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Chiral Perturbation Theory for Mesons

  • Stefan SchererEmail author
  • Matthias R. Schindler
Chapter
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Part of the Lecture Notes in Physics book series (LNP, volume 830)

Abstract

Chiral perturbation theory provides a systematic method for discussing the consequences of the global flavor symmetries of QCD at low energies by means of an effective field theory. The effective Lagrangian is expressed in terms of those hadronic degrees of freedom which, at low energies, appear as observable asymptotic states. At very low energies these are just the members of the pseudoscalar octet \((\pi,K,\eta)\) which are regarded as the Goldstone bosons of the spontaneous breaking of the chiral \(\hbox{SU}(3)_L\times\hbox{SU}(3)_R\) symmetry down to \(\hbox{SU}(3)_V.\) The nonvanishing masses of the light pseudoscalars in the “real” world are related to the explicit symmetry breaking in QCD by the light-quark masses

Keywords

Chiral Symmetry Goldstone Boson Effective Field Theory Dimensional Regularization Spontaneous Symmetry Breaking 
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.
    Adeva, B., et al., DIRAC Collaboration: Phys. Lett. B 619, 50 (2005)Google Scholar
  2. 2.
    Adler, S.L.: Phys. Rev. 177, 2426 (1969)ADSCrossRefGoogle Scholar
  3. 3.
    Adler, S.L., Bardeen, W.A.: Phys. Rev. 182, 1517 (1969)ADSCrossRefGoogle Scholar
  4. 4.
    Adler, S.L.: In: Deser, S., Grisaru, M., Pendleton, H. (eds.) Lectures on Elementary Particles and Quantum Field Theory, 1970 Brandeis University Summer Institute in Theoretical Physics, vol. 1. M.I.T. Press, Cambridge (1970)Google Scholar
  5. 5.
    Ahrens, J., et al.: Eur. Phys. J. A 23, 113 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    Akhoury, R., Alfakih, A.: Ann. Phys. 210, 81 (1991)MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 7.
    Ananthanarayan, B., Colangelo, G., Gasser, J., Leutwyler, H.: Phys. Rep. 353, 207 (2001)ADSzbMATHCrossRefGoogle Scholar
  8. 8.
    Antipov, Y.M., et al.: Phys. Lett. B 121, 445 (1983)ADSCrossRefGoogle Scholar
  9. 9.
    Balachandran, A.P., Trahern, C.G.: Lectures on Group Theory for Physicists. Bibliopolis, Naples (1984)Google Scholar
  10. 10.
    Balachandran, A.P., Marmo, G., Skagerstam, B.S., Stern, A.: Classical Topology and Quantum States (Chap. 12.2). World Scientific, Singapore (1991)Google Scholar
  11. 11.
    Bardeen, W.A.: Phys. Rev. 184, 1848 (1969)ADSCrossRefGoogle Scholar
  12. 12.
    Bär, O., Wiese, U.J.: Nucl. Phys. B 609, 225 (2001)ADSCrossRefGoogle Scholar
  13. 13.
    Batley, J.R., et al., NA48/2 Collaboration: Eur. Phys. J. C 54, 411 (2008)Google Scholar
  14. 14.
    Baym, G.: Phys. Rev. 117, 886 (1960)MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. 15.
    Bell, J.S., Jackiw, R.: Nuovo Cim. A 60, 47 (1969)ADSCrossRefGoogle Scholar
  16. 16.
    Bijnens, J., Cornet, F.: Nucl. Phys. B 296, 557 (1988)ADSCrossRefGoogle Scholar
  17. 17.
    Bijnens, J., Bramon, A., Cornet, F.: Z. Phys. C 46, 599 (1990)ADSCrossRefGoogle Scholar
  18. 18.
    Bijnens, J.: Int. J. Mod. Phys. A 8, 3045 (1993)ADSCrossRefGoogle Scholar
  19. 19.
    Bijnens, J., Ecker, G., Gasser, J.: In: Maiani, L., Pancheri, G., Paver, N. (eds.) The Second DA\(\Phi\)NE Physics Handbook, vol. 2, pp. 125–143. SIS, Frascati (1995)Google Scholar
  20. 20.
    Bijnens, J., Colangelo, G., Ecker, G., Gasser, J., Sainio, M.E.: Phys. Lett. B 374, 210 (1996)ADSCrossRefGoogle Scholar
  21. 21.
    Bijnens, J., Colangelo, G., Ecker, G., Gasser, J., Sainio, M.E.: Nucl. Phys. B 508, 263 (1997)ADSCrossRefGoogle Scholar
  22. 22.
    Bijnens, J., Colangelo, G., Ecker, G.: JHEP 9902, 020 (1999)ADSCrossRefGoogle Scholar
  23. 23.
    Bijnens, J., Girlanda, L., Talavera, P.: Eur. Phys. J. C 23, 539 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    Bijnens, J.: Prog. Part. Nucl. Phys. 58, 521 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    Bijnens, J., Jemos, I.: In: PoS (CD09), 087 (2009)Google Scholar
  26. 26.
    Bissegger, M., Fuhrer, A., Gasser, J., Kubis, B., Rusetsky, A.: Phys. Lett. B 659, 576 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    Bissegger, M., Fuhrer, A., Gasser, J., Kubis, B., Rusetsky, A.: Nucl. Phys. B 806, 178 (2009)ADSzbMATHCrossRefGoogle Scholar
  28. 28.
    Borasoy, B., Lipartia, E.: Phys. Rev. D 71, 014027 (2005)ADSCrossRefGoogle Scholar
  29. 29.
    Burgess, C.P.: Phys. Rep. 330, 193 (2000)ADSCrossRefGoogle Scholar
  30. 30.
    Bürgi, U.: Nucl. Phys. B 479, 392 (1996)ADSCrossRefGoogle Scholar
  31. 31.
    Cabibbo, N.: Phys. Rev. Lett. 93, 121801 (2004)ADSCrossRefGoogle Scholar
  32. 32.
    Cabibbo, N., Isidori, G.: JHEP 0503, 021 (2005)ADSCrossRefGoogle Scholar
  33. 33.
    Callan, C.G., Coleman, S.R., Wess, J., Zumino, B.: Phys. Rev. 177, 2247 (1969)ADSCrossRefGoogle Scholar
  34. 34.
    Chisholm, J.: Nucl. Phys. 26, 469 (1961)MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Colangelo, G., Gasser, J., Leutwyler, H.: Phys. Lett. B 488, 261 (2000)ADSCrossRefGoogle Scholar
  36. 36.
    Colangelo, G., Gasser, J., Leutwyler, H.: Phys. Rev. Lett. 86, 5008 (2001)ADSCrossRefGoogle Scholar
  37. 37.
    Colangelo, G., Gasser, J., Leutwyler, H.: Nucl. Phys. B 603, 125 (2001)ADSCrossRefGoogle Scholar
  38. 38.
    Colangelo, G., Gasser, J., Kubis, B., Rusetsky, A.: Phys. Lett. B 638, 187 (2006)ADSCrossRefGoogle Scholar
  39. 39.
    Colangelo, G., Gasser, J., Rusetsky, A.: Eur. Phys. J. C 59, 777 (2009)ADSCrossRefGoogle Scholar
  40. 40.
    Colangelo, G., et al.: arXiv:1011.4408 [hep-lat]Google Scholar
  41. 41.
    Coleman, S.: J. Math. Phys. 7, 787 (1966)ADSCrossRefGoogle Scholar
  42. 42.
    Coleman, S.R., Wess, J., Zumino, B.: Phys. Rev. 177, 2239 (1969)ADSCrossRefGoogle Scholar
  43. 43.
    Collins, J.C.: Renormalization. Cambridge University Press, Cambridge (1984)zbMATHCrossRefGoogle Scholar
  44. 44.
    Donoghue, J.F., Wyler, D.: Nucl. Phys. B 316, 289 (1989)ADSCrossRefGoogle Scholar
  45. 45.
    Donoghue, J.F.: In: PoS (EFT09), 001 (2009)Google Scholar
  46. 46.
    Ebertshäuser, T., Fearing, H.W., Scherer, S.: Phys. Rev. D 65, 054033 (2002)ADSCrossRefGoogle Scholar
  47. 47.
    Ecker, G., Gasser, J., Pich, A., de Rafael, E.: Nucl. Phys. B 321, 311 (1989)ADSCrossRefGoogle Scholar
  48. 48.
    Ecker, G.: arXiv:hep-ph/0507056Google Scholar
  49. 49.
    Fearing, H.W., Scherer, S.: Phys. Rev. D 53, 315 (1996)ADSCrossRefGoogle Scholar
  50. 50.
    Frlež, E., et al.: Phys. Rev. Lett. 93, 181804 (2004)ADSCrossRefGoogle Scholar
  51. 51.
    Gasser, J., Leutwyler, H.: Phys. Rep. 87, 77 (1982)ADSCrossRefGoogle Scholar
  52. 52.
    Gasser, J., Leutwyler, H.: Ann. Phys. 158, 142 (1984)MathSciNetADSCrossRefGoogle Scholar
  53. 53.
    Gasser, J., Leutwyler, H.: Nucl. Phys. B 250, 465 (1985)ADSCrossRefGoogle Scholar
  54. 54.
    Gasser, J., Sainio, M.E., Švarc, A.: Nucl. Phys. B 307, 779 (1988)ADSCrossRefGoogle Scholar
  55. 55.
    Gasser, J., Ivanov, M.A., Sainio, M.E.: Nucl. Phys. B 745, 84 (2006)ADSCrossRefGoogle Scholar
  56. 56.
    Gell-Mann, M., Oakes, R.J., Renner, B.: Phys. Rev. 175, 2195 (1968)ADSCrossRefGoogle Scholar
  57. 57.
    Georgi, H.: Weak Interactions and Modern Particle Theory. Benjamin/Cummings, Menlo Park (1984)Google Scholar
  58. 58.
    Georgi, H.: Ann. Rev. Nucl. Part. Sci. 43, 207 (1993)ADSCrossRefGoogle Scholar
  59. 59.
    Gerber, P., Leutwyler, H.: Nucl. Phys. B 321, 387 (1989)ADSCrossRefGoogle Scholar
  60. 60.
    Goldstone, J., Salam, A., Weinberg, S.: Phys. Rev. 127, 965 (1962)MathSciNetADSzbMATHCrossRefGoogle Scholar
  61. 61.
    Guskov, A., On behalf of the COMPASS collaboration: J. Phys. Conf. Ser. 110, 022016 (2008)Google Scholar
  62. 62.
    Holstein, B.R.: Comm. Nucl. Part. Phys. A 19, 221 (1990)Google Scholar
  63. 63.
    Itzykson, C., Zuber, J.B.: Quantum Field Theory. McGraw-Hill, New York (1980)Google Scholar
  64. 64.
    Jones, H.F.: Groups, Representations and Physics. Hilger, Bristol (1990)zbMATHCrossRefGoogle Scholar
  65. 65.
    Kamefuchi, S., O’Raifeartaigh, L., Salam, A.: Nucl. Phys. 28, 529 (1961)MathSciNetGoogle Scholar
  66. 66.
    Kaplan, D.B.: arXiv:nucl-th/9506035Google Scholar
  67. 67.
    Kermani, M., et al., CHAOS Collaboration: Phys. Rev. C 58, 3431 (1998)Google Scholar
  68. 68.
    Knecht, M., Moussallam, B., Stern, J., Fuchs, N.H.: Nucl. Phys. B 457, 513 (1995)ADSCrossRefGoogle Scholar
  69. 69.
    Leibbrandt, G.: Rev. Mod. Phys. 47, 849 (1975)MathSciNetADSCrossRefGoogle Scholar
  70. 70.
    Leutwyler, H.: In: Ellis, R.K., Hill, C.T., Lykken, J.D. (eds.) Perspectives in the Standard Model. Proceedings of the 1991 Advanced Theoretical Study Institute in Elementary Particle Physics, Boulder, CO, 2–28 June 1991. World Scientific, Singapore (1992)Google Scholar
  71. 71.
    Leutwyler, H.: Ann. Phys. 235, 165 (1994)MathSciNetADSCrossRefGoogle Scholar
  72. 72.
    Li, L.F., Pagels, H.: Phys. Rev. Lett. 26, 1204 (1971)ADSCrossRefGoogle Scholar
  73. 73.
    Manohar, A.V., Georgi, H.: Nucl. Phys. B 234, 189 (1984)ADSCrossRefGoogle Scholar
  74. 74.
    Manohar, A.V.: arXiv:hep-ph/9606222Google Scholar
  75. 75.
    Nakamura, K., et al., Particle Data Group: J. Phys. G 37, 075021 (2010)Google Scholar
  76. 76.
    Necco, S.: In: PoS (Confinement8), 024 (2008)Google Scholar
  77. 77.
    O’Raifeartaigh, L.: Group Structure of Gauge Theories. Cambridge University Press, Cambridge (1986)zbMATHCrossRefGoogle Scholar
  78. 78.
    Pich, A.: arXiv:hep-ph/9806303Google Scholar
  79. 79.
    Pich, A.: In: PoS (Confinement8), 026 (2008)Google Scholar
  80. 80.
    Pislak, S., et al., BNL-E865 Collaboration: Phys. Rev. Lett. 87, 221801 (2001)Google Scholar
  81. 81.
    Pislak, S., et al.: Phys. Rev. D 67, 072004 (2003) [Erratum, ibid. D 81, 119903 (2010)]ADSCrossRefGoogle Scholar
  82. 82.
    Polchinski, J.: arXiv:hep-th/9210046Google Scholar
  83. 83.
    Preston, M.A.: Physics of the Nucleus. Addison-Wesley, Reading (1962)zbMATHGoogle Scholar
  84. 84.
    Rosselet, L., et al.: Phys. Rev. D 15, 574 (1977)ADSCrossRefGoogle Scholar
  85. 85.
    Roy, S.M.: Phys. Lett. B 36, 353 (1971)ADSCrossRefGoogle Scholar
  86. 86.
    Scherer, S., Fearing, H.W.: Phys. Rev. D 52, 6445 (1995)ADSCrossRefGoogle Scholar
  87. 87.
    Scherer, S.: Adv. Nucl. Phys. 27, 277 (2003)CrossRefGoogle Scholar
  88. 88.
    Schwinger, J.S.: Phys. Lett. B 24, 473 (1967) ADSCrossRefGoogle Scholar
  89. 89.
    Terent’ev, M.V.: Yad. Fiz. 16, 162 (1972)Google Scholar
  90. 90.
    Terent’ev, M.V.: Sov. J. Nucl. Phys. 16, 87 (1973)MathSciNetGoogle Scholar
  91. 91.
    ’t Hooft, G., Veltman, M.J.: Nucl. Phys. B 44, 189 (1972)MathSciNetADSCrossRefGoogle Scholar
  92. 92.
    ’t Hooft, G., Veltman, M.J.: Nucl. Phys. B 153, 365 (1979)MathSciNetADSCrossRefGoogle Scholar
  93. 93.
    Unkmeir, C., Scherer, S., L’vov, A.I., Drechsel, D.: Phys. Rev. D 61, 034002 (2000)ADSCrossRefGoogle Scholar
  94. 94.
    Vafa, C., Witten, E.: Nucl. Phys. B 234, 173 (1984)MathSciNetADSCrossRefGoogle Scholar
  95. 95.
    Veltman, M.J.: Diagrammatica. The Path to Feynman Rules. Cambridge University Press, Cambridge (1994)CrossRefGoogle Scholar
  96. 96.
    Watson, K.M.: Phys. Rev. 95, 228 (1954)ADSzbMATHCrossRefGoogle Scholar
  97. 97.
    Weinberg, S.: Phys. Rev. Lett. 17, 616 (1966)ADSCrossRefGoogle Scholar
  98. 98.
    Weinberg, S.: Phys. Rev. Lett. 18, 188 (1967)ADSCrossRefGoogle Scholar
  99. 99.
    Weinberg, S.: Phys. Rev. 166, 1568 (1968)ADSCrossRefGoogle Scholar
  100. 100.
    Weinberg, S.: Physica A 96, 327 (1979)ADSCrossRefGoogle Scholar
  101. 101.
    Weinberg, S.: The Quantum Theory of Fields. Foundations, vol. I (Chap. 12). Cambridge University Press, Cambridge (1995)Google Scholar
  102. 102.
    Wess, J., Zumino, B.: Phys. Lett. B 37, 95 (1971)MathSciNetADSCrossRefGoogle Scholar
  103. 103.
    Witten, E.: Nucl. Phys. B 223, 422 (1983)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Johannes Gutenberg-Universität MainzInstitut für KernphysikMainzGermany
  2. 2.Department of Physics and AstronomyUniversity of South CarolinaColumbiaUSA
  3. 3.Department of PhysicsThe George Washington UniversityWashingtonUSA

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