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Operator Product Expansion, Renormalization Group and Weak Decays

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Quantum Field Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 558))

Abstract

A non-technical description of the Operator Product Expansion and Renormalization Group techniques as applied to weak decays of mesons is presented. We use this opportunity to summarize briefly the present status of the next-to-leading QCD corrections to weak decays and their implications for the unitarity triangle, the ratio έ/ε; the radiative decay BX sγ, and the rare decays \( K^ + \to \pi ^ + \nu \bar \nu \) and \( K_L \to \pi ^0 \nu \bar \nu \).

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References

  1. K.G. Wilson, Phys. Rev. 179 (1969) 1499

    Article  ADS  MathSciNet  Google Scholar 

  2. W. Zimmermann, in Proc. 1970 Brandeis Summer Institute in Theor. Phys, (eds. S. Deser, M. Grisaru and H. Pendleton), MIT Press, 1971, p.396

    Google Scholar 

  3. K.G. Wilson and W. Zimmermann, Commun. Math. Phys. 24 (1972) 87.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. W. Zimmermann, Ann. Phys. 77 (1973) 570.

    Article  ADS  Google Scholar 

  5. M.K. Gaillard and B.W. Lee, Phys. Rev. Lett. 33 (1974) 108.

    Article  ADS  Google Scholar 

  6. G. Altarelli and L. Maiani, Phys. Lett. B 52 (1974) 351.

    ADS  Google Scholar 

  7. N. Cabibbo, Phys. Rev. Lett. 10 (1963) 531.

    Article  ADS  Google Scholar 

  8. M. Kobayashi and K. Maskawa, Prog. Theor. Phys. 49 (1973) 652.

    Article  ADS  Google Scholar 

  9. E.C.G. Sudarshan and R.E. Marshak, Proc. Padua-Venice Conf. on Mesons and Recently Discovered Particles (1957).

    Google Scholar 

  10. R.P. Feynman and M. Gell-Mann, Phys. Rev. 109 (1958) 193.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. D. Zeppenfeld, Z. Phys. C 8 (1981) 77; L.L. Chau, Phys. Rev. D 43 (1991) 2176; M. Gronau, J.L. Rosner and D. London, Phys. Rev. Lett. 73 (1994) 21; O.F. Hernandez, M. Gronau, J.L. Rosner and D. London, Phys. Lett. B 333 (1994) 500, Phys. Rev. D 50 (1994) 4529.

    ADS  Google Scholar 

  12. E. Witten, Nucl. Phys. B 120 (1977) 189.

    Article  ADS  Google Scholar 

  13. E.C.G. Stueckelberg and A. Petermann, Helv. Phys. Acta 26 (1953) 499; M. Gell-Mann and F.E. Low, Phys. Rev. 95 (1954) 1300; N.N. Bogoliubov and D.V. Shirkov, Dokl. Acad. Nauk SSSR 103 (1955) 203, 391; L.V. Ovsyannikov, Dokl. Acad. Nauk SSSR 109 (1956) 1112; K. Symanzik, Commun. Math. Phys. 18 (1970) 227; C.G. Callan Jr, Phys. Rev. D 2 (1970) 1541.

    MATH  MathSciNet  Google Scholar 

  14. G. ’t Hooft, Nucl. Phys. B 61 (1973) 455.

    Article  ADS  MathSciNet  Google Scholar 

  15. S. Weinberg, Phys. Rev. D 8 (1973) 3497.

    ADS  Google Scholar 

  16. J. Chay, H. Georgi and B. Grinstein, Phys. Lett. B 247 (1990) 399.

    ADS  Google Scholar 

  17. I.I. Bigi, N.G. Uraltsev and A.I. Vainshtein, Phys. Lett. B 293 (1992) 430 [E: B 297 (1993) 477]. I.I. Bigi, M.A. Shifman, N.G. Uraltsev and A.I. Vainshtein, Phys. Rev. Lett. 71 (1993) 496; B. Blok, L. Koyrakh, M.A. Shifman and A.I. Vainshtein, Phys. Rev. D 49 (1994) 3356 [E: D 50 (1994) 3572].

    ADS  Google Scholar 

  18. A.V. Manohar and M.B. Wise, Phys. Rev. D 49 (1994) 1310.

    ADS  Google Scholar 

  19. Z. Ligeti and A.V. Manohax, Phys. Lett. B 433 (1998) 396; I. Bigi, M. Shifman, N. Uraltsev and A. Vainshtein, hep-ph/9805241; B.Grinstein and R.F. Lebed, hep-ph/9805404; N. Isgur, hep-ph/9811377.

    ADS  Google Scholar 

  20. T. Inami and C.S. Lim, Progr. Theor. Phys. 65 (1981) 297.

    Article  ADS  Google Scholar 

  21. G. Buchalla, A.J. Buras and M. Lautenbacher, Rev. Mod. Phys. 68 (1996) 1125.

    Article  ADS  Google Scholar 

  22. A.J. Buras and R. Fleischer, hep-ph/9704376, page 65 in [24].

    Google Scholar 

  23. A.J. Buras, hep-ph/9806471, to appear in Probing the Standard Model of Particle Interactions, eds. F. David and R. Gupta (Elsevier Science B.V., Amsterdam, 1998).

    Google Scholar 

  24. A.J. Buras and M. Lindner, Heavy Flavours II, World Scientific, 1998.

    Google Scholar 

  25. G. Buchalla, A.J. Buras and M.K. Harlander, Nucl. Phys. B 349 (1991) 1.

    Article  ADS  Google Scholar 

  26. G. Buchalla, A.J. Buras, M.K. Harlander, M.E. Lautenbacher and C. Salazar, Nucl. Phys. B 355 (1991) 305.

    Article  ADS  Google Scholar 

  27. P. Cho, M. Misiak and D. Wyler, Phys. Rev. D 54 (1996) 3329.

    ADS  Google Scholar 

  28. A. Ali, Th. Mannel and Ch. Greub, Zeit. Phys. C 67 (1995) 417.

    ADS  Google Scholar 

  29. W.A. Bardeen, A.J. Buras, D.W. Duke and T. Muta, Phys. Rev. D 18 (1978) 3998.

    ADS  Google Scholar 

  30. A.I. Vainshtein, V.I. Zakharov, and M.A. Shifman, JTEP 45 (1977) 670; F. Gilman and M.B. Wise, Phys. Rev. D 20 (1979) 2392; B. Guberina and R. Peccei, Nucl. Phys. B 163 (1980) 289.

    Google Scholar 

  31. G. Altarelli, G. Curci, G. Martinelli and S. Petrarca, Nucl. Phys. B 187 (1981) 461.

    Article  ADS  Google Scholar 

  32. A.J. Buras and P.H. Weisz, Nucl. Phys. B 333 (1990) 66.

    Article  ADS  Google Scholar 

  33. A.J. Buras, M. Jamin, M.E. Lautenbacher and P.H. Weisz, Nucl. Phys. B 370 (1992) 69; B 400 (1993) 37.

    Article  ADS  Google Scholar 

  34. A.J. Buras, M. Jamin and M.E. Lautenbacher, Nucl. Phys. B 400 (1993) 75.

    Article  ADS  Google Scholar 

  35. A.J. Buras, M. Jamin and M.E. Lautenbacher, Nucl. Phys. B 408 (1993) 209.

    Article  ADS  Google Scholar 

  36. M. Ciuchini, E. Franco, G. Martinelli and L. Reina, Phys. Lett. B 301 (1993) 263.

    ADS  Google Scholar 

  37. M. Ciuchini, E. Franco, G. Martinelli and L. Reina, Nucl. Phys. B 415 (1994) 403.

    Article  ADS  Google Scholar 

  38. K. Chetyrkin, M. Misiak and Münz, Nucl. Phys. B520 (1998) 279.

    Article  ADS  Google Scholar 

  39. M. Misiak and M. Münz, Phys. Lett. B344 (1995) 308.

    ADS  Google Scholar 

  40. K.G. Chetyrkin, M. Misiak and M. Münz, Phys. Lett. B400 (1997) 206; Erratum ibid. B425 (1998) 414.

    ADS  Google Scholar 

  41. G. Buchalla, Nucl. Phys. B 391 (1993) 501.

    Article  ADS  Google Scholar 

  42. E. Bagan, P. Ball, V.M. Braun and P. Gosdzinsky, Nucl. Phys. B 432 (1994) 3; E. Bagan et al., Phys. Lett. B 342 (1995) 362; B 351 (1995) 546.

    Article  ADS  Google Scholar 

  43. A. Lenz, U. Nierste and G. Ostermaier, Phys. Rev. D 56 (1997) 7228.

    ADS  Google Scholar 

  44. M. Jamin and A. Pich, Nucl. Phys. B425 (1994) 15.

    Article  ADS  Google Scholar 

  45. S. Herrlich and U. Nierste, Nucl. Phys. B419 (1994) 292.

    Article  ADS  Google Scholar 

  46. A.J. Buras, M. Jamin, and P.H. Weisz, Nucl. Phys. B347 (1990) 491.

    Article  ADS  Google Scholar 

  47. J. Urban, F. Krauss, U. Jentschura and G. Soff, Nucl. Phys. B523 (1998) 40.

    Article  ADS  Google Scholar 

  48. S. Herrlich and U. Nierste, Phys. Rev. D52 (1995) 6505; Nucl. Phys. B476 (1996) 27.

    ADS  Google Scholar 

  49. G. Buchalla and A.J. Buras, Nucl. Phys. B 398 (1993) 285.

    Article  ADS  Google Scholar 

  50. G. Buchalla and A.J. Buras, Nucl. Phys. B 400 (1993) 225.

    Article  ADS  Google Scholar 

  51. M. Misiak and J. Urban, hep-ph/9901278.

    Google Scholar 

  52. G. Buchalla and A.J. Buras, hep-ph/9901288.

    Google Scholar 

  53. G. Buchalla and A.J. Buras, Nucl. Phys. B 412 (1994) 106.

    Article  ADS  Google Scholar 

  54. G. Buchalla and A.J. Buras, Phys. Lett. B 336 (1994) 263.

    ADS  Google Scholar 

  55. A. J. Buras, M. E. Lautenbacher, M. Misiak and M. Münz, Nucl. Phys. B423 (1994) 349.

    Article  ADS  Google Scholar 

  56. M. Misiak, Nucl. Phys. B393 (1993) 23; Erratum, Nucl. Phys. B439 (1995) 461.

    Article  ADS  Google Scholar 

  57. A.J. Buras and M. Münz, Phys. Rev. D 52 (1995) 186.

    ADS  Google Scholar 

  58. A. Ali, and C. Greub, Z.Phys. C49 (1991) 431; Phys. Lett. B259 (1991) 182; B361 (1995) 146.

    Google Scholar 

  59. K. Adel and Y.P. Yao, Modern Physics Letters A8 (1993) 1679; Phys. Rev. D 49 (1994) 4945.

    Article  ADS  Google Scholar 

  60. N. Pott, Phys. Rev. D 54 (1996) 938.

    ADS  Google Scholar 

  61. C. Greub, T. Hurth and D. Wyler, Phys. Lett. B380 (1996) 385; Phys. Rev. D 54 (1996) 3350

    ADS  Google Scholar 

  62. C. Greub and T. Hurth, Phys. Rev. D 56 (1997) 2934; hep-ph/9809468.

    ADS  Google Scholar 

  63. A.J. Buras, A. Kwiatkowski and N. Pott, Phys. Lett. B 414 (1997) 157; Nucl. Phys. B 517 (1998) 353.

    ADS  Google Scholar 

  64. M. Ciuchini, G. Degrassi, P. Gambino and G.F. Giudice, Nucl. Phys. B 527 1998) 21.

    Article  ADS  Google Scholar 

  65. F.M. Borzumati and Ch. Greub, Phys. Rev. D 58 (1998) 07004; hep-ph/9809438.

    Google Scholar 

  66. P. Ciafaloni, A. Romanino, and A. Struraia, Nucl. Phys. B 524 (1998) 361.

    Article  ADS  Google Scholar 

  67. M. Beneke, G. Buchalla, C. Greub, A. Lenz and U. Nierste, hep-ph/9808385.

    Google Scholar 

  68. M. Beneke, F. Maltoni and I.Z. Rothstein, hep-ph/9808360.

    Google Scholar 

  69. M. Ciuchini, E. Franco, V. Lubicz, G. Martineli, I. Scimeni and L. Silvestrini, Nucl. Phys. B 523 (1998) 501.

    Article  ADS  Google Scholar 

  70. M. Ciuchini, et al. JHEP 9810 (1998) 008.

    Article  ADS  Google Scholar 

  71. M. Ciuchini, G. Degrassi, P. Gambino and G.F. Giudice, Nucl. Phys. B 534 (1998) 3.

    ADS  Google Scholar 

  72. G. Buchalla and A.J. Buras, Phys. Rev. D57 (1998) 216.

    ADS  Google Scholar 

  73. A. Czarnecki and W.J. Marciano, Phys. Rev. Lett. 81 (1998) 277.

    Article  ADS  Google Scholar 

  74. A. Strumia, Nucl. Phys. B532 (1998) 28.

    Article  ADS  Google Scholar 

  75. A.L. Kagan and M. Neubert, hep-ph/9805303.

    Google Scholar 

  76. P. Gambino, A. Kwiatkowski and N. Pott, hep-ph/9810400.

    Google Scholar 

  77. K. Chetyrkin, M. Misiak and Münz, Nucl. Phys. B518 (1998) 473.

    ADS  Google Scholar 

  78. S. Herrlich and U. Nierste, Nucl. Phys. B 445 (1995) 39.

    Article  ADS  Google Scholar 

  79. J. Alexander; D. Karlen; P. Rosnet; talks given at the 29th Intl. Conf. on High Energy Physics (ICHEP 98), Vancouver, Canada, 23–29 July 1998, to appear in the proceedings.

    Google Scholar 

  80. Particle Data Group, Phys. Rev. D 54 (1996) 1.

    Google Scholar 

  81. A.J. Buras, M.E. Lautenbacher and G. Ostermaier, Phys. Rev. D 50 (1994) 3433.

    ADS  Google Scholar 

  82. L. Wolfenstein, Phys. Rev. Lett. 51 (1983) 1945.

    Article  ADS  Google Scholar 

  83. L. Wolfenstein, Phys. Rev. Lett. 13 (1964) 562.

    Article  ADS  Google Scholar 

  84. J. M. Flynn and L. Randall, Phys. Lett. B224 (1989) 221; erratum Phys. Lett. B235 (1990) 412.

    ADS  Google Scholar 

  85. G. Buchalla, A. J. Buras, and M. K. Harlander, Nucl. Phys. B337 (1990) 313.

    Article  ADS  Google Scholar 

  86. R. Gupta, hep-ph/9801412; R.S. Sharpe, hep-lat/9811006.

    Google Scholar 

  87. G. D. Barr et al., Phys. Lett. B317 (1993) 233.

    ADS  Google Scholar 

  88. L. K. Gibbons et al., Phys. Rev. Lett. 70 (1993) 1203.

    Article  ADS  MathSciNet  Google Scholar 

  89. A. Ali, and C. Greub, Z.Phys. C60 (1993) 433.

    ADS  Google Scholar 

  90. A. J. Buras, M. Misiak, M. Münz and S. Pokorski, Nucl. Phys. B424 (1994) 374.

    Article  ADS  Google Scholar 

  91. L. Littenberg, Phys. Rev. D39 (1989) 3322.

    ADS  Google Scholar 

  92. G. Buchalla and A.J. Buras, Phys. Lett. B333 (1994) 221; Phys. Rev. D54 (1996) 6782.

    ADS  Google Scholar 

  93. W. Marciano and Z. Parsa, Phys. Rev. D53, R1 (1996).

    Google Scholar 

  94. D. Rein and L.M. Sehgal, Phys. Rev. D39 (1989) 3325; J.S. Hagelin and L.S. Littenberg, Prog. Part. Nucl. Phys. 23 (1989) 1; M. Lu and M.B. Wise, Phys. Lett. B324 (1994) 461; S. Fajfer, Nuovo Cim. 110A (1997) 397; C.Q. Geng, I.J. Hsu and Y.C. Lin, Phys. Rev. D54 (1996) 877.

    ADS  Google Scholar 

  95. G. Buchalla and G. Isidori, hep-ph/9806501.

    Google Scholar 

  96. S. Adler et al., Phys. Rev. Lett. 79, (1997) 2204.

    Article  ADS  Google Scholar 

  97. J. Adams et al., hep-ex/9806007.

    Google Scholar 

  98. Y. Grossman, Y. Nir and R. Rattazzi, [hep-ph/9701231] in [24]; Y. Grossman and Y. Nir, Phys. Lett. B398 (1997) 163

    Google Scholar 

  99. L. Littenberg and J. Sandweiss, eds., AGS2000, Experiments for the 21st Century, BNL 52512.

    Google Scholar 

  100. P. Cooper, M. Crisler, B. Tschirhart and J. Ritchie (CKM collaboration), EOI for measuring Bγ(K + → π+νν-) at the Main Injector, Fermilab EOI 14, 1996.

    Google Scholar 

  101. K. Arisaka et al., KAMI conceptual design report, FNAL, June 1991.

    Google Scholar 

  102. T. Inagaki, T. Sato and T. Shinkawa, Experiment to search for the decay K L → π0νν-at KEK 12 GeV proton synchrotron, 30 Nov. 1991.

    Google Scholar 

  103. R. Fleischer, Int. J. of Mod. Phys. A12 (1997) 2459.

    Article  ADS  Google Scholar 

  104. W. A. Bardeen, A. J. Buras and J.-M. Gerard, Phys. Lett. B192 (1987) 138; A. Pich and E. de Rafael, Nucl. Phys. B358 (1991) 311; M. Neubert and B. Stech, Phys. Rev. D 44 (1991) 775; M. Jamin and A. Pich, Nucl. Phys. B425 (1994) 15; J. Kambor, J. Missimer and D. Wyler, Nucl. Phys. B346 (1990) 17; Phys. Lett. B261 (1991) 496; V. Antonelli, S. Bertolini, M. Fabrichesi, and E.I. Lashin, Nucl. Phys. B469 (1996) 181; J. Bijnens and J. Prades, hep-ph/9811472.

    ADS  Google Scholar 

  105. M. Neubert and B. Stech, [hep-ph/9705292], page 294 in [24]; B. Stech [hep-ph/9706384]; M.Neubert, Nucl. Phys. B (Proc. Suppl.) 64 (1998) 474, [hep-ph/9801269].

    Google Scholar 

  106. A.J. Buras and L. Silvestrini, hep-ph/9812392.

    Google Scholar 

  107. A. Ali, hep-ph/9812434.

    Google Scholar 

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Buras, A.J. (2000). Operator Product Expansion, Renormalization Group and Weak Decays. In: Breitenlohner, P., Maison, D. (eds) Quantum Field Theory. Lecture Notes in Physics, vol 558. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44482-3_5

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