Non-linear QCD dynamics in two-photon interactions at high energies

  • V. P. Gonçalves
  • M. S. Kugeratski
  • E. R. Cazaroto
  • F. Carvalho
  • F. S. Navarra
Regular Article - Theoretical Physics

Abstract

Perturbative QCD predicts that the growth of the gluon density at high energies should saturate, forming a Color Glass Condensate (CGC), which is described in mean field approximation by the Balitsky–Kovchegov (BK) equation. In this paper we study the γγ interactions at high energies and estimate the main observables which will be probed at future linear colliders using the color dipole picture. We discuss in detail the dipole–dipole cross section and propose a new relation between this quantity and the dipole scattering amplitude. The total γγ, γ γ cross sections and the real photon structure function \(F_{2}^{\gamma }(x,Q^{2})\) are calculated using the recent solution of the BK equation with running coupling constant and the predictions are compared with those obtained using phenomenological models for the dipole–dipole cross section and scattering amplitude. We demonstrate that these models are able to describe the LEP data at high energies, but predict a very different behavior for the observables at higher energies. Therefore we conclude that the study of γγ interactions can be useful to constrain the QCD dynamics.

Keywords

Light Quark Mass BFKL Equation HERA Data Color Glass Condensate Dipole Cross Section 

References

  1. 1.
    A.H. Mueller, Nucl. Phys. B 415, 373 (1994) ADSCrossRefGoogle Scholar
  2. 2.
    A.H. Mueller, B. Patel, Nucl. Phys. B 425, 471 (1994) ADSCrossRefGoogle Scholar
  3. 3.
    N.N. Nikolaev, B.G. Zakharov, Z. Phys. C 49, 607 (1991) Google Scholar
  4. 4.
    N.N. Nikolaev, B.G. Zakharov, Z. Phys. C 53, 331 (1992) ADSGoogle Scholar
  5. 5.
    L.N. Lipatov, Sov. J. Nucl. Phys. 23, 338 (1976) Google Scholar
  6. 6.
    E.A. Kuraev, L.N. Lipatov, V.S. Fadin, J. Exp. Theor. Phys. 45, 1999 (1977) MathSciNetGoogle Scholar
  7. 7.
    I.I. Balitskii, L.N. Lipatov, Sov. J. Nucl. Phys. 28, 822 (1978) Google Scholar
  8. 8.
    F. Gelis, E. Iancu, J. Jalilian-Marian, R. Venugopalan, arXiv:1002.0333 [hep-ph]
  9. 9.
    E. Iancu, R. Venugopalan, arXiv:hep-ph/0303204
  10. 10.
    A.M. Stasto, Acta Phys. Pol. B 35, 3069 (2004) ADSGoogle Scholar
  11. 11.
    H. Weigert, Prog. Part. Nucl. Phys. 55, 461 (2005) MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    J. Jalilian-Marian, Y.V. Kovchegov, Prog. Part. Nucl. Phys. 56, 104 (2006) ADSCrossRefGoogle Scholar
  13. 13.
    Y.V. Kovchegov, H. Weigert, Nucl. Phys. A 784, 188 (2007) ADSCrossRefGoogle Scholar
  14. 14.
    Y.V. Kovchegov, H. Weigert, Nucl. Phys. A 789, 260 (2007) ADSCrossRefGoogle Scholar
  15. 15.
    Y.V. Kovchegov, J. Kuokkanen, K. Rummukainen, H. Weigert, Nucl. Phys. A 823, 47 (2009) ADSCrossRefGoogle Scholar
  16. 16.
    J.L. Albacete, Y.V. Kovchegov, Phys. Rev. D 75, 125021 (2007) ADSGoogle Scholar
  17. 17.
    I. Balitsky, Phys. Rev. D 75, 014001 (2007) ADSCrossRefGoogle Scholar
  18. 18.
    I. Balitsky, G.A. Chirilli, Phys. Rev. D 77, 014019 (2008) ADSGoogle Scholar
  19. 19.
    J.L. Albacete, N. Armesto, J.G. Milhano, C.A. Salgado, Phys. Rev. D 80, 034031 (2009) ADSGoogle Scholar
  20. 20.
    H. Weigert, J. Kuokkanen, K. Rummukainen, AIP Conf. Proc. 1105, 394 (2009) ADSCrossRefGoogle Scholar
  21. 21.
    M.A. Betemps, V.P. Goncalves, J.T. de Santana Amaral, Eur. Phys. J. C 66, 137 (2010) ADSCrossRefGoogle Scholar
  22. 22.
    V.P. Goncalves, M.V.T. Machado, A.R. Meneses, Eur. Phys. J. C 68, 133 (2010) ADSCrossRefGoogle Scholar
  23. 23.
    J.L. Albacete, C. Marquet, Phys. Lett. B 687, 174 (2010) ADSGoogle Scholar
  24. 24.
    R. Nisius, Phys. Rep. 332, 165 (2000) ADSCrossRefGoogle Scholar
  25. 25.
    J. Bartels, A. De Roeck, H. Lotter, Phys. Lett. B 389, 742 (1996) ADSGoogle Scholar
  26. 26.
    J. Bartels, C. Ewerz, R. Staritzbichler, Phys. Lett. B 492, 56 (2000) ADSGoogle Scholar
  27. 27.
    A. Bialas, W. Czyz, W. Florkowski, Eur. Phys. J. C 2, 683 (1998) ADSGoogle Scholar
  28. 28.
    J. Kwiecinski, L. Motyka, Eur. Phys. J. C 18, 343 (2000) ADSCrossRefGoogle Scholar
  29. 29.
    N.N. Nikolaev, B.G. Zakharov, V.R. Zoller, J. Exp. Theor. Phys. 93, 957 (2001) ADSCrossRefGoogle Scholar
  30. 30.
    S.J. Brodsky, F. Hautmann, D.E. Soper, Phys. Rev. D 56, 6957 (1997) ADSGoogle Scholar
  31. 31.
    S.J. Brodsky, F. Hautmann, D.E. Soper, Phys. Rev. Lett. 78, 803 (1997) ADSCrossRefGoogle Scholar
  32. 32.
    M. Boonekamp, A. De Roeck, C. Royon, S. Wallon, Nucl. Phys. B 555, 540 (1999) ADSCrossRefGoogle Scholar
  33. 33.
    S.J. Brodsky, V.S. Fadin, V.T. Kim, L.N. Lipatov, G.B. Pivovarov, Pisma ZHETF 76, 306 (2002). [JETP Lett. 76, 249 (2002)] Google Scholar
  34. 34.
    V.P. Goncalves, M.V.T. Machado, W.K. Sauter, J. Phys. G 34, 1673 (2007) ADSCrossRefGoogle Scholar
  35. 35.
    F. Caporale, D.Y. Ivanov, A. Papa, Eur. Phys. J. C 58, 1 (2008) ADSCrossRefGoogle Scholar
  36. 36.
    K. Golec-Biernat, M. Wüsthoff, Phys. Rev. D 60, 114023 (1999) ADSGoogle Scholar
  37. 37.
    K. Golec-Biernat, M. Wüsthoff, Phys. Rev. D 59, 014017 (1998) ADSGoogle Scholar
  38. 38.
    J. Bartels, K. Golec-Biernat, H. Kowalski, Phys. Rev. D 66, 014001 (2002) ADSCrossRefGoogle Scholar
  39. 39.
    H. Kowalski, D. Teaney, Phys. Rev. D 68, 114005 (2003) ADSGoogle Scholar
  40. 40.
    H. Kowalski, L. Motyka, G. Watt, Phys. Rev. D 74, 074016 (2006) ADSGoogle Scholar
  41. 41.
    J.R. Forshaw, R. Sandapen, G. Shaw, Phys. Lett. B 594, 283 (2004) ADSGoogle Scholar
  42. 42.
    J.R. Forshaw, R. Sandapen, G. Shaw, J. High Energy Phys. 0611, 025 (2006) ADSCrossRefGoogle Scholar
  43. 43.
    D. Kharzeev, Y.V. Kovchegov, K. Tuchin, Phys. Lett. B 599, 23 (2004) ADSGoogle Scholar
  44. 44.
    E. Iancu, K. Itakura, S. Munier, Phys. Lett. B 590, 199 (2004) ADSGoogle Scholar
  45. 45.
    A. Dumitru, A. Hayashigaki, J. Jalilian-Marian, Nucl. Phys. A 765, 464 (2006) ADSCrossRefGoogle Scholar
  46. 46.
    A. Dumitru, A. Hayashigaki, J. Jalilian-Marian, Nucl. Phys. A 770, 57 (2006) ADSCrossRefGoogle Scholar
  47. 47.
    V.P. Goncalves, M.S. Kugeratski, M.V.T. Machado, F.S. Navarra, Phys. Lett. B 643, 273 (2006) ADSGoogle Scholar
  48. 48.
    C. Marquet, R.B. Peschanski, G. Soyez, Phys. Rev. D 76, 034011 (2007) ADSGoogle Scholar
  49. 49.
    C. Marquet, Phys. Rev. D 76, 094017 (2007) ADSGoogle Scholar
  50. 50.
    D. Boer, A. Utermann, E. Wessels, Phys. Rev. D 77, 054014 (2008) ADSGoogle Scholar
  51. 51.
    G. Soyez, Phys. Lett. B 655, 32 (2007) ADSGoogle Scholar
  52. 52.
    G. Watt, H. Kowalski, Phys. Rev. D 78, 014016 (2008) ADSGoogle Scholar
  53. 53.
    N. Timneanu, J. Kwiecinski, L. Motyka, Eur. Phys. J. C 23, 513 (2002) ADSCrossRefGoogle Scholar
  54. 54.
    N.N. Nikolaev, J. Speth, V.R. Zoller, Eur. Phys. J. C 22, 637 (2002) ADSCrossRefGoogle Scholar
  55. 55.
    N.N. Nikolaev, J. Speth, V.R. Zoller, J. Exp. Theor. Phys. 93, 957 (2001). [Zh. Eksp. Teor. Fiz. 93, 1104 (2001)] ADSCrossRefGoogle Scholar
  56. 56.
    A. Donnachie, H.G. Dosch, M. Rueter, Phys. Rev. D 59, 074011 (1999) ADSGoogle Scholar
  57. 57.
    J.L. Albacete, N. Armesto, J.G. Milhano, P.Q. Arias, C.A. Salgado, arXiv:1012.4408 [hep-ph]
  58. 58.
    A.H. Mueller, A.I. Shoshi, Nucl. Phys. B 692, 175 (2004) ADSMATHCrossRefGoogle Scholar
  59. 59.
    E. Iancu, A.H. Mueller, S. Munier, Phys. Lett. B 606, 342 (2005) ADSGoogle Scholar
  60. 60.
    E. Iancu, D.N. Triantafyllopoulos, Nucl. Phys. A 756, 419 (2005) ADSCrossRefGoogle Scholar
  61. 61.
    A.H. Mueller, A.I. Shoshi, S.M.H. Wong, Nucl. Phys. B 715, 440 (2005) ADSCrossRefGoogle Scholar
  62. 62.
    E. Iancu, D.N. Triantafyllopoulos, Phys. Lett. B 610, 253 (2005) ADSGoogle Scholar
  63. 63.
    E. Levin, M. Lublinsky, Nucl. Phys. A 763, 172 (2005) ADSCrossRefGoogle Scholar
  64. 64.
    A. Kovner, M. Lublinsky, Phys. Rev. D 71, 085004 (2005) ADSGoogle Scholar
  65. 65.
    A. Kovner, M. Lublinsky, Phys. Rev. Lett. 94, 181603 (2005) ADSCrossRefGoogle Scholar
  66. 66.
    E. Iancu, Y. Hatta, C. Marquet, G. Soyez, D.N. Triantafyllopoulos, Nucl. Phys. A 773, 95 (2006) ADSCrossRefGoogle Scholar
  67. 67.
    A. Dumitru, E. Iancu, L. Portugal, G. Soyez, D.N. Triantafyllopoulos, J. High Energy Phys. 0708, 062 (2007) ADSCrossRefGoogle Scholar
  68. 68.
    H. Navelet, S. Wallon, Nucl. Phys. B 522, 237 (1998) ADSCrossRefGoogle Scholar
  69. 69.
    A.H. Mueller, G.P. Salam, Nucl. Phys. B 475, 293 (1996) ADSCrossRefGoogle Scholar
  70. 70.
    E. Iancu, A.H. Mueller, Nucl. Phys. A 730, 460 (2004) ADSCrossRefGoogle Scholar
  71. 71.
    G.P. Salam, Nucl. Phys. B 461, 512 (1996) ADSCrossRefGoogle Scholar
  72. 72.
    E. Iancu, M.S. Kugeratski, D.N. Triantafyllopoulos, Nucl. Phys. A 808, 95 (2008) ADSCrossRefGoogle Scholar
  73. 73.
    E. Iancu, K. Itakura, L. McLerran, Nucl. Phys. A 708, 327 (2002) ADSMATHCrossRefGoogle Scholar
  74. 74.
    A.H. Mueller, D.N. Triantafyllopoulos, Nucl. Phys. B 640, 331 (2002) ADSMATHCrossRefGoogle Scholar
  75. 75.
    N. Armesto, M.A. Braun, Eur. Phys. J. C 20, 517 (2001) ADSCrossRefGoogle Scholar
  76. 76.
    M.A. Braun, Phys. Lett. B 576, 115 (2003) ADSGoogle Scholar
  77. 77.
    J.L. Albacete, N. Armesto, J.G. Milhano, C.A. Salgado, U.A. Wiedemann, Phys. Rev. D 71, 014003 (2005) ADSGoogle Scholar
  78. 78.
  79. 79.
    M. Acciarri et al. (L3 Collaboration), Phys. Lett. B 519, 33 (2001) ADSGoogle Scholar
  80. 80.
    M. Acciarri et al. (L3 Collaboration), Phys. Lett. B 453, 333 (1999) ADSGoogle Scholar
  81. 81.
    M. Acciarri et al. (L3 Collaboration), Phys. Lett. B 447, 147 (1999) ADSGoogle Scholar
  82. 82.
    G. Abbiendi et al. (OPAL Collaboration), Eur. Phys. J. C 18, 15 (2000) ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2011

Authors and Affiliations

  • V. P. Gonçalves
    • 1
  • M. S. Kugeratski
    • 2
  • E. R. Cazaroto
    • 3
  • F. Carvalho
    • 4
  • F. S. Navarra
    • 3
  1. 1.Instituto de Física e MatemáticaUniversidade Federal de PelotasPelotasBrazil
  2. 2.Centro de Engenharia da MobilidadeUniversidade Federal de Santa CatarinaJoinvilleBrazil
  3. 3.Instituto de FísicaUniversidade de São PauloSão PauloBrazil
  4. 4.Departamento de Ciências Exatas e da TerraUniversidade Federal de São PauloDiademaBrazil

Personalised recommendations