Advertisement

The European Physical Journal A

, Volume 37, Issue 1, pp 15–32 | Cite as

Two photons into π0π0

  • J. A. OllerEmail author
  • L. RocaEmail author
Regular Article — Theoretical Physics

Abstract

We perform a theoretical study based on dispersion relations of the reaction γγπ 0 π 0 emphasizing the low-energy region. We discuss how the ƒ 0(980) signal emerges in γγππ within the dispersive approach and how this fixes to a large extent the phase of the isoscalar S-wave γγππ amplitude above the \( K\bar K \) threshold. This allows us to make sharper predictions for the cross-section at lower energies and our results could then be used to distinguish between different ππ isoscalar S-wave parameterizations with the advent of new precise data on πππ 0 π 0. We compare our dispersive approach with an updated calculation employing the unitary chiral perturbation theory (U gC PT). We also pay special attention to the role played by the σ-resonance in γγππ and calculate its coupling and width to γγ, for which we obtain Γ(σγγ) = (1.68 ± 0.15) keV.

PACS

11.55.Fv Dispersion relations 12.39.Fe Chiral Lagrangians 11.80.Et Partial-wave analysis 13.60.Le Meson production 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.A. Oller, E. Oset, Nucl. Phys. A 620, 438 (1997); 652, 407 (1999)(E).CrossRefADSGoogle Scholar
  2. 2.
    J.A. Oller, E. Oset, Phys. Rev. D 60, 074023 (1999).CrossRefADSGoogle Scholar
  3. 3.
    A. Dobado, J.R. Peláez, Phys. Rev. D 56, 3057 (1997); J.A. Oller, E. Oset, J.R. Peláez, Phys. Rev. Lett. 80, 3452 (1998); Phys. Rev. D 59, 074001 (1999); 60, 099906 (1999)(E); 75, 099903 (2007).CrossRefADSGoogle Scholar
  4. 4.
    J.R. Peláez, Phys. Rev. Lett. 92, 102001 (2004); J.R. Peláez, G. Rios, Phys. Rev. Lett. 97, 242002 (2006).CrossRefADSGoogle Scholar
  5. 5.
    T. Hannah, Phys. Rev. D 60, 017502 (1999).CrossRefADSGoogle Scholar
  6. 6.
    S. Weinberg, Physica A 96, 327 (1979).CrossRefADSGoogle Scholar
  7. 7.
    J. Gasser, H. Leutwyler, Ann. Phys. (N.Y.) 158, 142 (1984); Nucl. Phys. B 250, 465 (1985).CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    I. Caprini, G. Colangelo, H. Leutwyler, Phys. Rev. Lett. 96, 132001 (2006).CrossRefADSGoogle Scholar
  9. 9.
    F.J. Ynduráin, R. García-Martín, J.R. Peláez, Phys. Rev. D 76, 074034 (2007).CrossRefGoogle Scholar
  10. 10.
    M. Albaladejo, J.A. Oller, arXiv:0801.4929 [hep-ph]; arXiv:0711.1977 [hep-ph].Google Scholar
  11. 11.
    J. Bijnens, F. Cornet, Nucl. Phys. B 296, 557 (1988).CrossRefADSGoogle Scholar
  12. 12.
    J.F. Donoghue, B.R. Holstein, Y.C. Lin, Phys. Rev. D 37, 2423 (1988).CrossRefADSGoogle Scholar
  13. 13.
    Crystal Ball Collaboration (H. Marsiske et al.), Phys. Rev. D 41, 3324 (1990).CrossRefADSGoogle Scholar
  14. 14.
    S. Bellucci, J. Gasser, M.E. Sainio, Nucl. Phys. B 423, 80 (1994).CrossRefADSGoogle Scholar
  15. 15.
    J. Gasser, M.A. Ivanov, M.E. Sainio, Nucl. Phys. B 728, 31 (2005).CrossRefADSGoogle Scholar
  16. 16.
    G. Ecker, J. Gasser, A. Pich, E. de Rafael, Nucl. Phys. B 321, 311 (1989); G. Ecker, J. Gasser, H. Leutwyler, A. Pich, E. de Rafael, Phys. Lett. B 223, 425 (1989).CrossRefADSGoogle Scholar
  17. 17.
    A. Dobado, J.R. Peláez, Z. Phys. C 57, 501 (1993).CrossRefADSGoogle Scholar
  18. 18.
    J.F. Donoghue, B. Holstein, Phys. Rev. D 48, 137 (1993).CrossRefADSGoogle Scholar
  19. 19.
    J.A. Oller, E. Oset, Nucl. Phys. A 629, 739 (1998).CrossRefADSGoogle Scholar
  20. 20.
    J.A. Oller, Phys. Lett. B 426, 7 (1998).CrossRefADSGoogle Scholar
  21. 21.
    T.S.H. Lee, J.A. Oller, E. Oset, A. Ramos, Nucl. Phys. A 643, 402 (1998).CrossRefADSGoogle Scholar
  22. 22.
    U.G. Meissner, J.A. Oller, Nucl. Phys. A 679, 671 (2001).CrossRefADSGoogle Scholar
  23. 23.
    J.A. Oller, E. Oset, J.E. Palomar, Phys. Rev. D 63, 114009 (2001).CrossRefADSGoogle Scholar
  24. 24.
    E. Oset, J.A. Oller, U.G. Meissner, Eur. Phys. J. A 12, 435 (2001).CrossRefADSGoogle Scholar
  25. 25.
    E. Oset, J.R. Peláez, L. Roca, Phys. Rev. D 67, 073013 (2003); 77, 073001 (2008).CrossRefADSGoogle Scholar
  26. 26.
    M.R. Pennington, Phys. Rev. Lett. 97, 011601 (2006).CrossRefADSGoogle Scholar
  27. 27.
    D. Morgan, M.R. Pennington, Z. Phys. C 37, 431 (1988); 39, 590 (1988)(E); Phys. Lett. B 272, 134 (1991).CrossRefADSGoogle Scholar
  28. 28.
    M.R. Pennington, in The DAΦNE Physics Handbook, edited by L. Maiani, G. Panchieri, N. Paver (INFN, Frascati, 1992) p. 379.Google Scholar
  29. 29.
    J.A. Oller, L. Roca, C. Schat, Phys. Lett. B 659, 201 (2008).CrossRefADSGoogle Scholar
  30. 30.
    J.A. Oller, L. Roca, Phys. Lett. B 651, 139 (2007); J.A. Oller, L. Roca, C. Schat, arXiv:0711.2125 [hep-ph].CrossRefADSGoogle Scholar
  31. 31.
    Belle Collaboration (T. Mori et al.), Phys. Rev. D 75, 051101 (2007).CrossRefADSGoogle Scholar
  32. 32.
    J. Boyer et al., Phys. Rev. D 42, 1350 (1990).CrossRefADSGoogle Scholar
  33. 33.
    CELLO Collaboration (H.J. Behrend et al.), Z. Phys. C 56, 381 (1992).CrossRefADSGoogle Scholar
  34. 34.
    M.R. Pennington, T. Mori, S. Uehara, Y. Watanabe, arXiv:0803.3389 [hep-ph].Google Scholar
  35. 35.
    J. Babcock, J.L. Rosner, Phys. Rev. D 14, 1286 (1976).CrossRefADSGoogle Scholar
  36. 36.
    S. Godfrey, N. Isgur, Phys. Rev. D 32, 189 (1985).CrossRefADSGoogle Scholar
  37. 37.
    T. Barnes, Phys. Lett. B 165, 434 (1985).CrossRefADSGoogle Scholar
  38. 38.
    M.S. Chanowitz, Proceedings of the VIth International Workshop on Photon-Photon Collisions, Lake Tahoe, edited by U. Karshon (World Scientific, Singapore, 1988) p. 205.Google Scholar
  39. 39.
    S. Narison, G. Veneziano, Int. J. Mod. Phys. A 4, 2751 (1989).CrossRefADSGoogle Scholar
  40. 40.
    Z.P. Li, F.E. Close, T. Barnes, Phys. Rev. D 43, 2161 (1991).CrossRefADSGoogle Scholar
  41. 41.
    C.R. Munz, Nucl. Phys. A 609, 364 (1996).CrossRefADSGoogle Scholar
  42. 42.
    N.N. Achasov, Phys. At. Nucl. 65, 546 (2002) (Yad. Fiz. 65, 573 (2002)).CrossRefGoogle Scholar
  43. 43.
    S. Krewald, R.H. Lemmer, F.P. Sassen, Phys. Rev. D 69, 016003 (2004).CrossRefADSGoogle Scholar
  44. 44.
    S. Rodriguez, M. Napsuciale, Phys. Rev. D 71, 074008 (2005).CrossRefADSGoogle Scholar
  45. 45.
    C. Hanhart, Yu.S. Kalashnikova, A.E. Kudryavtsev, A.V. Nefediev, Phys. Rev. D 75, 074015 (2007).CrossRefADSGoogle Scholar
  46. 46.
    G. Mennessier, P. Minkowski, S. Narison, W. Ochs, arXiv: hep-ph/0707.4511.Google Scholar
  47. 47.
    B. Hyams et al., Nucl. Phys. B 64, 134 (1973).CrossRefADSGoogle Scholar
  48. 48.
    R. Kaminski, L. Lesniak, K. Rybicki, Z. Phys. C 74, 79 (1997).CrossRefGoogle Scholar
  49. 49.
    G. Grayer et al., Nucl. Phys. B 75, 189 (1974).CrossRefADSGoogle Scholar
  50. 50.
    BNL-E865 Collaboration (S. Pislak et al.), Phys. Rev. Lett. 87, 221801 (2001); Phys. Rev. D 67, 072004 (2003).CrossRefADSGoogle Scholar
  51. 51.
    NA48/2Collaboration (L. Masetti), arXiv:hep-ex/0610071.Google Scholar
  52. 52.
    M.J. Losty et al., Nucl. Phys. B 69, 185 (1974).CrossRefADSGoogle Scholar
  53. 53.
    W. Hoogland et al., Nucl. Phys. B 126, 109 (1977).CrossRefADSGoogle Scholar
  54. 54.
    G. Colangelo, J. Gasser, H. Leutwyler, Nucl. Phys. B 603, 125 (2001).CrossRefADSGoogle Scholar
  55. 55.
    J.R. Peláez, F.J. Ynduráin, Phys. Rev. D 68, 074005 (2003); 71, 074016 (2005).CrossRefADSGoogle Scholar
  56. 56.
    F.J. Ynduráin, Phys. Lett. B 578, 99 (2004); 586, 439 (2004)(E).CrossRefADSGoogle Scholar
  57. 57.
    F.J. Ynduráin, Phys. Lett. B 612, 245 (2005).CrossRefADSGoogle Scholar
  58. 58.
    F.J. Ynduráin, arXiv:hep-ph/0510317.Google Scholar
  59. 59.
    B. Ananthanarayan, I. Caprini, G. Colangelo, J. Gasser, H. Leutwyler, Phys. Lett. B 602, 218 (2004).CrossRefADSGoogle Scholar
  60. 60.
    J.F. Donoghue, J. Gasser, H. Leutwyler, Nucl. Phys. B 343, 341 (1990).CrossRefADSGoogle Scholar
  61. 61.
    B. Moussallam, Eur. Phys. J. C 14, 111 (2000).ADSGoogle Scholar
  62. 62.
    F.E. Low, Phys. Rev. 96, 1428 (1954); M. Gell-Mann, M.L. Goldberger, Phys. Rev. 96, 1433 (1954).zbMATHCrossRefADSMathSciNetGoogle Scholar
  63. 63.
    ARGUS Collaboration (H. Albrecht et al.), Z. Phys. C 48, 183 (1990).CrossRefGoogle Scholar
  64. 64.
    TASSO Collaboration (M. Althoff et al.), Z. Phys. C 29, 189 (1985); CELLO Collaboration (H.J. Behrend et al.), Z. Phys. C 43, 91 (1989).CrossRefADSGoogle Scholar
  65. 65.
    N.N. Achasov, Proceedings of the 14th International Seminar on High Energy Physics: Quarks 2006, St. Petersburg, Russia, arXiv: hep-ph/0609261.Google Scholar
  66. 66.
    G. Mennessier, Z. Phys. C 16, 241 (1983).CrossRefADSGoogle Scholar
  67. 67.
    W. Wetzel et al., Nucl. Phys. B 115, 208 (1976); V.A. Polychromatos et al., Phys. Rev. D 19, 1317 (1979); D. Cohen et al., Phys. Rev. D 22, 2595 (1980); E. Etkin et al., Phys. Rev. D 25, 1786 (1982).CrossRefADSGoogle Scholar
  68. 68.
    Pyungwon Ko, Phys. Rev. D 41, 1531 (1990).CrossRefADSGoogle Scholar
  69. 69.
    J.F. Donoghue, B. Holstein, D. Wyler, Phys. Rev. D 47, 2089 (1993).CrossRefADSGoogle Scholar
  70. 70.
    S. Weinberg, Phys. Rev. Lett. 18, 507 (1967).CrossRefADSGoogle Scholar
  71. 71.
    K. Kawarabayashi, M. Suzuki, Phys. Rev. Lett. 16, 255 (1966); Riazuddin, Fayyazuddin, Phys. Rev. 147, 1071 (1966).CrossRefADSMathSciNetGoogle Scholar
  72. 72.
    J. Prades, Z. Phys. C 63, 491 (1994); 11, 571 (1999)(E).CrossRefADSGoogle Scholar
  73. 73.
    J. Bijnens, C. Bruno, E. de Rafael, Nucl. Phys. B 390, 501 (1993).CrossRefADSGoogle Scholar
  74. 74.
    P. Ko, Phys. Rev. D 47, 3933 (1993).CrossRefADSGoogle Scholar
  75. 75.
    W.-M. Yao et al., J. Phys. G 33, 1 (2006).CrossRefADSGoogle Scholar
  76. 76.
    L. Roca, J.E. Palomar, E. Oset, H.C. Chiang, Nucl. Phys. A 744, 127 (2004); AIP Conf. Proc. 814, 634 (2006).CrossRefADSGoogle Scholar
  77. 77.
    J.A. Oller, Phys. Rev. D 71, 054030 (2005).CrossRefADSGoogle Scholar
  78. 78.
    J.A. Oller, Nucl. Phys. A 714, 161 (2003); J.E. Palomar, L. Roca, E. Oset, M.J. Vicente Vacas, Nucl. Phys. A 729, 743 (2003); E. Marco, S. Hirenzaki, E. Oset, H. Toki, Phys. Lett. B 470, 20 (1999).CrossRefADSGoogle Scholar
  79. 79.
    S. Weinberg, Phys. Lett. B 251, 288 (1990); Nucl. Phys. B 363, 3 (1991).CrossRefADSMathSciNetGoogle Scholar
  80. 80.
    E. Epelbaum, W. Gloeckle, U.G. Meissner, Nucl. Phys. A 637, 107 (1998); 671, 295 (2000).CrossRefADSGoogle Scholar
  81. 81.
    D.R. Entem, R. Machleidt, Phys. Rev. C 68, 041001 (2003); S.K. Bogner, T.T.S. Kuo, A. Schwenk, D.R. Entem, R. Machleidt, Phys. Lett. B 576, 265 (2003).CrossRefADSGoogle Scholar
  82. 82.
    E. Oset, H. Toki, M. Mizobe, T.T. Takahashi, Prog. Theor. Phys. 103, 351 (2000).CrossRefADSGoogle Scholar
  83. 83.
    J. Schwinger, Ann. Phys. 2, 407 (1957); M. Gell-Mann, M. Lévy, Nuovo Cimento 16, 705 (1960); B.W. Lee, Nucl. Phys. B 9, 649 (1969); S. Gasiorowicz, D.A. Geffen, R.J. Schecther, Y. Ueda, Phys. Rev. D 3, 2874 (1971); 8, 987 (1973)(E); H. Pagels, Phys. Rep. C 16, 219 (1975); N.A. Törnqvist, Eur. Phys. J. C 11, 359 (1999).zbMATHCrossRefADSMathSciNetGoogle Scholar
  84. 84.
    J.A. Oller, Nucl. Phys. A 727, 353 (2003).CrossRefADSGoogle Scholar
  85. 85.
    J.A. Oller, Proceedings of the Workshop Possible Existence of the σ-meson and its implications to Hadron Physics, KEK Proc. 2000-4, NUP B-2000-1, p. 33; Soryushiron Kenkyu 102, 33 (2001); arXiv:hep-ph/0007349.Google Scholar
  86. 86.
    S. Weinberg, The Quantum Theory of Fields, Vol. 1: Foundations (Cambridge University Press, 1995).Google Scholar
  87. 87.
    U.G. Meissner, Phys. Rep. 161, 213 (1988).CrossRefADSGoogle Scholar
  88. 88.
    J. Bernabéu, J. Prades, arXiv:0802.1830 [hep-ph].Google Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  1. 1.Departamento de FísicaUniversidad de MurciaMurciaSpain

Personalised recommendations