Graw Hill, 1965)Google Scholar
  44. 34.
    G. Höler et al., Nucl.Phys. BI 14 (1976) 505 and references therein.CrossRefGoogle Scholar
  45. 35.
    G. Höler, F. Kaiser, R. Koch and E. Pietarinen, “Handbook of pion-nucleon scattering” (Fachs-information-Zeutrum, Karlsruhe, 1979) p.427 and references therein.Google Scholar
  46. 36.
    L. Maiani, G. Martinelli, M.L. Paciello, B. Taglienti, Nucl.Phys. B293 (1987) 420.ADSCrossRefGoogle Scholar
  47. 37.
    S. Güsken et al., CERN-TH 5027/88 (1988).Google Scholar
  48. 38.
    Bacilieri et al., (Ape Collaboration), presented by F.Rapuano at the XXIV HEP Conference, Münich, August 1988, R.Kothaus and J.H.Kühn eds, Springer-Verlag (1989) 804.Google Scholar
  49. 39.
    G. Martinelli, Phys.Lett. 141B (1984) 395.ADSGoogle Scholar
  50. 40.
    C. Bernard, A. Soni and T. Draper, Phys.Rev. D36 (1987) 363.Google Scholar
  51. 41.
    G. Curci, E. Franco, L. Maiani and G. Martinelli, Phys.Lett. 202B (1988) 363.ADSGoogle Scholar
  52. 42.
    C. Bernard, T. Draper, G. Hockney and A. Soni, Talk given by C. Bernard at the “Int. Symposium: Field Theory on the Lattice”, Seillac (France), Nucl.Phys. B (Proc. Sup.) 4 (1988) 483.ADSCrossRefGoogle Scholar
  53. 43.
    N. Cabibbo, G. Martinelli and R. Petronzio, Nucl.Phys. B244 (1984) 381.ADSCrossRefGoogle Scholar
  54. 44.
    R.C. Brower, M.B. Gavela, R. Gupta and G. Maturana, Phys.Rev.Lett. 53 (1984) 1318.ADSCrossRefGoogle Scholar
  55. 45.
    L. Maiani and G. Martinelli, Phys.Lett. B181 (1986) 344.ADSGoogle Scholar
  56. 46.
    G. Kilcup, Proceedings of the Rencontre de Moriond, March 1989.Google Scholar
  57. 47.
    J.F. Donoghue, E. Golowich and B.R. Holstein, Phys.Lett. B199 (1986) 442.Google Scholar
  58. 48.
    M.B. Gavela, L. Maiani, G. Martinelli, O. Pène and S. Petrarca, Phys.Lett. 211B (1988) 139.ADSGoogle Scholar
  59. 49.
    M.A. Shifman, A.I. Vainshtein and V.J. Zakharov, Nucl.Phys. B120 (1977) 346;ADSGoogle Scholar
  60. 49a.
    M.A. Shifman, A.I. Vainshtein and V.J. Zakharov, Sov.Phys. Jept. 45 (1977) 670.Google Scholar
  61. 50.
    J. Bijens and M.B. Wise, Phys.Lett. B137 (1984) 245ADSGoogle Scholar
  62. 50a.
    J.F. Donoghue, E. Golowich, B.R. Holstein and J. Trampetic, Phys.Lett. B179 (1986) 361ADSGoogle Scholar
  63. 50aa.
    J.F. Donoghue, E. Golowich, B.R. Holstein and J. Trampetic, Phys.Lett. B188 (1987) 511ADSGoogle Scholar
  64. 50b.
    A. Buras and J.M. Gèrard, Phys.Lett B192 (1987) 156ADSGoogle Scholar
  65. 50c.
    S. Sharpe, Phys.Lett. B194 (1987) 551.ADSGoogle Scholar
  66. 51.
    E. Franco, L. Maiani, G. Martinelli and A. Morelli, Nucl.Phys. B317 (1989) 63.ADSCrossRefGoogle Scholar
  67. 52.
    L. Wolfenstein, Phys.Rev.Lett. 51 (1983) 1945.ADSCrossRefGoogle Scholar
  68. 53.
    R. Gupta, G. Guralnik, W. Kilcup, A. Patel and S.R. Sharpe, Phys.Lett. B192 (1987) 149.ADSGoogle Scholar
  69. 54.
    C. Bernard, A. El-Khadra and A. Soni, Proceedings of the Conference on Lattice Field Theory, Fermilab 22–28 September 88, Nucl. Phys. B (Proc. Suppl.) 9 (1989) 186.Google Scholar
  70. 55.
    M. Crisafulli et al., Phys.Lett. B233 (1989) 90.ADSGoogle Scholar
  71. 56.
    N. Cabibbo, Phys.Rev.Lett. 10 (1963) 531ADSCrossRefGoogle Scholar
  72. 56a.
    M. Kobayashi and K. Maskawa, Prog.Theor. Phys. 49 (1972) 282.CrossRefGoogle Scholar
  73. 57.
    The Tagged Photon Spectrometer Collaboration, J.C. Anjos et al., Fermilab Preprint FNAL88/141-E(1988).Google Scholar
  74. 58.
    MARK 3 Collaboration, D. Hitlin, Proceedings of the 1987 International Symposium on Lepton and Photon Interactions at High Energies, ed. W. Bartel and R. Ruckl, North-Holland, Amsterdam (1987)Google Scholar
  75. 58a.
    R. Schindler,in Proceedings of the XXXIII International Conference on High Energy Physics, vol. 1, p.745, ed. S. C. Loken, World Scientific (1987)Google Scholar
  76. 58b.
    D. Coffman, Ph.D. Thesis, California Institute of Technology, CALT-68–1415 (1987).Google Scholar
  77. 59.
    For a review see for example PJ. Franzini, Phys.Rep. C173 (1989) 1.ADSCrossRefGoogle Scholar
  78. 60.
    E. Eichten, Nucl. Phys. B (Proc. Suppl.) 4 (1988) 170.ADSCrossRefGoogle Scholar
  79. 61.
    T.M. Aliev et al., Sov.J.Nucl. Phys. 40 (1984) 527.Google Scholar
  80. 62.
    M. Wirbel, B. Stech and M. Bauer, Z. Phys. C29 (1985) 637.ADSGoogle Scholar
  81. 63.
    B. Grinstein et al., University of Toronto Preprint, UTPT-88–12 (1988).Google Scholar
  82. 64.
    G. Heatlie, G. Martinelli, C. Pittore, G.C. Rossi, C.T. Sachrajda, in preparation.Google Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Guido Martinelli
    • 1
    • 2
  1. 1.Dipartimento di FisicaUniversità di Roma “La Sapienza”RomaItaly
  2. 2.INFN - Sezione di RomaItaly

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