Running coupling and power corrections in non-linear evolution at the high-energy limit

Nuclear Physics A

Volumn 784, Issue 1-4, 2007, Pages 282-340

  Gardi, Einan ^a,b   Kuokkanen, Janne ^c   Rummukainen, Kari ^c,d   Weigert, Heribert ^e  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^c UNIVERSITY OF OULU   (Finland)

^d CERN   (Switzerland)

^e OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846677680     PISSN: 03759474     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysa.2006.12.004     Document Type: Article

References (109)

1. McLerran L.D., and Venugopalan R. Computing quark and gluon distribution functions for very large nuclei. Phys. Rev. D 49 (1994) 2233-2241. hep-ph/9309289
2. McLerran L.D., and Venugopalan R. Gluon distribution functions for very large nuclei at small transverse momentum. Phys. Rev. D 49 (1994) 3352-3355. hep-ph/9311205
3. McLerran L.D., and Venugopalan R. Green's functions in the color field of a large nucleus. Phys. Rev. D 50 (1994) 2225-2233. hep-ph/9402335
4. Kovchegov Y.V. Non-Abelian Weizsaecker-Williams field and a two-dimensional effective color charge density for a very large nucleus. Phys. Rev. D 54 (1996) 5463-5469. hep-ph/9605446
5. Kovchegov Y.V. Quantum structure of the non-Abelian Weizsaecker-Williams field for a very large nucleus. Phys. Rev. D 55 (1997) 5445-5455. hep-ph/9701229
6. Jalilian-Marian J., Kovner A., McLerran L.D., and Weigert H. The intrinsic glue distribution at very small x. Phys. Rev. D 55 (1997) 5414-5428. hep-ph/9606337
7. Lam C.S., and Mahlon G. Color neutrality and the gluon distribution in a very large nucleus. Phys. Rev. D 61 (2000) 014005. hep-ph/9907281
8. Lam C.S., and Mahlon G. Longitudinal resolution in a large relativistic nucleus: Adding a dimension to the McLerran-Venugopalan model. Phys. Rev. D 62 (2000) 114023. hep-ph/0007133
9. Lam C.S., and Mahlon G. Non-Gaussian correlations in the McLerran-Venugopalan model. Phys. Rev. D 64 (2001) 016004. hep-ph/0102337
10. Balitsky Y.Y., and Lipatov L.N. Sov. J. Nucl. Phys. 28 (1978) 822
11. Lipatov L.N. Sov. J. Nucl. Phys. 23 (1976) 642
12. Kuraev E.A., Lipatov L.N., and Fadin V.S. Multi-reggeon processes in the Yang-Mills theory. Sov. Phys. JETP 44 (1976) 443-450
13. Kuraev E.A., Lipatov L.N., and Fadin V.S. The Pomeranchuk singularity in non-Abelian gauge theories. Sov. Phys. JETP 45 (1977) 199-204
14. Lipatov L.N. Sov. Phys. JETP 63 (1986) 904
15. Jalilian-Marian J., Kovner A., Leonidov A., and Weigert H. The BFKL equation from the Wilson renormalization group. Nucl. Phys. B 504 (1997) 415-431. hep-ph/9701284
16. Jalilian-Marian J., Kovner A., Leonidov A., and Weigert H. The Wilson renormalization group for low x physics: Towards the high density regime. Phys. Rev. D 59 (1999) 014014. hep-ph/9706377
17. Jalilian-Marian J., Kovner A., and Weigert H. The Wilson renormalization group for low x physics: Gluon evolution at finite parton density. Phys. Rev. D 59 (1999) 014015. hep-ph/9709432
18. Jalilian-Marian J., Kovner A., Leonidov A., and Weigert H. Unitarization of gluon distribution in the doubly logarithmic regime at high density. Phys. Rev. D 59 (1999) 034007. hep-ph/9807462
19. Kovner A., Milhano J.G., and Weigert H. Relating different approaches to nonlinear QCD evolution at finite gluon density. Phys. Rev. D 62 (2000) 114005. hep-ph/0004014
20. Weigert H. Unitarity at small Bjorken x. Nucl. Phys. A 703 (2002) 823-860. hep-ph/0004044
21. Iancu E., Leonidov A., and McLerran L.D. Nonlinear gluon evolution in the color glass condensate, I. Nucl. Phys. A 692 (2001) 583-645. hep-ph/0011241
22. Ferreiro E., Iancu E., Leonidov A., and McLerran L. Nonlinear gluon evolution in the color glass condensate, II. Nucl. Phys. A 703 (2002) 489-538. hep-ph/0109115
23. Balitsky I. Operator expansion for high-energy scattering. Nucl. Phys. B 463 (1996) 99-160. hep-ph/9509348
24. Balitsky I. Operator expansion for diffractive high-energy scattering. hep-ph/9706411
25. Balitsky I. Factorization and high-energy effective action. Phys. Rev. D 60 (1999) 014020. hep-ph/9812311
26. 2 structure function of a nucleus including multiple pomeron exchanges. Phys. Rev. D 60 (1999) 034008. hep-ph/9901281
27. Kovchegov Y.V. Unitarization of the BFKL pomeron on a nucleus. Phys. Rev. D 61 (2000) 074018. hep-ph/9905214
28. Mueller A.H. Soft gluons in the infinite momentum wave function and the BFKL pomeron. Nucl. Phys. B 415 (1994) 373-385
29. Mueller A.H., and Patel B. Single and double BFKL pomeron exchange and a dipole picture of high-energy hard processes. Nucl. Phys. B 425 (1994) 471-488. hep-ph/9403256
30. Mueller A.H. Unitarity and the BFKL pomeron. Nucl. Phys. B 437 (1995) 107-126. hep-ph/9408245
31. Chen Z., and Mueller A.H. The dipole picture of high-energy scattering, the BFKL equation and many gluon compound states. Nucl. Phys. B 451 (1995) 579-604
32. Mueller A.H., and Salam G.P. Large multiplicity fluctuations and saturation effects in onium collisions. Nucl. Phys. B 475 (1996) 293-320. hep-ph/9605302
33. Golec-Biernat K., Motyka L., and Stasto A.M. Diffusion into infra-red and unitarization of the BFKL pomeron. Phys. Rev. D 65 (2002) 074037. hep-ph/0110325
34. Anderson K.D., Ross D.A., and Sotiropoulos M.G. Running coupling and borel singularities at small x. Nucl. Phys. B 515 (1998) 249-268. hep-ph/9705466
35. Ciafaloni M., and Camici G. Energy scale(s) and next-to-leading BFKL equation. Phys. Lett. B 430 (1998) 349-354. hep-ph/9803389
36. Fadin V.S., and Lipatov L.N. BFKL pomeron in the next-to-leading approximation. Phys. Lett. B 429 (1998) 127-134. hep-ph/9802290
37. Kovchegov Y.V., and Mueller A.H. Running coupling effects in BFKL evolution. Phys. Lett. B 439 (1998) 428-436. hep-ph/9805208
38. Brodsky S.J., Fadin V.S., Kim V.T., Lipatov L.N., and Pivovarov G.B. The QCD pomeron with optimal renormalization. JETP Lett. 70 (1999) 155-160. hep-ph/9901229
39. Ball R.D., and Forte S. All order running coupling BFKL evolution from GLAP (and vice versa). Nucl. Phys. B 742 (2006) 158-175. hep-ph/0601049
40. Altarelli G., Ball R.D., and Forte S. Resummation of singlet parton evolution at small x. Nucl. Phys. B 575 (2000) 313-329. hep-ph/9911273
41. Ciafaloni M., Colferai D., and Salam G.P. Renormalization group improved small-x equation. Phys. Rev. D 60 (1999) 114036. hep-ph/9905566
42. Ciafaloni M., Colferai D., Salam G.P., and Stasto A.M. Renormalisation group improved small-x green's function. Phys. Rev. D 68 (2003) 114003. hep-ph/0307188
43. Thorne R.S. The running coupling BFKL anomalous dimensions and splitting functions. Phys. Rev. D 64 (2001) 074005. hep-ph/0103210
44. Iancu E., Itakura K., and Munier S. Saturation and BFKL dynamics in the Hera data at small x. Phys. Lett. B 590 (2004) 199-208. hep-ph/0310338
45. Rummukainen K., and Weigert H. Universal features of JIMWLK and BK evolution at small x. Nucl. Phys. A 739 (2004) 183-226. hep-ph/0309306
46. Bigi I.I.Y., Shifman M.A., Uraltsev N.G., and Vainshtein A.I. The pole mass of the heavy quark. Perturbation theory and beyond. Phys. Rev. D 50 (1994) 2234-2246. hep-ph/9402360
47. Smith B.H., and Voloshin M.B. Normalization of QCD corrections in top quark decay. Phys. Lett. B 340 (1994) 176-180. hep-ph/9405204
48. Beneke M., and Braun V.M. Naive nonabelianization and resummation of fermion bubble chains. Phys. Lett. B 348 (1995) 513-520. hep-ph/9411229
49. n corrections in QCD: Techniques and applications to the τ hadronic width and the heavy quark pole mass. Nucl. Phys. B 452 (1995) 563-625. hep-ph/9502300
50. Dokshitzer Y.L., Marchesini G., and Webber B.R. Dispersive approach to power-behaved contributions in QCD hard processes. Nucl. Phys. B 469 (1996) 93-142. hep-ph/9512336
51. Grunberg G. On power corrections in the dispersive approach. JHEP 9811 (1998) 006. hep-ph/9807494
52. Gardi E., and Grunberg G. Power corrections in the single dressed gluon approximation: The average thrust as a case study. JHEP 9911 (1999) 016. hep-ph/9908458
53. - annihilation. JHEP 0004 (2000) 030. hep-ph/0003179
54. Cacciari M., and Gardi E. Heavy-quark fragmentation. Nucl. Phys. B 664 (2003) 299-340. hep-ph/0301047
55. - annihilation. JHEP 0308 (2003) 030. hep-ph/0306094
56. Balitsky I.I., and Belitsky A.V. Nonlinear evolution in high-density QCD. Nucl. Phys. B 629 (2002) 290-322. hep-ph/0110158
57. Gotsman E., Levin E., Maor U., and Naftali E. A modified Balitsky-Kovchegov equation. Nucl. Phys. A 750 (2005) 391-405. hep-ph/0411242
58. Iancu E., Leonidov A., and McLerran L. The colour glass condensate: An introduction. hep-ph/0202270
59. Iancu E., and Venugopalan R. The color glass condensate and high energy scattering in QCD. hep-ph/0303204
60. b j: The color glass condensate. Prog. Part. Nucl. Phys. 55 (2005) 461-565. hep-ph/0501087
61. Jalilian-Marian J., and Kovchegov Y.V. Saturation physics and deuteron gold collisions at RHIC. Prog. Part. Nucl. Phys. 56 (2006) 104-231. hep-ph/0505052
62. 2 and its implications on diffraction. Phys. Rev. D 59 (1999) 014017. hep-ph/9807513
63. Golec-Biernat K., and Wüsthoff M. Saturation in diffractive deep inelastic scattering. Phys. Rev. D 60 (1999) 114023. hep-ph/9903358
64. * p cross-section in the low x region. Phys. Rev. Lett. 86 (2001) 596-599. hep-ph/0007192
65. Baier R., Kovner A., and Wiedemann U.A. Saturation and parton level Cronin effect: Enhancement vs. suppression of gluon production in pA and AA collisions. Phys. Rev. D 68 (2003) 054009. hep-ph/0305265
66. t suppression in pA collisions. Phys. Rev. D 68 (2003) 094013. hep-ph/0307037
67. Jalilian-Marian J., Nara Y., and Venugopalan R. The Cronin effect, quantum evolution and the color glass condensate. Phys. Lett. B 577 (2003) 54-60. nucl-th/0307022
68. Albacete J.L., Armesto N., Kovner A., Salgado C.A., and Wiedemann U.A. Energy dependence of the Cronin effect from non-linear QCD evolution. Phys. Rev. Lett. 92 (2004) 082001. hep-ph/0307179
69. N N) = 200 GeV. Phys. Rev. Lett. 93 (2004) 242303. nucl-ex/0403005
70. Hentschinski M., Weigert H., and Schafer A. Extension of the color glass condensate approach to diffractive reactions. Phys. Rev. D 73 (2006) 051501. hep-ph/0509272
71. Braun V.M., Korchemsky G.P., and Mueller D. The uses of conformal symmetry in QCD. Prog. Part. Nucl. Phys. 51 (2003) 311-398. hep-ph/0306057
72. c → ∞ (BFKL pomeron fan diagrams). Eur. Phys. J. C 16 (2000) 337-347. hep-ph/0001268
73. Kimber M.A., Kwiecinski J., and Martin A.D. Gluon shadowing in the low x region probed by the LHC. Phys. Lett. B 508 (2001) 58-64. hep-ph/0101099
74. Armesto N., and Braun M.A. Parton densities and dipole cross-sections at small x in large nuclei. Eur. Phys. J. C 20 (2001) 517-522. hep-ph/0104038
75. Levin E., and Lublinsky M. Parton densities and saturation scale from non-linear evolution in dis on nuclei. Nucl. Phys. A 696 (2001) 833-850. hep-ph/0104108
76. Lublinsky M. Scaling phenomena from non-linear evolution in high energy DIS. Eur. Phys. J. C 21 (2001) 513-519. hep-ph/0106112
77. Albacete J.L., Armesto N., Milhano J.G., Salgado C.A., and Wiedemann U.A. Numerical analysis of the Balitsky-Kovchegov equation with running coupling: Dependence of the saturation scale on nuclear size and rapidity. hep-ph/0408216
78. Mueller A.H., and Triantafyllopoulos D.N. The energy dependence of the saturation momentum. Nucl. Phys. B 640 (2002) 331-350. hep-ph/0205167
79. Iancu E., Itakura K., and McLerran L. Geometric scaling above the saturation scale. Nucl. Phys. A 708 (2002) 327-352. hep-ph/0203137
80. Brodsky S.J., Lepage G.P., and Mackenzie P.B. On the elimination of scale ambiguities in perturbative quantum chromodynamics. Phys. Rev. D 28 (1983) 228
81. Brodsky S.J., Ellis J.R., Gardi E., Karliner M., and Samuel M.A. Pade approximants, optimal renormalization scales, and momentum flow in Feynman diagrams. Phys. Rev. D 56 (1997) 6980-6992. hep-ph/9706467
82. Brodsky S.J., Gardi E., Grunberg G., and Rathsman J. Disentangling running coupling and conformal effects in QCD. Phys. Rev. D 63 (2001) 094017. hep-ph/0002065
83. Neubert M. Scale setting in QCD and the momentum flow in Feynman diagrams. Phys. Rev. D 51 (1995) 5924-5941. hep-ph/9412265
84. Dokshitzer Y.L., Marchesini G., and Webber B.R. Dispersive approach to power-behaved contributions in QCD hard processes. Nucl. Phys. B 469 (1996) 93-142. hep-ph/9512336
85. Lautrup B. On high order estimates in QED. Phys. Lett. B 69 (1977) 109-111
86. G. 't Hooft, Can we make sense out of 'quantum chromodynamics'?, Lectures given at Int. School of Subnuclear Physics, Erice, Sicily, 23 July-10 August 1977
87. Mueller A.H. On the structure of infrared renormalons in physical processes at high-energies. Nucl. Phys. B 250 (1985) 327
88. Parisi G. Singularities of the borel transform in renormalizable theories. Phys. Lett. B 76 (1978) 65-66
89. David F. On the ambiguity of composite operators, I.R. renormalons and the status of the operator product expansion. Nucl. Phys. B 234 (1984) 237-251
90. Zakharov V.I. QCD perturbative expansions in large orders. Nucl. Phys. B 385 (1992) 452-480
91. Beneke M. Renormalons. Phys. Rep. 317 (1999) 1-142. hep-ph/9807443
92. Beneke M., and Braun V.M. Renormalons and power corrections. hep-ph/0010208
93. Grunberg G. Renormalization group improved perturbative QCD. Phys. Lett. B 95 (1980) 70
94. Grunberg G. The Renormalization scheme invariant Borel transform and the QED renormalons. Phys. Lett. B 304 (1993) 183-188
95. Gardi E., and Roberts R.G. The interplay between Sudakov resummation, renormalons and higher twist in deep inelastic scattering. Nucl. Phys. B 653 (2003) 227-255. hep-ph/0210429
96. Gardi E., Korchemsky G.P., Ross D.A., and Tafat S. Power corrections in deep inelastic structure functions at large Bjorken x. Nucl. Phys. B 636 (2002) 385-417. hep-ph/0203161
97. Braun V.M., Gardi E., and Gottwald S. Renormalon approach to higher-twist distribution amplitudes and the convergence of the conformal expansion. Nucl. Phys. B 685 (2004) 171-226. hep-ph/0401158
98. Beneke M., and Braun V.M. Naive nonabelianization and resummation of fermion bubble chains. Phys. Lett. B 348 (1995) 513-520. hep-ph/9411229
99. Gardi E., Grunberg G., and Karliner M. Can the QCD running coupling have a causal analyticity structure?. JHEP 9807 (1998) 007. hep-ph/9806462
100. s (0) value. Phys. Rev. Lett. 79 (1997) 1209-1212. hep-ph/9704333
101. s γ spectrum by dressed gluon exponentiation. JHEP 0506 (2005) 030. hep-ph/0502159
102. Hebecker A., and Weigert H. Small-x parton distributions of large hadronic targets. Phys. Lett. B 432 (1998) 215-221. hep-ph/9804217
103. Y. Kovchegov, H. Weigert, Triumvirate of running couplings in small-x evolution, 2006, in preparation
104. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. ninth Dover printing, tenth GPO printing ed. (1964), Dover, New York
105. Broadhurst D.J. Large n expansion of QED: Asymptotic photon propagator and contributions to the muon anomaly, for any number of loops. Z. Phys. C 58 (1993) 339-346
106. Lovett-Turner C.N., and Maxwell C.J. All orders renormalon resummations for some QCD observables. Nucl. Phys. B 452 (1995) 188-212. hep-ph/9505224
107. Kalmykov M.Y. Gauss hypergeometric function: Reduction, ε{lunate}-expansion for integer/half-integer parameters and Feynman diagrams. JHEP 0604 (2006) 056. hep-th/0602028
108. Remiddi E., and Vermaseren J.A.M. Harmonic polylogarithms. Int. J. Mod. Phys. A 15 (2000) 725-754. hep-ph/9905237
109. Smirnov V.A. Evaluating Feynman Integrals (2004), Springer, Berlin