Evolution of twist-3 multiparton correlation functions relevant to single transverse-spin asymmetry

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 79, Issue 1, 2009, Pages

  Kang, Zhong Bo ^a   Qiu, Jian Wei ^a  

^a IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 60449091127     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.79.016003     Document Type: Article

References (112)

1. D.L. Adams (E581 and E704 Collaborations), Phys. Lett. B 261, 201 (1991); PYLBAJ 0370-2693 10.1016/0370-2693(91)91351-U
2. D.L. Adams (FNAp-E704 Collaboration), Phys. Lett. B 264, 462 (1991); PYLBAJ 0370-2693 10.1016/0370-2693(91)90378-4
3. K. Krueger, Phys. Lett. B 459, 412 (1999). PYLBAJ 0370-2693 10.1016/S0370-2693(99)00677-2
4. A. Bravar (Spin Muon Collaboration), Nucl. Phys. A666, 314 (2000); NUPABL 0375-9474
5. A. Airapetian (HERMES Collaboration), Phys. Rev. Lett. 84, 4047 (2000); PRLTAO 0031-9007 10.1103/PhysRevLett.84.4047
6. A. Airapetian HERMES Collaboration Phys. Rev. D PRVDAQ 0556-2821 64, 097101 (2001); 10.1103/PhysRevD.64.097101
7. A. Airapetian HERMES Collaboration Phys. Rev. Lett. 94, 012002 (2005); PRLTAO 0031-9007 10.1103/PhysRevLett.94.012002
8. V.Y. Alexakhin (COMPASS Collaboration), Phys. Rev. Lett. 94, 202002 (2005); PRLTAO 0031-9007 10.1103/PhysRevLett.94.202002
9. E.S. Ageev (COMPASS Collaboration), Nucl. Phys. NUPBBO 0550-3213 B765, 31 (2007); 10.1016/j.nuclphysb.2006.10.027
10. M. Alekseev (COMPASS Collaboration), arXiv:0802.2160;
11. S. Levorato (COMPASS Collaboration), Second International Workshop on Transverse Polarisation Phenomena in Hard Processes (Transversity 2008), 2008, Ferrara, Italy;
12. H. Avakian, P.E. Bosted, V. Burkert, and L. Elouadrhiri (CLAS Collaboration), AIP Conf. Proc. 792, 945 (2005). APCPCS 0094-243X 10.1063/1.2122193
13. J. Adams (STAR Collaboration), Phys. Rev. Lett. 92, 171801 (2004); PRLTAO 0031-9007 10.1103/PhysRevLett.92.171801
14. B.I. Abelev (STAR Collaboration), Phys. Rev. Lett. 99, 142003 (2007); PRLTAO 0031-9007 10.1103/PhysRevLett.99.142003
15. B.I. Abelev Phys. Rev. Lett. 101, 222001 (2008); PRLTAO 0031-9007 10.1103/PhysRevLett.101.222001
16. S.S. Adler (PHENIX Collaboration), Phys. Rev. Lett. 95, 202001 (2005); PRLTAO 0031-9007 10.1103/PhysRevLett.95.202001
17. M. Chiu (PHENIX Collaboration), The 18th International Symposium on Spin Physics (Spin 2008), Charlottesville, Virginia, 2008;
18. I. Arsene (BRAHMS Collaboration), Phys. Rev. Lett. 101, 042001 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.042001
19. J.C. Collins, D.E. Soper, and G. Sterman, Adv. Ser. Dir. High Energy Phys. ASDPEM 0218-0324 5, 1 (1988), and references therein.
20. J. Pumplin, D.R. Stump, J. Huston, H.L. Lai, P. Nadolsky, and W.K. Tung, J. High Energy Phys. JHEPFG 1029-8479 07 (2002) 012; 10.1088/1126-6708/2002/07/ 012
21. P.M. Nadolsky, Phys. Rev. D PRVDAQ 1550-7998 78, 013004 (2008), and references therein. 10.1103/PhysRevD.78.013004
22. A.D. Martin, R.G. Roberts, W.J. Stirling, and R.S. Thorne, Eur. Phys. J. C 23, 73 (2002); EPCFFB 1434-6044 10.1007/s100520100842
23. A.D. Martin, W.J. Stirling, R.S. Thorne, and G. Watt, Phys. Lett. B 652, 292 (2007), and references therein. PYLBAJ 0370-2693 10.1016/j.physletb.2007.07. 040
24. A.V. Efremov and O.V. Teryaev, Yad. Fiz. 36, 242 (1982) IDFZA7 0044-0027
25. [A.V. Efremov O.V. Teryaev Sov. J. Nucl. Phys. 36, 140 (1982)]; SJNCAS 0038-5506
26. A.V. Efremov O.V. Teryaev Phys. Lett. 150B, 383 (1985). PYLBAJ 0370-2693 10.1016/0370-2693(85)90999-2
27. J.W. Qiu and G. Sterman, Phys. Rev. Lett. 67, 2264 (1991); PRLTAO 0031-9007 10.1103/PhysRevLett.67.2264
28. J.W. Qiu G. Sterman Nucl. Phys. NUPBBO 0550-3213 B378, 52 (1992). 10.1016/0550-3213(92)90003-T
29. J.W. Qiu and G. Sterman, AIP Conf. Proc. 223, 249 (1991); APCPCS 0094-243X 10.1063/1.40488
30. J.W. Qiu G. Sterman Nucl. Phys. NUPBBO 0550-3213 B353, 137 (1991). 10.1016/0550-3213(91)90504-Q
31. J.W. Qiu and G. Sterman, Phys. Rev. D PRVDAQ 0556-2821 59, 014004 (1998). 10.1103/PhysRevD.59.014004
32. H. Eguchi, Y. Koike, and K. Tanaka, Nucl. Phys. NUPBBO 0550-3213 B752, 1 (2006); 10.1016/j.nuclphysb.2006.05.036
33. H. Eguchi Y. Koike K. Tanaka Nucl. Phys. NUPBBO 0550-3213 B763, 198 (2007); 10.1016/j.nuclphysb.2006.11.016
34. Y. Koike and K. Tanaka, Phys. Lett. B 646, 232 (2007); PYLBAJ 0370-2693 10.1016/j.physletb.2007.01.044
35. Y. Koike K. Tanaka Phys. Lett. B 668, 458(E) (2008); PYLBAJ 0370-2693 10.1016/j.physletb.2008.09.026
36. Y. Koike K. Tanaka Phys. Rev. D PRVDAQ 1550-7998 76, 011502 (2007). 10.1103/PhysRevD.76.011502
37. D.W. Sivers, Phys. Rev. D PRVDAQ 0556-2821 41, 83 (1990); 10.1103/PhysRevD.41.83
38. D.W. Sivers Phys. Rev. D PRVDAQ 0556-2821 43, 261 (1991). 10.1103/PhysRevD.43.261
39. S.J. Brodsky, D.S. Hwang, and I. Schmidt, Phys. Lett. B 530, 99 (2002); PYLBAJ 0370-2693 10.1016/S0370-2693(02)01320-5
40. S.J. Brodsky D.S. Hwang I. Schmidt Nucl. Phys. NUPBBO 0550-3213 B642, 344 (2002). 10.1016/S0550-3213(02)00617-X
41. P.J. Mulders and R.D. Tangerman, Nucl. Phys. NUPBBO 0550-3213 B461, 197 (1996); 10.1016/0550-3213(95)00632-X
42. P.J. Mulders R.D. Tangerman Nucl. Phys. NUPBBO 0550-3213 B484, 538(E) (1997); 10.1016/S0550-3213(96)00648-7
43. D. Boer and P.J. Mulders, Phys. Rev. D PRVDAQ 0556-2821 57, 5780 (1998); 10.1103/PhysRevD.57.5780
44. A. Bacchetta, M. Diehl, K. Goeke, A. Metz, P.J. Mulders, and M. Schlegel, J. High Energy Phys. JHEPFG 1029-8479 02 (2007) 093. 10.1088/1126-6708/2007/02/ 093
45. J.C. Collins, Phys. Lett. B 536, 43 (2002); PYLBAJ 0370-2693 10.1016/S0370-2693(02)01819-1
46. A.V. Belitsky, X. Ji, and F. Yuan, Nucl. Phys. NUPBBO 0550-3213 B656, 165 (2003); 10.1016/S0550-3213(03)00121-4
47. X. Ji, J.P. Ma, and F. Yuan, Phys. Rev. D PRVDAQ 1550-7998 71, 034005 (2005); 10.1103/PhysRevD.71.034005
48. X. Ji J.P. Ma F. Yuan Phys. Lett. B 597, 299 (2004). PYLBAJ 0370-2693 10.1016/j.physletb.2004.07.026
49. D. Boer, P.J. Mulders, and F. Pijlman, Nucl. Phys. NUPBBO 0550-3213 B667, 201 (2003). 10.1016/S0550-3213(03)00527-3
50. X. Ji, J.W. Qiu, W. Vogelsang, and F. Yuan, Phys. Rev. Lett. 97, 082002 (2006); PRLTAO 0031-9007 10.1103/PhysRevLett.97.082002
51. X. Ji J.W. Qiu F. Yuan Phys. Rev. D PRVDAQ 1550-7998 73, 094017 (2006); 10.1103/PhysRevD.73.094017
52. X. Ji J.W. Qiu F. Yuan Phys. Lett. B 638, 178 (2006); PYLBAJ 0370-2693 10.1016/j.physletb.2006.05.044
53. Y. Koike, W. Vogelsang, and F. Yuan, Phys. Lett. B 659, 878 (2008). PYLBAJ 0370-2693 10.1016/j.physletb.2007.11.096
54. Y. Kanazawa and Y. Koike, Phys. Lett. B 478, 121 (2000); PYLBAJ 0370-2693 10.1016/S0370-2693(00)00261-6
55. Y. Kanazawa Y. Koike Phys. Rev. D PRVDAQ 0556-2821 64, 034019 (2001). 10.1103/PhysRevD.64.034019
56. A. Bacchetta, C.J. Bomhof, P.J. Mulders, and F. Pijlman, Phys. Rev. D PRVDAQ 1550-7998 72, 034030 (2005); 10.1103/PhysRevD.72.034030
57. C.J. Bomhof, P.J. Mulders, and F. Pijlman, Eur. Phys. J. C EPCFFB 1434-6044 47, 147 (2006). 10.1140/epjc/s2006-02554-2
58. D. Boer and W. Vogelsang, Phys. Rev. D PRVDAQ 0556-2821 69, 094025 (2004). 10.1103/PhysRevD.69.094025
59. W. Vogelsang and F. Yuan, Phys. Rev. D PRVDAQ 1550-7998 72, 054028 (2005). 10.1103/PhysRevD.72.054028
60. J.W. Qiu, W. Vogelsang, and F. Yuan, Phys. Lett. B 650, 373 (2007); PYLBAJ 0370-2693 10.1016/j.physletb.2007.05.023
61. J.W. Qiu W. Vogelsang F. Yuan Phys. Rev. D PRVDAQ 1550-7998 76, 074029 (2007). 10.1103/PhysRevD.76.074029
62. C.J. Bomhof, P.J. Mulders, W. Vogelsang, and F. Yuan, Phys. Rev. D PRVDAQ 1550-7998 75, 074019 (2007). 10.1103/PhysRevD.75.074019
63. A. Bacchetta, C. Bomhof, U. D'Alesio, P.J. Mulders, and F. Murgia, Phys. Rev. Lett. 99, 212002 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.212002
64. M. Anselmino, M. Boglione, and F. Murgia, Phys. Lett. B 362, 164 (1995); PYLBAJ 0370-2693 10.1016/0370-2693(95)01168-P
65. U. D'Alesio and F. Murgia, Phys. Rev. D PRVDAQ 1550-7998 70, 074009 (2004); 10.1103/PhysRevD.70.074009
66. M. Anselmino, M. Boglione, U. D'Alesio, E. Leader, S. Melis, and F. Murgia, Phys. Rev. D PRVDAQ 1550-7998 73, 014020 (2006). 10.1103/PhysRevD.73. 014020
67. M. Anselmino,, Phys. Rev. D PRVDAQ 1550-7998 72, 094007 (2005); 10.1103/PhysRevD.72.094007
68. M. Anselmino Phys. Rev. D PRVDAQ 1550-7998 72, 099903(E) (2005). 10.1103/PhysRevD.72.099903
69. X.D. Ji, Phys. Lett. B 289, 137 (1992). PYLBAJ 0370-2693 10.1016/0370-2693(92)91375-J
70. Z.B. Kang and J.W. Qiu, Phys. Rev. D PRVDAQ 1550-7998 78, 034005 (2008); 10.1103/PhysRevD.78.034005
71. Z.B. Kang, J.W. Qiu, W. Vogelsang, and F. Yuan, Phys. Rev. D PRVDAQ 1550-7998 78, 114013 (2008). 10.1103/PhysRevD.78.114013
72. F. Yuan and J. Zhou, Phys. Lett. B 668, 216 (2008). PYLBAJ 0370-2693 10.1016/j.physletb.2008.08.045
73. M. Anselmino, M. Boglione, U. D'Alesio, E. Leader, and F. Murgia, Phys. Rev. D PRVDAQ 1550-7998 70, 074025 (2004). 10.1103/PhysRevD.70.074025
74. P.J. Mulders and J. Rodrigues, Phys. Rev. D PRVDAQ 1550-7998 63, 094021 (2001). 10.1103/PhysRevD.63.094021
75. C.J. Bomhof and P.J. Mulders, J. High Energy Phys. JHEPFG 1029-8479 02 (2007) 029; 10.1088/1126-6708/2007/02/029
76. C.J. Bomhof P.J. Mulders Nucl. Phys. NUPBBO 0550-3213 B795, 409 (2008). 10.1016/j.nuclphysb.2007.11.024
77. C. Kouvaris, J.W. Qiu, W. Vogelsang, and F. Yuan, Phys. Rev. D PRVDAQ 1550-7998 74, 114013 (2006). 10.1103/PhysRevD.74.114013
78. M. Anselmino, arXiv:0805.2677, and references therein.
79. See, for example, A.P. Bukhvostov, E.A. Kuraev, and L.N. Lipatov, Sov. J. Nucl. Phys. 38, 263 (1983); SJNCAS 0038-5506
80. A.P. Bukhvostov, G.V. Frolov, L.N. Lipatov, and E.A. Kuraev, Nucl. Phys. NUPBBO 0550-3213 B258, 601 (1985); 10.1016/0550-3213(85)90628-5
81. P.G. Ratcliffe, Nucl. Phys. NUPBBO 0550-3213 B264, 493 (1986); 10.1016/0550-3213(86)90495-5
82. I.I. Balitsky and V.M. Braun, Nucl. Phys. NUPBBO 0550-3213 B311, 541 (1989); 10.1016/0550-3213(89)90168-5
83. X.D. Ji and C.h. Chou, Phys. Rev. D PRVDAQ 0556-2821 42, 3637 (1990); 10.1103/PhysRevD.42.3637
84. J. Kodaira, Y. Yasui, K. Tanaka, and T. Uematsu, Phys. Lett. B 387, 855 (1996); PYLBAJ 0370-2693 10.1016/0370-2693(96)01087-8
85. S.E. Derkachov, G.P. Korchemsky, and A.N. Manashov, Nucl. Phys. NUPBBO 0550-3213 B566, 203 (2000); 10.1016/S0550-3213(99)00702-6
86. V.M. Braun, G.P. Korchemsky, and A.N. Manashov, Nucl. Phys. NUPBBO 0550-3213 B603, 69 (2001), and references therein. 10.1016/S0550-3213(01)00165-1
87. See, for example, V.M. Braun, S.E. Derkachov, and A.N. Manashov, Phys. Rev. Lett. 81, 2020 (1998); PRLTAO 0031-9007 10.1103/PhysRevLett.81.2020
88. A. Ali, V.M. Braun, and G. Hiller, Phys. Lett. B 266, 117 (1991); PYLBAJ 0370-2693 10.1016/0370-2693(91)90753-D
89. A.V. Belitsky, Nucl. Phys. NUPBBO 0550-3213 B558, 259 (1999); 10.1016/S0550-3213(99)00402-2
90. A.V. Belitsky Nucl. Phys. NUPBBO 0550-3213 B574, 407 (2000); 10.1016/S0550-3213(00)00003-1
91. A.V. Belitsky, V.M. Braun, A.S. Gorsky, and G.P. Korchemsky, Int. J. Mod. Phys. A 19, 4715 (2004), and references therein. IMPAEF 0217-751X 10.1142/S0217751X04019895
92. See, for example, I.I. Balitsky, V.M. Braun, Y. Koike, and K. Tanaka, Phys. Rev. Lett. 77, 3078 (1996); PRLTAO 0031-9007 10.1103/PhysRevLett.77.3078
93. A.V. Belitsky and D. Mueller, Nucl. Phys. NUPBBO 0550-3213 B503, 279 (1997); 10.1016/S0550-3213(97)00432-X
94. A.V. Belitsky, Phys. Lett. B 453, 59 (1999), and references therein. PYLBAJ 0370-2693 10.1016/S0370-2693(99)00326-3
95. A.A. Henneman, D. Boer, and P.J. Mulders, Nucl. Phys. NUPBBO 0550-3213 B620, 331 (2002). 10.1016/S0550-3213(01)00557-0
96. J.C. Collins and J.W. Qiu, 1550-7998 39, 1398 (1989). 10.1103/PhysRevD.39.1398
97. A.H. Mueller, Phys. Rep. 73, 237 (1981). PRPLCM 0370-1573 10.1016/0370-1573(81)90030-2
98. R.K. Ellis, W. Furmanski, and R. Petronzio, Nucl. Phys. NUPBBO 0550-3213 B212, 29 (1983). 10.1016/0550-3213(83)90597-7
99. J.W. Qiu, Phys. Rev. D PRVDAQ 0556-2821 42, 30 (1990). 10.1103/PhysRevD.42.30
100. R. Brock (CTEQ Collaboration), Rev. Mod. Phys. 67, 157 (1995). RMPHAT 0034-6861 10.1103/RevModPhys.67.157
101. G. Sterman, arXiv:hep-ph/9606312.
102. Yu. Dokshitzer, Sov. Phys. JETP 46, 641 (1977); SPHJAR 0038-5646
103. V.N. Gribov and L.N. Lipatov, Sov. J. Nucl. Phys. SJNCAS 0038-5506 15, 438 (1972);
104. V.N. Gribov L.N. Lipatov Sov. J. Nucl. Phys. SJNCAS 0038-5506 15, 675 (1972);
105. G. Alteralli and G. Parisi, Nucl. Phys. NUPBBO 0550-3213 B126, 298 (1977). 10.1016/0550-3213(77)90384-4
106. W. Vogelsang and F. Yuan, International Symposium on Spin Physics (Spin 2008), Charlottesville, VA, 2008.
107. R.L. Jaffe, Nucl. Phys. NUPBBO 0550-3213 B229, 205 (1983). 10.1016/0550-3213(83)90361-9
108. M. Luo, J.W. Qiu, and G. Sterman, Phys. Rev. D PRVDAQ 0556-2821 49, 4493 (1994). 10.1103/PhysRevD.49.4493
109. V. Barone, A. Drago, and P.G. Ratcliffe, Phys. Rep. 359, 1 (2002); PRPLCM 0370-1573 10.1016/S0370-1573(01)00051-5
110. X. Artru and M. Mekhfi, Z. Phys. C 45, 669 (1990); ZPCFD2 0170-9739 10.1007/BF01556280
111. J.C. Collins, Nucl. Phys. NUPBBO 0550-3213 B396, 161 (1993). 10.1016/0550-3213(93)90262-N
112. J. Pumplin, D.R. Stump, J. Huston, H.L. Lai, P. Nadolsky, and W.K. Tung, J. High Energy Phys. JHEPFG 1029-8479 07 (2002) 012. 10.1088/1126-6708/2002/07/ 012