A complete leading-order renormalization-scheme-consistent calculation of structure functions

Nuclear Physics B

Volumn 512, Issue 1-2, 1998, Pages 323-392

  Thorne, Robert S ^a  

^a RUTHERFORD APPLETON LABORATORY   (United Kingdom)

Author keywords

Deep inelastic scattering; Small x; Structure function

Indexed keywords

EID: 0032536222     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(97)00690-1     Document Type: Article

References (90)

1. [1] H1 collaboration, Nucl. Phys. B 470 (1996) 3.
2. [2] ZEUS collaboration: M. Derrick et al., Z. Phys. C 69 (1996) 607; Z. Phys. C 72 (1996) 399.
3. [2] ZEUS collaboration: M. Derrick et al., Z. Phys. C 69 (1996) 607; Z. Phys. C 72 (1996) 399.
4. [3] G. Altarelli and G. Parisi, Nucl. Phys. B 126 (1977) 298; Yu.L. Dokshitzer, Sov. J. JETP 46 (1977) 641; L.N.Lipatov, Sov. J. Nucl. Phys. 20 ( 1975) 95; V.N. Gribov and L.N. Lipatov, Sov. J. Nucl. Phys. 15 (1972) 438.
5. [3] G. Altarelli and G. Parisi, Nucl. Phys. B 126 (1977) 298; Yu.L. Dokshitzer, Sov. J. JETP 46 (1977) 641; L.N.Lipatov, Sov. J. Nucl. Phys. 20 ( 1975) 95; V.N. Gribov and L.N. Lipatov, Sov. J. Nucl. Phys. 15 (1972) 438.
6. [3] G. Altarelli and G. Parisi, Nucl. Phys. B 126 (1977) 298; Yu.L. Dokshitzer, Sov. J. JETP 46 (1977) 641; L.N.Lipatov, Sov. J. Nucl. Phys. 20 ( 1975) 95; V.N. Gribov and L.N. Lipatov, Sov. J. Nucl. Phys. 15 (1972) 438.
7. [3] G. Altarelli and G. Parisi, Nucl. Phys. B 126 (1977) 298; Yu.L. Dokshitzer, Sov. J. JETP 46 (1977) 641; L.N.Lipatov, Sov. J. Nucl. Phys. 20 ( 1975) 95; V.N. Gribov and L.N. Lipatov, Sov. J. Nucl. Phys. 15 (1972) 438.
8. [4] A. Donnachie and P.V. Landshoff, Nucl. Phys. B 244 (1984) 322; B 267 (1986) 690.
9. [4] A. Donnachie and P.V. Landshoff, Nucl. Phys. B 244 (1984) 322; B 267 (1986) 690.
10. [5] A.D. Martin, R.G. Rcberts and W.J. Stirling, Phys. Rev. D 47 (1993) 867; Phys. Lett. B 306 (1993) 145.
11. [5] A.D. Martin, R.G. Rcberts and W.J. Stirling, Phys. Rev. D 47 (1993) 867; Phys. Lett. B 306 (1993) 145.
12. [6] A. de Rújula et al., Phys. Rev. D 10 ( 1974) 1649.
13. [7] L.N. Lipatov, Sov. J. Nucl. Phys. 23 (1976) 338; E.A. Kuraev, L.N. Lipatov and V.S. Fadin Sov. J. JETP 45 (1977) 199; Ya. Balitskii and L.N. Lipatov, Sov. J. Nucl. Phys. 28 (1978) 6.
14. [7] L.N. Lipatov, Sov. J. Nucl. Phys. 23 (1976) 338; E.A. Kuraev, L.N. Lipatov and V.S. Fadin Sov. J. JETP 45 (1977) 199; Ya. Balitskii and L.N. Lipatov, Sov. J. Nucl. Phys. 28 (1978) 6.
15. [7] L.N. Lipatov, Sov. J. Nucl. Phys. 23 (1976) 338; E.A. Kuraev, L.N. Lipatov and V.S. Fadin Sov. J. JETP 45 (1977) 199; Ya. Balitskii and L.N. Lipatov, Sov. J. Nucl. Phys. 28 (1978) 6.
16. [8] A.D Martin, R.G. Roberts and W.J. Stirling, Phys. Lett. B 354 (1995) 155; H.L. Lai et al., Phys. Rev. D 51 (1995) 4763.
17. [8] A.D Martin, R.G. Roberts and W.J. Stirling, Phys. Lett. B 354 (1995) 155; H.L. Lai et al., Phys. Rev. D 51 (1995) 4763.
18. [9] M.Glück, E. Reya and A. Vogt, Z. Phys. C 48 (1990) 471; C 53 (1992) 127; Phys. Lett. B 306 (1993) 391; Z. Phys. C 67 (1995) 433.
19. [9] M.Glück, E. Reya and A. Vogt, Z. Phys. C 48 (1990) 471; C 53 (1992) 127; Phys. Lett. B 306 (1993) 391; Z. Phys. C 67 (1995) 433.
20. [9] M.Glück, E. Reya and A. Vogt, Z. Phys. C 48 (1990) 471; C 53 (1992) 127; Phys. Lett. B 306 (1993) 391; Z. Phys. C 67 (1995) 433.
21. [9] M.Glück, E. Reya and A. Vogt, Z. Phys. C 48 (1990) 471; C 53 (1992) 127; Phys. Lett. B 306 (1993) 391; Z. Phys. C 67 (1995) 433.
22. [10] R.D. Ball and S. Forte, Phys. Lett. B 335 (1994) 77.
23. [11] R.D. Ball and S. Forte, Phys. Lett. B 336 (1994) 77.
24. [12] J.C. Collins, D.E. Soper and G. Sterman, in Perturbative Quantum Chromodynamics, ed. A.H. Mueller (World Scientific, Singapore, 1989), and references therein.
25. [13] S. Catani, M. Ciafaloni and F. Hautmann, Phys. Lett. B 242 (1990) 97; Nucl. Phys. B 366 (1991) 135; Phys. Lett. B 307 (1993) 147.
26. [13] S. Catani, M. Ciafaloni and F. Hautmann, Phys. Lett. B 242 (1990) 97; Nucl. Phys. B 366 (1991) 135; Phys. Lett. B 307 (1993) 147.
27. [13] S. Catani, M. Ciafaloni and F. Hautmann, Phys. Lett. B 242 (1990) 97; Nucl. Phys. B 366 (1991) 135; Phys. Lett. B 307 (1993) 147.
28. [14] J.C. Collins and R.K. Ellis, Nucl. Phys. B 360 (1991) 3.
29. [15] A.J. Askew, J. Kwieciński, A.D. Martin and P.J. Sutton, Phys. Rev. D 49 (1994) 4402; A.J. Askew et al., Phys. Lett. B 325 (1994) 212.
30. [15] A.J. Askew, J. Kwieciński, A.D. Martin and P.J. Sutton, Phys. Rev. D 49 (1994) 4402; A.J. Askew et al., Phys. Lett. B 325 (1994) 212.
31. [16] J. Kwieciński, A.D. Martin and P.J. Sutton, Phys. Rev. D 53 (6094) 1996; Z. Phys. C 71 (1996) 585.
32. [16] J. Kwieciński, A.D. Martin and P.J. Sutton, Phys. Rev. D 53 (6094) 1996; Z. Phys. C 71 (1996) 585.
33. [17] M. Ciafaloni, Nucl. Phys. B 296 (1988) 49; S. Catani, F. Fiorani and G. Marchesini, Phys. Lett. B 234 (1990) 339; Nucl. Phys. B 336 (1990) 18. [18] S. Catani and F. Hautmann, Phys. Lett. B 315 (1993) 157; Nucl. Phys. B 427 (1994) 475.
34. [17] M. Ciafaloni, Nucl. Phys. B 296 (1988) 49; S. Catani, F. Fiorani and G. Marchesini, Phys. Lett. B 234 (1990) 339; Nucl. Phys. B 336 (1990) 18. [18] S. Catani and F. Hautmann, Phys. Lett. B 315 (1993) 157; Nucl. Phys. B 427 (1994) 475.
35. [17] M. Ciafaloni, Nucl. Phys. B 296 (1988) 49; S. Catani, F. Fiorani and G. Marchesini, Phys. Lett. B 234 (1990) 339; Nucl. Phys. B 336 (1990) 18. [18] S. Catani and F. Hautmann, Phys. Lett. B 315 (1993) 157; Nucl. Phys. B 427 (1994) 475.
36. [17] M. Ciafaloni, Nucl. Phys. B 296 (1988) 49; S. Catani, F. Fiorani and G. Marchesini, Phys. Lett. B 234 (1990) 339; Nucl. Phys. B 336 (1990) 18. [18] S. Catani and F. Hautmann, Phys. Lett. B 315 (1993) 157; Nucl. Phys. B 427 (1994) 475.
37. [17] M. Ciafaloni, Nucl. Phys. B 296 (1988) 49; S. Catani, F. Fiorani and G. Marchesini, Phys. Lett. B 234 (1990) 339; Nucl. Phys. B 336 (1990) 18. [18] S. Catani and F. Hautmann, Phys. Lett. B 315 (1993) 157; Nucl. Phys. B 427 (1994) 475.
38. [19] T. Jaroszewicz, Phys. Lett. B 116 (1982) 291.
39. [20] R.D. Ball and S. Forte, Phys. Lett. B 351 (1995) 313; B 358 (1995) 365.
40. [20] R.D. Ball and S. Forte, Phys. Lett. B 351 (1995) 313; B 358 (1995) 365.
41. [21] R.K. Ellis, F. Hautmann and B.R. Webber, Phys. Lett. B 348 (1995) 582.
42. [22] J.R. Forshaw, R.G. Roberts and R.S. Thorne, Phys. Lett. B 356 (1995) 79.
43. [23] J. Blümlein, S. Riemarsma and A. Vogt, Proc. of the Int. Workshop QCD and QED in higher orders, Rheinsburg, Germany, April, 1996, ed. J. Blümlein, F. Jegerlehner and T. Riemann, Nucl. Phys. B (Proc. Suppl.), 51C (1996) p. 30; hep-ph/9607329, Proc. of the Int. Workshop on Deep Inelastic Scattering, Rome, April, 1996, p. 572.
44. [23] J. Blümlein, S. Riemarsma and A. Vogt, Proc. of the Int. Workshop QCD and QED in higher orders, Rheinsburg, Germany, April, 1996, ed. J. Blümlein, F. Jegerlehner and T. Riemann, Nucl. Phys. B (Proc. Suppl.), 51C (1996) p. 30; hep-ph/9607329, Proc. of the Int. Workshop on Deep Inelastic Scattering, Rome, April, 1996, p. 572.
45. [23] J. Blümlein, S. Riemarsma and A. Vogt, Proc. of the Int. Workshop QCD and QED in higher orders, Rheinsburg, Germany, April, 1996, ed. J. Blümlein, F. Jegerlehner and T. Riemann, Nucl. Phys. B (Proc. Suppl.), 51C (1996) p. 30; hep-ph/9607329, Proc. of the Int. Workshop on Deep Inelastic Scattering, Rome, April, 1996, p. 572.
46. [24] S. Catani, Z. Phys. C 70 (1996) 263.
47. [25] M. Ciafaloni, Phys. Lett. B 356 (1995) 74.
48. [26] A.D. Martin, W.J. Stirling and R.G. Roberts, Phys. Lett. B 387 (1996) 419.
49. [27] R.D. Ball and S. Forte, hep-ph/9607289, Proc. of the Int. Workshop on Deep Inelastic Scattering, Rome, April, 1996, p. 208.
50. [28] S. Forte and R.D. Ball, hep-ph/9607291, Proc. of the Int. Workshop on Deep Inelastic Scattering, Rome, April, 1996, p. 172.
51. [29] I. Bojak and M. Ernst, hep-ph/9609378, Phys. Lett. B 397 (1997) 296.
52. [30] R.S. Thorne, Phys. Lett. B 392 (1997) 463.
53. [31] S. Catani, talk at UK workshop on HERA physics, September 1995, unpublished; hep-ph/9609263, Z. Phys. C 75 (1997) 665; hep-ph/9608310, Proc. of the Int. Workshop on Deep Inelastic Scattering, Rome, April, 1996, p. 172.
54. [31] S. Catani, talk at UK workshop on HERA physics, September 1995, unpublished; hep-ph/9609263, Z. Phys. C 75 (1997) 665; hep-ph/9608310, Proc. of the Int. Workshop on Deep Inelastic Scattering, Rome, April, 1996, p. 172.
55. [31] S. Catani, talk at UK workshop on HERA physics, September 1995, unpublished; hep-ph/9609263, Z. Phys. C 75 (1997) 665; hep-ph/9608310, Proc. of the Int. Workshop on Deep Inelastic Scattering, Rome, April, 1996, p. 172.
56. [32] R.S. Thorne, RAL-TR-96-065, hep-ph/9701241.
57. [33] A.D. Martin, R.G. Roberts and W.J. Stirling, Phys. Lett. B 266 (1991) 173.
58. [34] G. Altarelli, R.K. Ellis and G. Martinelli, Nucl. Phys. B 157 (1979) 461.
59. [35] J. Blümlein et al., Proc. of the 1996 HERA Physics Workshop, ed. G. Ingelman, R. Klanner and A. De Roeck, DESY, Hamburg, 1996, Vol. 1, p. 23.
60. [36] L.N. Lipatov and V.S. Fadin, Sov. J. Nucl. Phys. 50 (1989) 712; V.S. Fadin, R. Fiore and A. Quartarolo, Phys. Rev. D 53 ( 1996) 2729; V. Del Duca, Phys. Rev. D 54 (1996) 989;
61. [36] L.N. Lipatov and V.S. Fadin, Sov. J. Nucl. Phys. 50 (1989) 712; V.S. Fadin, R. Fiore and A. Quartarolo, Phys. Rev. D 53 ( 1996) 2729; V. Del Duca, Phys. Rev. D 54 (1996) 989;
62. [36] L.N. Lipatov and V.S. Fadin, Sov. J. Nucl. Phys. 50 (1989) 712; V.S. Fadin, R. Fiore and A. Quartarolo, Phys. Rev. D 53 ( 1996) 2729; V. Del Duca, Phys. Rev. D 54 (1996) 989;
63. G. Camici and M. Ciafaloni, Phys. Lett. B 386 (1996) 341.
64. [37 ] R.D. Ball and S. Forte, Phys. Lett. B 359 ( 1995) 362.
65. [38] R. Kirschner and L.N. Lipatov, Nucl. Phys. B 213 (1983) 122.
66. [39] B.I. Ermolaev, S.I. Manaenkov and M.G. Ryskin, Z. Phys. C 69 (1996) 259; J. Blümlein and A. Vogt, Acta Phys. Polon. B 27 (1996) 1309; Phys. Lett. B 370 ( 1996) 149.
67. [39] B.I. Ermolaev, S.I. Manaenkov and M.G. Ryskin, Z. Phys. C 69 (1996) 259; J. Blümlein and A. Vogt, Acta Phys. Polon. B 27 (1996) 1309; Phys. Lett. B 370 ( 1996) 149.
68. [39] B.I. Ermolaev, S.I. Manaenkov and M.G. Ryskin, Z. Phys. C 69 (1996) 259; J. Blümlein and A. Vogt, Acta Phys. Polon. B 27 (1996) 1309; Phys. Lett. B 370 ( 1996) 149.
69. [40] J. Bartels, B.I. Ermolaev and M.G. Ryskin, hep-ph/9603204, preprint DESY-96-025, March 1996; Z. Phys. C 70 (1996) 273; J. Blümlein and A. Vogt, Phys. Lett. B 386 (1996) 350; hep-ph/9610203, Proc. of the 1996 HERA Physics Workshop, ed. G. lngelman, R. Klanner, and A. De Roeck, DESY, Hamburg, 1996, Vol. 2, p. 799; Proc. of the Int. Conf. SPIN'96, Amsterdam, September 1996, ed. K. de Jager, P. Mulders et al. (World Scientific. Singapore, 1996), in print.
70. [40] J. Bartels, B.I. Ermolaev and M.G. Ryskin, hep-ph/9603204, preprint DESY-96-025, March 1996; Z. Phys. C 70 (1996) 273; J. Blümlein and A. Vogt, Phys. Lett. B 386 (1996) 350; hep-ph/9610203, Proc. of the 1996 HERA Physics Workshop, ed. G. lngelman, R. Klanner, and A. De Roeck, DESY, Hamburg, 1996, Vol. 2, p. 799; Proc. of the Int. Conf. SPIN'96, Amsterdam, September 1996, ed. K. de Jager, P. Mulders et al. (World Scientific. Singapore, 1996), in print.
71. [40] J. Bartels, B.I. Ermolaev and M.G. Ryskin, hep-ph/9603204, preprint DESY-96-025, March 1996; Z. Phys. C 70 (1996) 273; J. Blümlein and A. Vogt, Phys. Lett. B 386 (1996) 350; hep-ph/9610203, Proc. of the 1996 HERA Physics Workshop, ed. G. lngelman, R. Klanner, and A. De Roeck, DESY, Hamburg, 1996, Vol. 2, p. 799; Proc. of the Int. Conf. SPIN'96, Amsterdam, September 1996, ed. K. de Jager, P. Mulders et al. (World Scientific. Singapore, 1996), in print.
72. [40] J. Bartels, B.I. Ermolaev and M.G. Ryskin, hep-ph/9603204, preprint DESY-96-025, March 1996; Z. Phys. C 70 (1996) 273; J. Blümlein and A. Vogt, Phys. Lett. B 386 (1996) 350; hep-ph/9610203, Proc. of the 1996 HERA Physics Workshop, ed. G. lngelman, R. Klanner, and A. De Roeck, DESY, Hamburg, 1996, Vol. 2, p. 799; Proc. of the Int. Conf. SPIN'96, Amsterdam, September 1996, ed. K. de Jager, P. Mulders et al. (World Scientific. Singapore, 1996), in print.
73. [40] J. Bartels, B.I. Ermolaev and M.G. Ryskin, hep-ph/9603204, preprint DESY-96-025, March 1996; Z. Phys. C 70 (1996) 273; J. Blümlein and A. Vogt, Phys. Lett. B 386 (1996) 350; hep-ph/9610203, Proc. of the 1996 HERA Physics Workshop, ed. G. lngelman, R. Klanner, and A. De Roeck, DESY, Hamburg, 1996, Vol. 2, p. 799; Proc. of the Int. Conf. SPIN'96, Amsterdam, September 1996, ed. K. de Jager, P. Mulders et al. (World Scientific. Singapore, 1996), in print.
74. [41] J.C. Collins and W.K. Tung, Nucl. Phys. B 278 (1986) 934.
75. [42] EMC collaboration: J.J. Aubert et al., Nucl. Phys. B 213 (1983) 31.
76. [43] H1 collaboration: C. Adloff et. al., Z. Phys. C 72 (1996) 593.
77. [44] CCFR collaboration: A.O. Bazarko et al., Z. Phys. C 65 (1995) 189.
78. [45] WA70 collaboration: M. Bonesini et al., Z. Phys. C 38 (1988) 371.
79. [46] BCDMS collaboration: A.C. Benvenuti et al., Phys. Lett. B 223 (1989) 485.
80. [47] NMC collaboration, hep-ph/9610231, Nucl. Phys. B 438 (1997) 3.
81. [48] NMC collaboration: M. Arneodo et al., Phys. Lett. B 364 ( 1995) 107.
82. [49] CCFR collaboration: PZ. Quintas et al., Phys. Rev. Lett. 71 (1993) 1307.
83. [50] E665 collaboration: M.R. Adams et al., Phys. Rev. D 54 (1996) 3006.
84. [51] L.W. Whitlow et al., Phys. Lett. B 282 (1992) 475; L.W. Whitlow et al., preprint SLAC-357 (1990).
85. [51] L.W. Whitlow et al., Phys. Lett. B 282 (1992) 475; L.W. Whitlow et al., preprint SLAC-357 (1990).
86. [52] H1 collaboration, Phys. Lett. B 393 (1997) 452.
87. [53] M. Glück, E. Reya and M. Stratmann, Nucl. Phys. B 422 (1994) 37.
88. [54] R.D. Ball and A. De Roeck, hep-ph/9609309, Proc. of the Int. Workshop on Deep Inelastic Scattering, Rome, April, 1996, p. 669.
89. [55] H1 collaboration, paper pa02-073, submitted to ICHEP 1996 (Warsaw, July, 1996).
90. [56] H1 collaboration, paper pa03-049, submitted to ICHEP 1996 (Warsaw, July, 1996).