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The European Physical Journal C

, Volume 58, Issue 2, pp 193–215 | Cite as

Sum rules and dualities for generalized parton distributions: is there a holographic principle?

  • K. Kumerički
  • D. Müller
  • K. Passek-KumeričkiEmail author
Regular Article - Theoretical Physics

Abstract

To leading order approximation, the physical content of generalized parton distributions (GPDs) that is accessible in deep virtual electroproduction of photons or mesons is contained in their value on the cross-over trajectory. This trajectory separates the t-channel and s-channel dominated GPD regions. The underlying Lorentz covariance implies correspondence between these two regions through their relation to GPDs on the cross-over trajectory. This point of view leads to a family of GPD sum rules which are a quark analogue of finite energy sum rules and it guides us to a new phenomenological GPD concept. As an example, we discuss the constraints from the JLab/Hall A data on the dominant u-quark GPD H. The question arises whether GPDs are governed by some kind of holographic principle.

PACS

11.30.Cp 13.60.Fz 11.30.Ly 11.55.Hx 

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References

  1. 1.
    D. Müller, D. Robaschik, B. Geyer, F.-M. Dittes, J. Hořejši, Fortschr. Phys. 42, 101 (1994). hep-ph/9812448 Google Scholar
  2. 2.
    A.V. Radyushkin, Phys. Lett. B 380, 417 (1996). hep-ph/9604317 ADSGoogle Scholar
  3. 3.
    X. Ji, Phys. Rev. D 55, 7114 (1997). hep-ph/9609381 ADSGoogle Scholar
  4. 4.
    J. Collins, L. Frankfurt, M. Strikman, Phys. Rev. D 56, 2982 (1997). hep-ph/9611433 ADSGoogle Scholar
  5. 5.
    J. Collins, A. Freund, Phys. Rev. D 59, 074009 (1999). hep-ph/9801262 ADSGoogle Scholar
  6. 6.
    M. Diehl, Phys. Rep. 388, 41 (2003). hep-ph/0307382 ADSGoogle Scholar
  7. 7.
    A.V. Belitsky, A.V. Radyushkin, Phys. Rep. 418, 1 (2005). hep-ph/0504030 ADSGoogle Scholar
  8. 8.
    X. Ji, Phys. Rev. Lett. 78, 610 (1997). hep-ph/9603249 ADSGoogle Scholar
  9. 9.
    H1, C. Adloff et al., Phys. Lett. B 517, 47 (2001). hep-ex/0107005 ADSGoogle Scholar
  10. 10.
    HERMES, A. Airapetian et al., Phys. Rev. Lett. 87, 182001 (2001). hep-ex/0106068 ADSGoogle Scholar
  11. 11.
    CLAS, S. Stepanyan, Phys. Rev. Lett. 87, 182002 (2001). hep-ex/0107043 ADSGoogle Scholar
  12. 12.
    ZEUS, S. Chekanov et al., Phys. Lett. B 573, 46 (2003). hep-ex/0305028 ADSGoogle Scholar
  13. 13.
    H1, A. Aktas et al., Eur. Phys. J. C 44, 1 (2005). hep-ex/0505061 Google Scholar
  14. 14.
    Jefferson Lab Hall A and Hall A DVCS, C.M. Camacho et al., Phys. Rev. Lett. 97, 262002 (2006). nucl-ex/0607029 ADSGoogle Scholar
  15. 15.
    HERMES, A. Airapetian et al., Phys. Rev. D 75, 011103 (2007). hep-ex/0605108 ADSGoogle Scholar
  16. 16.
    CLAS, S. Chen et al., Phys. Rev. Lett. 97, 072002 (2006). hep-ex/0605012 ADSGoogle Scholar
  17. 17.
    Jefferson Lab Hall A, M. Mazouz et al., Phys. Rev. Lett. 99, 242501 (2007). nucl-ex/0709.0450 ADSGoogle Scholar
  18. 18.
    H1, F.D. Aaron et al., Phys. Lett. B 659, 796 (2008). hep-ex/0709.4114 ADSGoogle Scholar
  19. 19.
    CLAS, F.X. Girod et al., Deeply virtual Compton scattering beam-spin asymmetries (2007). hep-ex/0711.4805
  20. 20.
    HERMES, A. Airapetian et al., Measurement of azimuthal asymmetries with respect to both beam charge and transverse target polarization in exclusive electroproduction of real photons (2008). hep-ex/0802.2499
  21. 21.
    ZEUS, J. Breitweg et al., Eur. Phys. J. C 6, 603 (1999). hep-ex/9808020 ADSGoogle Scholar
  22. 22.
    H1, C. Adloff et al., Eur. Phys. J. C 13, 371 (2000). hep-ex/9902019 ADSGoogle Scholar
  23. 23.
    ZEUS, J. Breitweg et al., Eur. Phys. J. C 12, 393 (2000). hep-ex/9908026 ADSGoogle Scholar
  24. 24.
    HERMES, A. Airapetian et al., Phys. Lett. B 659, 486 (2008). hep-ex/0707.0222 ADSGoogle Scholar
  25. 25.
    M. Guidal, S. Morrow, Exclusive ρ 0 electroproduction on the proton: GPDs or not GPDs? (2007). hep-ph/0711.3743
  26. 26.
    M. Vanderhaeghen, P.A.M. Guichon, M. Guidal, Phys. Rev. Lett. 80, 5064 (1998) ADSGoogle Scholar
  27. 27.
    A.V. Belitsky, D. Müller, A. Kirchner, Nucl. Phys. B 629, 323 (2002). hep-ph/0112108 ADSGoogle Scholar
  28. 28.
    A. Kirchner, D. Müller, Eur. Phys. J. C 32, 347 (2003). hep-ph/0302007 ADSGoogle Scholar
  29. 29.
    V. Guzey, T. Teckentrup, Phys. Rev. D 74, 054027 (2006). hep-ph/0607099 ADSGoogle Scholar
  30. 30.
    M.V. Polyakov, M. Vanderhaeghen, Taming deeply virtual Compton scattering (2008). hep-ph/0803.1271
  31. 31.
    A. Freund, M.F. McDermott, Phys. Rev. D 65, 091901 (2002). hep-ph/0106124 ADSGoogle Scholar
  32. 32.
    A. Freund, M. McDermott, Eur. Phys. J. C 23, 651 (2002). hep-ph/0111472 ADSGoogle Scholar
  33. 33.
    K. Kumerički, D. Müller, K. Passek-Kumerički, A. Schäfer, Phys. Lett. B 648, 186 (2007). hep-ph/0605237 ADSGoogle Scholar
  34. 34.
    K. Kumerički, D. Müller, K. Passek-Kumerički, Nucl. Phys. B 794, 244 (2008). hep-ph/0703179 zbMATHADSGoogle Scholar
  35. 35.
    J.M. Laget, Phys. Lett. B 489, 313 (2000). hep-ph/0003213 ADSGoogle Scholar
  36. 36.
    F. Cano, J.M. Laget, Phys. Lett. B 551, 317 (2003). hep-ph/0209362. Erratum-ibid. B 571 (2003) 250 ADSGoogle Scholar
  37. 37.
    M. Capua, S. Fazio, R. Fiore, L. Jenkovszky, F. Paccanoni, Phys. Lett. B 645, 161 (2007). hep-ph/0605319 ADSGoogle Scholar
  38. 38.
    J.M. Laget, Phys. Rev. C 76, 052201 (2007). hep-ph/0708.1250 ADSGoogle Scholar
  39. 39.
    K. Kumerički, D. Müller, K. Passek-Kumerički, Fitting DVCS at NLO and beyond (2007). hep-ph/0710.5649
  40. 40.
    M.V. Polyakov, Phys. Lett. B 659, 542 (2008). hep-ph/0707.2509 ADSGoogle Scholar
  41. 41.
    M.V. Polyakov, Educing GPDs from amplitudes of hard exclusive processes (2007). hep-ph/0711.1820
  42. 42.
    D. Müller, A. Schäfer, Nucl. Phys. B 739, 1 (2006). hep-ph/0509204 zbMATHGoogle Scholar
  43. 43.
    O.V. Teryaev, Analytic properties of hard exclusive amplitudes (2005). hep-ph/0510031
  44. 44.
    L. Frankfurt, A. Freund, V. Guzey, M. Strikman, Phys. Lett. B 418, 345 (1998). hep-ph/9703449. Erratum-ibid. B429 (1998) 414 ADSGoogle Scholar
  45. 45.
    Z. Chen, Nucl. Phys. B 525, 369 (1998). hep-ph/9705279 ADSGoogle Scholar
  46. 46.
    M. Diehl, D.Y. Ivanov, Eur. Phys. J. C 52, 919 (2007). hep-ph/0707.0351 ADSGoogle Scholar
  47. 47.
    I.V. Anikin, O.V. Teryaev, Phys. Rev. D 76, 056007 (2007). hep-ph/0704.2185 ADSGoogle Scholar
  48. 48.
    P.V. Pobylitsa, Phys. Rev. D 66, 094002 (2002). hep-ph/0204337 ADSGoogle Scholar
  49. 49.
    P.V. Pobylitsa, Phys. Rev. D 70, 034004 (2004). hep-ph/0211160 ADSGoogle Scholar
  50. 50.
    P.V. Pobylitsa, Phys. Rev. D 67, 034009 (2003). hep-ph/0210150 ADSGoogle Scholar
  51. 51.
    A. Freund, Phys. Lett. B 472, 412 (2000). hep-ph/9903488 ADSGoogle Scholar
  52. 52.
    P.D.B. Collins, An Introduction to Regge Theory and High Energy Physics (Cambridge University Press, Cambridge, 1977) Google Scholar
  53. 53.
    J.M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998). hep-th/9711200 zbMATHADSMathSciNetGoogle Scholar
  54. 54.
    S.S. Gubser, I.R. Klebanov, A.M. Polyakov, Phys. Lett. B 428, 105 (1998). hep-th/9802109 ADSMathSciNetGoogle Scholar
  55. 55.
    E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998). hep-th/9802150 zbMATHMathSciNetGoogle Scholar
  56. 56.
    M. Guidal, Discussion on the recent proton-DVCS results of Jefferson Lab (2008). hep-ph/0803.1592
  57. 57.
    A.V. Radyushkin, Phys. Rev. D 56, 5524 (1997). hep-ph/9704207 ADSGoogle Scholar
  58. 58.
    V.M. Braun, G.P. Korchemsky, D. Müller, Prog. Part. Nucl. Phys. 51, 311 (2003). hep-ph/0306057 ADSGoogle Scholar
  59. 59.
    A.V. Belitsky, B. Geyer, D. Müller, A. Schäfer, Phys. Lett. B 421, 312 (1998). hep-ph/9710427 ADSGoogle Scholar
  60. 60.
    A.G. Shuvaev, Phys. Rev. D 60, 116005 (1999). hep-ph/9902318 ADSGoogle Scholar
  61. 61.
    J.D. Noritzsch, Phys. Rev. D 62, 054015 (2000). hep-ph/0004012 ADSGoogle Scholar
  62. 62.
    I.I. Balitsky, V.M. Braun, Nucl. Phys. B 311, 541 (1989). ADSGoogle Scholar
  63. 63.
    N. Kivel, L. Mankiewicz, Nucl. Phys. B 557, 271 (1999). hep-ph/9903531 ADSGoogle Scholar
  64. 64.
    A. Manashov, M. Kirch, A. Schäfer, Phys. Rev. Lett. 95, 012002 (2005). hep-ph/0503109 ADSGoogle Scholar
  65. 65.
    M. Kirch, A. Manashov, A. Schäfer, Phys. Rev. D 72, 114006 (2005). hep-ph/0509330 ADSGoogle Scholar
  66. 66.
    M. Diehl, T. Feldmann, R. Jakob, P. Kroll, Eur. Phys. J. C 8, 409 (1999). hep-ph/9811253 ADSGoogle Scholar
  67. 67.
    S.J. Brodsky, M. Diehl, D.S. Hwang, Nucl. Phys. B 596, 99 (2001). hep-ph/0009254 ADSGoogle Scholar
  68. 68.
    M. Diehl, T. Feldmann, R. Jakob, P. Kroll, Nucl. Phys. B 596, 33 (2001). hep-ph/0009255. Erratum-ibid. B 605 (2001) 647 zbMATHADSGoogle Scholar
  69. 69.
    A. Mukherjee, I.V. Musatov, H.C. Pauli, A.V. Radyushkin, Phys. Rev. D 67, 073014 (2003). hep-ph/0205315 ADSGoogle Scholar
  70. 70.
    B.C. Tiburzi, W. Detmold, G.A. Miller, Phys. Rev. D 70, 093008 (2004). hep-ph/0408365 ADSGoogle Scholar
  71. 71.
    D.S. Hwang, D. Müller, Phys. Lett. B 660, 350 (2008). hep-ph/0710.1567 ADSGoogle Scholar
  72. 72.
    A.V. Radyushkin, Phys. Rev. D 59, 014030 (1999). hep-ph/9805342 ADSGoogle Scholar
  73. 73.
    A.V. Radyushkin, Phys. Lett. B 449, 81 (1999). hep-ph/9810466 ADSGoogle Scholar
  74. 74.
    K. Goeke, M.V. Polyakov, M. Vanderhaeghen, Prog. Part. Nucl. Phys. 47, 401 (2001). hep-ph/0106012 ADSGoogle Scholar
  75. 75.
    A.V. Radyushkin, Phys. Rev. D 58, 114008 (1998). hep-ph/9803316 ADSGoogle Scholar
  76. 76.
    S. Boffi, B. Pasquini, Generalized parton distributions and the structure of the nucleon (2007). hep-ph/0711.2625
  77. 77.
    LHPC and SESAM, P. Hägler et al., Phys. Rev. D 68, 034505 (2003). hep-lat/0304018 Google Scholar
  78. 78.
    LHPC, P. Hägler et al., Eur. Phys. J. A 24S1, 29 (2005). hep-ph/0410017 Google Scholar
  79. 79.
    LHPC and SESAM, P. Hägler et al., Phys. Rev. Lett. 93, 112001 (2004). hep-lat/0312014 Google Scholar
  80. 80.
    QCDSF, M. Göckeler et al., Phys. Rev. Lett. 92, 042002 (2004). hep-ph/0304249 Google Scholar
  81. 81.
    QCDSF and UKQCD, M. Göckeler et al., Phys. Lett. B 627, 113 (2005). hep-lat/0507001 Google Scholar
  82. 82.
    R.G. Edwards et al., PoS LAT 2006, 121 (2006). hep-lat/0610007 Google Scholar
  83. 83.
    LHPC, P. Hägler et al., Nucleon Generalized Parton Distributions from Full Lattice QCD (2007). hep-lat/0705.4295
  84. 84.
    M.V. Polyakov, A.G. Shuvaev, On ‘dual’ parametrizations of generalized parton distributions (2002). hep-ph/0207153
  85. 85.
    M. Diehl, T. Gousset, B. Pire, O.V. Teryaev, Phys. Rev. Lett. 81, 1782 (1998). hep-ph/9805380 ADSGoogle Scholar
  86. 86.
    O.V. Teryaev, Phys. Lett. B 510, 125 (2001). hep-ph/0102303 zbMATHADSGoogle Scholar
  87. 87.
    F.-M. Dittes, D. Müller, D. Robaschik, B. Geyer, J. Hořejši, Phys. Lett. B 209, 325 (1988) ADSGoogle Scholar
  88. 88.
    K. Kumerički, D. Müller, K. Passek-Kumerički, A. Schäfer, in preparation Google Scholar
  89. 89.
    S. Ahmad, H. Honkanen, S. Liuti, S.K. Taneja, Generalized parton distributions from hadronic observables (2007). hep-ph/0709.0016
  90. 90.
    F.J. Yndurain, Phys. Lett. B 74, 68 (1978) ADSGoogle Scholar
  91. 91.
    S. Ahmad, H. Honkanen, S. Liuti, S.K. Taneja, Phys. Rev. D 75, 094003 (2006). hep-ph/0611046 ADSGoogle Scholar
  92. 92.
    A.V. Belitsky, D. Müller, L. Niedermeier, A. Schäfer, Phys. Lett. B 474, 163 (2000). hep-ph/9908337 ADSGoogle Scholar
  93. 93.
    L. Mankiewicz, G. Piller, A. Radyushkin, Eur. Phys. J. C 10, 307 (1999). hep-ph/9812467 ADSGoogle Scholar
  94. 94.
    M.V. Polyakov, C. Weiss, Phys. Rev. D 60, 114017 (1999). hep-ph/9902451 ADSGoogle Scholar
  95. 95.
    W.I. Weisberger, Phys. Rev. D 5, 2600 (1972) ADSGoogle Scholar
  96. 96.
    S.J. Brodsky, F.E. Close, J.F. Gunion, Phys. Rev. D 5, 1384 (1972) ADSGoogle Scholar
  97. 97.
    A.V. Belitsky, D. Müller, A. Kirchner, A. Schäfer, Phys. Rev. D 64, 116002 (2001). hep-ph/0011314 ADSGoogle Scholar
  98. 98.
    S.V. Goloskokov, P. Kroll, Eur. Phys. J. C 42, 281 (2005). hep-ph/0501242 ADSGoogle Scholar
  99. 99.
    S.V. Goloskokov, P. Kroll, Eur. Phys. J. C 53, 367 (2008). hep-ph/0708.3569 ADSGoogle Scholar
  100. 100.
    K. Goeke et al., Phys. Rev. D 75, 094021 (2007). hep-ph/0702030 ADSGoogle Scholar
  101. 101.
    F. Ellinghaus, DVCS at HERMES: recent results (2007). hep/0710.5768
  102. 102.
    A. Freund, M. McDermott, M. Strikman, Phys. Rev. D 67, 036001 (2003). hep-ph/0208160 ADSGoogle Scholar
  103. 103.
    W.L. van Neerven, A. Vogt, Nucl. Phys. B 588, 345 (2000). hep-ph/0006154 ADSGoogle Scholar
  104. 104.
    S. Forte, Int. J. Mod. Phys. A 21, 769 (2006). hep-ph/0509371 ADSGoogle Scholar
  105. 105.
    D.Y. Ivanov, Exclusive vector meson electroproduction (2007). hep-ph/0712.3193
  106. 106.
    D. Müller, Pomeron dominance in deeply virtual Compton scattering and the femto holographic image of the proton (2006). hep-ph/0605013
  107. 107.
    A.V. Belitsky, D. Müller, Phys. Lett. B 417, 129 (1998). hep-ph/9709379 ADSGoogle Scholar
  108. 108.
    A.V. Belitsky, D. Müller, Nucl. Phys. B 537, 397 (1999). hep-ph/9804379 ADSGoogle Scholar
  109. 109.
    A.V. Belitsky, A. Freund, D. Müller, Nucl. Phys. B 574, 347 (2000). hep-ph/9912379 ADSGoogle Scholar
  110. 110.
    D. Müller, Phys. Lett. B 634, 227 (2006). hep-ph/0510109 ADSGoogle Scholar
  111. 111.
    K. Kumerički, D. Müller, K. Passek-Kumerički, Talk given at the conference exclusive reactions at high momentum transfer, new port news, 2007, May 21–24; http://conferences.jlab.org/exclusive/talks/DMueller.pdf
  112. 112.
    J. Noritzsch, private communication Google Scholar
  113. 113.
    A.G. Shuvaev, K.J. Golec-Biernat, A.D. Martin, M.G. Ryskin, Phys. Rev. D 60, 014015 (1999). hep-ph/9902410 ADSGoogle Scholar
  114. 114.
    M. Diehl, W. Kugler, Phys. Lett. B 660, 202 (2008). hep-ph/0711.2184 ADSGoogle Scholar
  115. 115.
    A.D. Martin, M.G. Ryskin, T. Teubner, Phys. Rev. D 62, 014022 (2000). hep-ph/9912551 ADSGoogle Scholar
  116. 116.
    P.V. Landshoff, J.C. Polkinghorne, Phys. Rep. 5, 1 (1972) ADSGoogle Scholar
  117. 117.
    B.I. Ermolaev, M. Greco, S.I. Troyan, Nucl. Phys. B 594, 71 (2001). hep-ph/0009037 zbMATHADSGoogle Scholar
  118. 118.
    X. Ji, J. Phys. G 24, 1181 (1998). hep-ph/9807358 ADSGoogle Scholar
  119. 119.
    A.V. Afanasev, C.E. Carlson, Phys. Rev. Lett. 94, 212301 (2005). hep-ph/0502128 ADSGoogle Scholar
  120. 120.
    A.D. Polyanin, A.V. Manzhirov, Handbook of Integral Equations (CRC Press LLC, Boca Raton, 1998) zbMATHGoogle Scholar
  121. 121.
    R. Dolen, D. Horn, C. Schmid, Phys. Rev. 166, 1768 (1968) ADSGoogle Scholar
  122. 122.
    M.J. Creutz, S.D. Drell, E.A. Paschos, Phys. Rev. 178, 2300 (1969) ADSGoogle Scholar
  123. 123.
    A. Belitsky, A. Kirchner, D. Müller, A. Schäfer, Phys. Lett. B 510, 117 (2001). hep-ph/0103343 ADSGoogle Scholar
  124. 124.
    F. Carlson, Sur une classe de séries de Taylor. PhD thesis, Uppsala University (1914) Google Scholar
  125. 125.
    I.M. Gelfand, G.E. Shilov, Generalized Functions, vol. I. (Academic, New York, 1964) Google Scholar
  126. 126.
    K.M. Semenov-Tian-Shansky, Forward-like functions for dual parametrization of GPDs from nonlocal chiral quark model (2008). hep-ph/0803.2218
  127. 127.
    F.E. Close, Q. Zhao, Phys. Rev. D 66, 054001 (2002). hep-ph/0202181 ADSGoogle Scholar
  128. 128.
    M. Diehl, T. Feldmann, R. Jakob, P. Kroll, Eur. Phys. J. C 39, 1 (2005). hep-ph/0408173 ADSGoogle Scholar
  129. 129.
    M. Guidal, M.V. Polyakov, A.V. Radyushkin, M. Vanderhaeghen, Phys. Rev. D 72, 054013 (2005). hep-ph/0410251 ADSGoogle Scholar
  130. 130.
    G. Veneziano, Nuovo Cim. A 57, 190 (1968) ADSGoogle Scholar
  131. 131.
    F. Yuan, Phys. Rev. D 69, 051501 (2004). hep-ph/0311288 ADSGoogle Scholar
  132. 132.
    J.P. Ralston, B. Pire, Phys. Rev. D 66, 111501 (2002). hep-ph/0110075 ADSGoogle Scholar
  133. 133.
    J. Kogut, D. Soper, Phys. Rev. D 1, 2901 (1970) ADSGoogle Scholar
  134. 134.
    M. Diehl, Eur. Phys. J. C 25, 223 (2002). hep-ph/0205208. Erratum-ibid. C31 (2003) 277 ADSGoogle Scholar
  135. 135.
    M. Burkardt, GPDs with ζ≠0 (2007). hep-ph/0711.1881
  136. 136.
    I.V. Anikin, B. Pire, O.V. Teryaev, Phys. Rev. D 62, 071501 (2000). hep-ph/0003203 ADSGoogle Scholar
  137. 137.
    N. Kivel, M.V. Polyakov, Nucl. Phys. B 600, 334 (2001). hep-ph/0010150 ADSGoogle Scholar
  138. 138.
    A.V. Belitsky, D. Müller, Nucl. Phys. B 589, 611 (2000). hep-ph/0007031 ADSGoogle Scholar
  139. 139.
    A.V. Belitsky, D. Müller, Phys. Lett. B 513, 349 (2001). hep-ph/0105046 ADSGoogle Scholar
  140. 140.
    D.Y. Ivanov, L. Szymanowski, G. Krasnikov, JETP Lett. 80, 226 (2004). hep-ph/0407207. Pisma Zh. Eksp. Teor. Fiz. 80, 255 (2004) ADSGoogle Scholar
  141. 141.
    W. Melnitchouk, R. Ent, C. Keppel, Phys. Rep. 406, 127 (2005). hep-ph/0501217 ADSGoogle Scholar
  142. 142.
    S. Brodsky, Y. Frishman, G. Lepage, C. Sachradja, Phys. Lett. B 91, 239 (1980) ADSGoogle Scholar
  143. 143.
    A. Efremov, A. Radyushkin, Phys. Lett. B 94, 245 (1980) ADSGoogle Scholar
  144. 144.
    L.N. Lipatov, Sov. Phys. JETP 63, 904 (1986) Google Scholar
  145. 145.
    L.N. Lipatov, Phys. Lett. B 309, 394 (1993) ADSGoogle Scholar
  146. 146.
    D. Müller, Phys. Rev. D 58, 054005 (1998). hep-ph/9704406 ADSGoogle Scholar
  147. 147.
    L.N. Lipatov, JETP Lett. 59, 596 (1994) ADSGoogle Scholar
  148. 148.
    L.D. Faddeev, G.P. Korchemsky, Phys. Lett. B 342, 311 (1995). hep-th/9404173 ADSGoogle Scholar
  149. 149.
    G.P. Korchemsky, Nucl. Phys. B 443, 255 (1995). hep-ph/9501232 ADSGoogle Scholar
  150. 150.
    V.M. Braun, S.E. Derkachov, G.P. Korchemsky, A.N. Manashov, Nucl. Phys. B 553, 355 (1999). hep-ph/9902375 ADSGoogle Scholar
  151. 151.
    A.V. Belitsky, Nucl. Phys. B 574, 407 (2000). hep-ph/9907420 ADSGoogle Scholar
  152. 152.
    N. Beisert, Phys. Rep. 405, 1 (2005). hep-th/0407277 ADSMathSciNetGoogle Scholar
  153. 153.
    A.V. Belitsky, G.P. Korchemsky, D. Mueller, Nucl. Phys. B 735, 17 (2006). hep-th/0509121 zbMATHADSGoogle Scholar
  154. 154.
    S.J. Brodsky, G.F. de Teramond, Phys. Lett. B 582, 211 (2004). hep-th/0310227 ADSGoogle Scholar
  155. 155.
    G.F. de Teramond, S.J. Brodsky, Phys. Rev. Lett. 94, 201601 (2005). hep-th/0501022 ADSGoogle Scholar
  156. 156.
    H.R. Grigoryan, A.V. Radyushkin, Phys. Lett. B 650, 421 (2007). hep-ph/0703069 ADSGoogle Scholar
  157. 157.
    J. Polchinski, M.J. Strassler, Phys. Rev. Lett. 88, 031601 (2002). hep-th/0109174 ADSMathSciNetGoogle Scholar
  158. 158.
    R.C. Brower, J. Polchinski, M.J. Strassler, C.-I. Tan, J. High Energy Phys. 0712, 005 (2007). hep-th/0603115 ADSMathSciNetGoogle Scholar
  159. 159.
    D.M. Hofman, J. Maldacena, Conformal collider physics: Energy and charge correlations (2008). hep-th/0803.1467

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2008

Authors and Affiliations

  • K. Kumerički
    • 1
  • D. Müller
    • 2
  • K. Passek-Kumerički
    • 3
    Email author
  1. 1.Department of Physics, Faculty of ScienceUniversity of ZagrebZagrebCroatia
  2. 2.Institut für Theoretische Physik IIRuhr-Universität BochumBochumGermany
  3. 3.Theoretical Physics DivisionRudjer Bošković InstituteZagrebCroatia

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