The renormalization scale-setting problem in QCD

Progress in Particle and Nuclear Physics

Volumn 72, Issue , 2013, Pages 44-98

  Wu, Xing Gang ^a   Brodsky, Stanley J ^b   Mojaza, Matin ^b,c  

^a CHONGQING UNIVERSITY   (China)

^b SLAC NATIONAL ACCELERATOR LABORATORY   (United States)

^c UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

Author keywords

BLM PMC; QCD; Renormalization group; Renormalization scale

Indexed keywords

BLM/PMC; CORRESPONDENCE PRINCIPLE; MINIMUM SENSITIVITIES; QCD; RENORMALIZATION; RENORMALIZATION GROUP; RENORMALIZATION GROUP EQUATIONS; THE STANDARD MODEL;

STATISTICAL MECHANICS;

FORECASTING;

EID: 84880315166     PISSN: 01466410     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ppnp.2013.06.001     Document Type: Review

References (234)

1. H.D. Politzer Phys. Rev. Lett. 30 1973 1346
2. D. Gross, and F. Wilczek Phys. Rev. Lett. 30 1973 1343
3. E.C.G. Stuckelberg, and A. Peterman Helv. Phys. Acta 26 1953 499
4. M. Gell-Mann, and F.E. Low Phys. Rev. 95 1954 1300
5. N.N. Bogoliubov, and D.V. Shirkov Dokl. Akad. Nauk SSSR 103 1955 391
6. A. Peterman Phys. Rep. 53 1979 157
7. C.G. Callan Phys. Rev. D 2 1970 1541
8. K. Symanzik Commun. Math. Phys. 18 1970 227
9. W. Celmaster, and R.J. Gonsalves Phys. Rev. D 20 1979 1420
10. W. Celmaster, and R.J. Gonsalves Phys. Rev. Lett. 42 1979 1435
11. L.F. Abbott Phys. Rev. Lett. 44 1980 1569
12. A.J. Buras Rev. Modern Phys. 52 1980 199
13. G. Grunberg Phys. Lett. B 95 1980 70
14. G. Grunberg Phys. Lett. B 110 1982 501
15. G. Grunberg Phys. Rev. D 29 1984 2315
16. G. Grunberg Phys. Rev. D 40 1984 680
17. P.M. Stevenson Phys. Lett. B 100 1981 61
18. P.M. Stevenson Phys. Rev. D 23 1981 2916
19. P.M. Stevenson Nuclear Phys. B 203 1982 472
20. P.M. Stevenson Nuclear Phys. B 231 1984 65
21. S.J. Brodsky, G.P. Lepage, and P.B. Mackenzie Phys. Rev. D 28 1983 228
22. J.C. Ward Phys. Rev. 78 1950 182
23. Y. Takahashi Nuovo Cimento 6 1957 371
24. S.J. Brodsky, and H.J. Lu Phys. Rev. D 51 1995 3652
25. P.A. Baikov, K.G. Chetyrkin, and J.H. Kuhn PoS RADCOR 2007 2007 023 arXiv:0810.4048
26. P.A. Baikov, K.G. Chetyrkin, J.H. Kuhn, and J. Rittinger J. High Energy Phys. 1207 2012 017
27. P.A. Baikov, K.G. Chetyrkin, J.H. Kuhn, and C. Sturm Nuclear Phys. B 867 2013 182
28. A.L. Kataev, and S.A. Larin Pisma Zh. Eksp. Teor. Fiz. 96 2012 64
29. K. Nakamura Particle Data Group J. Phys. G 37 2010 075021
30. S.J. Brodsky, and P. Huet Phys. Lett. B 417 1998 145
31. J. Blumlein, and W.L. van Neerven Phys. Lett. B 450 1999 417
32. M. Binger, and S.J. Brodsky Phys. Rev. D 74 2006 054016
33. C.H. Chang, and X.G. Wu Eur. Phys. J. C 38 2004 267
34. C.H. Chang, J.X. Wang, and X.G. Wu Phys. Rev. D 70 2004 114019
35. D.J. Gross, and A. Neveu Phys. Rev. D 10 1974 3235
36. B. Lautrup Phys. Lett. B 69 1977 109
37. G. t' Hooft A. Zichichi, The Whys of Subnuclear Physics, Proc. Int. School, Erice, Italy, 1977 1978 Plenum New York
38. M. Beneke Phys. Rep. 317 1999 1
39. C.F. Berger Phys. Rev. D 80 2009 074036
40. A.L. Kataev Phys. Lett. B 691 2010 82
41. S.J. Brodsky, and X.G. Wu Phys. Rev. D 86 2012 014021
42. U. Langenfeld, S. Moch, and P. Uwer Phys. Rev. D 80 2009 054009
43. M. Aliev, H. Lacker, U. Langenfeld, S. Moch, P. Uwer, and M. Wiedermann Comput. Phys. Commun. 182 2011 1034
44. T. Aaltonen CDF Collaboration Phys. Rev. D 105 2010 012001
45. V.M. Abazov D0 Collaboration Phys. Rev. D 84 2011 012008
46. V.M. Abazov D0 Collaboration PLB 704 2011 403
47. G. Aad ATLAS Collaboration Phys. Lett. B 707 2012 459 J. High Energy Phys. 1205 2012 059
48. S. Chatrchyan CMS Collaboration Phys. Rev. D 84 2011 092004
49. S. Chatrchyan CMS Collaboration J. High Energy Phys. 1107 2011 049
50. S.J. Brodsky, and L.D. Giustino Phys. Rev. D 86 2012 085026
51. S.J. Brodsky, and X.G. Wu Phys. Rev. D 85 2012 034038
52. S.J. Brodsky, and X.G. Wu Phys. Rev. Lett. 109 2012 042002
53. S.J. Brodsky, and X.G. Wu Phys. Rev. D 86 2012 054018
54. W.A. Bardeen, A.J. Buras, D.W. Duke, and T. Muta Phys. Rev. D 18 1978 3998
55. M. Mojaza, S.J. Brodsky, and X.G. Wu Phys. Rev. Lett. 110 2013 192001
56. H.J. Lu, and S.J. Brodsky Phys. Rev. D 48 1993 3310
57. G. t' Hooft A. Zichichi, The Whys of Subnuclear Physics, Proceedings of the International School of Subnuclear Physics, Erice, Italy, 1977 Subnuclear Series vol. 15 1979 Plenum New York 943
58. S.J. Brodsky, and H.J. Lu hep-ph/9211308
59. S.J. Brodsky, SLAC-PUB-6304.
60. G. Kramer, and B. Lampe Z. Phys. C 39 1988 101
61. G. Kramer, and B. Lampe Z. Phys. A 339 1991 189
62. S.J. Brodsky, M. Mojaza, and X.G. Wu arXiv:1304.4631
63. G.M. Prosperi, M. Raciti, and C. Simolo Prog. Part. Nucl. Phys. 58 2007 387
64. K.A. Milton, I.L. Solovtsov, and O.P. Solovtsova Phys. Lett. B 439 1998 421 Phys. Rev. D 60 1999 016001
65. K.A. Milton, I.L. Solovtsov, O.P. Solovtsova, and V.I. Yasnov Eur. Phys. J. C 14 2000 495
66. K.A. Milton, I.L. Solovtsov, and O.P. Solovtsova Phys. Rev. D 64 2001 016005
67. O.P. Solovtsova Theoret. and Math. Phys. 134 2003 365
68. D.V. Shirkov Theoret. and Math. Phys. 127 2001 409
69. D.V. Shirkov Eur. Phys. J. C 22 2001 331
70. G. t' Hooft Nuclear Phys. B 61 1973 455
71. S. Weinberg Phys. Rev. D 8 1973 3497
72. H. Georgi, and H.D. Politzer Phys. Rev. D 14 1976 1829
73. A.L. Kataev, and M.D. Vardiashvili Phys. Lett. B 221 1989 377
74. A.L. Kataev, and M.D. Vardiashvili Phys. Lett. B 241 1990 644 (erratum)
75. T. Appelquist, and J. Carazzone Phys. Rev. D 11 1975 2856
76. I.B. Khriplovich Yad. Fiz. 10 1969 409
77. G. t'Hooft C.P. Korthals-Altes, Proc. Colloquium on Renormalization of Yang-Mills Fields and Application to Particle Physics, Marseille, 1972 Nuclear Phys. B 254 1985 11
78. W.E. Caswell Phys. Rev. Lett. 33 1974 244
79. D.R.T. Jones Nuclear Phys. B 75 1974 531
80. E.S. Egorian, and O.V. Tarasov Teoret. Mat. Fiz. 41 1979 26
81. O.V. Tarasov, A.A. Vladimirov, and A. Yu Zharkov Phys. Lett. B 93 1980 429
82. S.A. Larin, and J.A.M. Vermaseren Phys. Lett. B 303 1993 334
83. T. van Ritbergen, J.A.M. Vermaseren, and S.A. Larin Phys. Lett. B 400 1997 379
84. K.G. Chetykin Nuclear Phys. B 710 2005 499
85. M. Czakon Nuclear Phys. B 710 2005 485
86. T. van Ritbergen, A.N. Schellekens, and J.A.M. Vermaseren Int. J. Mod. Phys. A 14 1999 41
87. M. Mojaza, C. Pica, and F. Sannino Phys. Rev. D 82 2010 116009
88. L.D. Landau W. Pauli, Niels Bohr and the Development of Physics 1955 Pergamon London
89. M. Beneke, and V.M. Braun Phys. Lett. B 348 1995 513
90. M. Neubert Phys. Rev. D 51 1995 5924
91. C.N. Lovett-Turner, and C.J. Maxwell Nuclear Phys. B 432 1994 147 Nuclear Phys. B 452 1995 188
92. P. Ball, M. Beneke, and V.M. Braun Nuclear Phys. B 452 1995 563
93. S.V. Mikhailov J. High Energy Phys. 0706 2007 009
94. W. Furmanski, and R. Petronzio Z. Phys. C 11 1982 293
95. K.G. Chetyrkin, B.A. Kniehl, and M. Steinhauser Phys. Rev. Lett. 79 1997 2184
96. E. Gardi, M. Karliner, and G. Grunberg J. High Energy Phys. 9807 1998 007
97. R. Corless Adv. Comput. Math. 5 1996 329
98. B. Magradze Int. J. Mod. Phys. A 15 2000 2715
99. W.J. Marciano Phys. Rev. D 29 1984 580
100. L.F. Abbott Phys. Rev. Lett. 44 1980 1569
101. E. Monsay, and C. Rosenzweig Phys. Rev. D 23 1981 1217
102. A. Dhar, and V. Gupta Phys. Rev. D 29 1984 2822
103. V. Grupta, D.V. Shirkov, and O.V. Tarasov Int. J. Mod. Phys. A 6 1991 3381
104. S.G. Gorishny, A.L. Kataev, and S.A. Larin Phys. Lett. B 259 1991 144
105. S.A. Larin, and J.A.M. Vermaseren Phys. Lett. B 259 1991 345
106. J. Ellis, and M. Karliner Phys. Lett. B 313 1993 131
107. H.J. Lu, and C.A.R. Sa de Melo Phys. Lett. B 273 1991 260 Phys. Lett. B 285(E) 1992 399
108. H.J. Lu Phys. Rev. D 45 1992 1217
109. B.L. Ioffe, V.S. Fadin, and L.N. Lipatov Quantum Chromodynamics Perturbative and Nonperturbative Aspects 2010 Cambridge University Press
110. N.V. Krasnikov Nuclear Phys. B 192 1981 497
111. A.C. Mattingly, and P.M. Stevenson Phys. Rev. D 49 1994 437
112. A.L. Kataev, and V.V. Starshenko Mod. Phys. lett. A 10 1995 235
113. G.P. Lepage, and P.B. Mackenzie Phys. Rev. D 48 1993 2250
114. S.J. Brodsky, V.S. Fadin, V.T. Kim, L.N. Lipatov, and G.B. Pivovarov JETP Lett. 70 1999 155
115. G. Grunberg, and A.L. Kataev Phys. Lett. B 279 1992 352
116. G. Grunberg, Ecole Polytechnique preprint A063-0791.
117. G. Grunberg Phys. Rev. D 46 1992 2228
118. S.J. Brodsky, M.S. Gill, M. Melles, and J. Rathsman Phys. Rev. D 58 1998 116006
119. R.J. Crewther Phys. Rev. Lett. 28 1972 1421
120. D.J. Broadhurst, and A.L. Kataev Phys. Lett. B 315 1993 179
121. S.J. Brodsky, G.T. Gabadadze, A.L. Kataev, and H.J. Lu Phys. Lett. B 372 1996 133
122. P.A. Baikov, K.G. Chetyrkin, and J.H. Kuhn Phys. Rev. Lett. 104 2010 132004
123. A.L. Kataev, and S.V. Mikhailov Teoret. Mat. Fiz. 170 2012 174
124. A.L. Kataev, and S.V. Mikhailov Teoret. Mat. Fiz. 170 2012 139
125. D.V. Shirkov Theoret. and Math. Phys. 93 1992 466
126. K.A. Milton, and O.P. Solovtsova Phys. Rev. D 57 1998 5402
127. M. Binger, and S.J. Brodsky Phys. Rev. D 69 2004 095007
128. J. Shigemitsu Nuclear Phys. Proc. Suppl. 53 1997 16
129. C.T.H. Davies Nuclear Phys. Proc. Suppl. 47 1996 409
130. C.T.H. Davies Phys. Lett. B 345 1995 42
131. C.T.H. Davies Phys. Rev. D 56 1997 2755
132. A. Spitz Phys. Rev. D 60 1999 074502
133. L. Clavelli, and P.W. Coulter hep-ph/9507261
134. J.A. Bagger, K.T. Matchev, and D.M. Pierce Phys. Lett. B 348 1995 443
135. D.M. Pierce, J.A. Bagger, K.T. Matchev, and R. Zhang Nuclear Phys. B 491 1997 3
136. H.J. Lu, and C.A.R. Sa de Melo Phys. Lett. B 273 1991 260
137. H.J. Lu Phys. Rev. D 45 1992 1217
138. S.J. Brodsky, G.T. Gabadadze, A.L. Kataev, and H.J. Lu Phys. Lett. B 372 1996 133
139. S.J. Brodsky, J.R. Ellis, E. Gardi, M. Karliner, and M.A. Samuel Phys. Rev. D 56 1997 6980
140. K. Hornbostel, G.P. Lepage, and C. Morningstar Phys. Rev. D 67 2003 034023
141. E. Braaten, and Y.Q. Chen Phys. Rev. D 57 1998 4236
142. J. Aldins, T. Kinoshita, S.J. Brodsky, and A.J. Dufner Phys. Rev. Lett. 23 1969 441
143. P.A. Baikov, K.G. Chetyrkin, and J.H. Kuhn Phys. Rev. Lett. 101 2008 012002
144. P.A. Baikov, K.G. Chetyrkin, and J.H. Kuhn Nuclear Phys. Proc. Suppl. 189 2009 49
145. K. Nakamura J. Phys. G 37 2010 075021
146. P.A. Baikov, K.G. Chetyrkin, J.H. Kuhn, and J. Rittinger J. High Energy Phys. 1207 2012 017
147. P.A. Baikov, K.G. Chetyrkin, J.H. Kuhn, and J. Rittinger Phys. Lett. B 714 2012 62
148. R. Marshall Z. Phys. C 43 1989 595
149. R. Ammar CLEO Collaboration Phys. Rev. D 57 1998 1350
150. G. Dissertori J. High Energy Phys. 0802 2008 040
151. S. Bethke Eur. Phys. J. C 64 2009 689
152. S.J. Brodsky, L. Di Giustino, SLAC-PUB-14425.
153. S.J. Brodsky, and X.G. Wu Phys. Rev. D 85 2012 114040
154. A.L. Kataev arXiv:1207.1808
155. K.G. Chetyrkin, A.L. Kataev, and F.V. Tkachov Nuclear Phys. B 174 1980 345
156. M.R. Pennington, and G.G. Ross Phys. Lett. B 102 1981 167
157. C.S. Lam, and T.M. Yan Phys. Rev. D 16 1977 703
158. V.N. Gribov, and L,N. Lipatov Sov. J. Nucl. Phys. 15 1972 438
159. G. Altarelli, and G. Parisi Nuclear Phys. B 126 1977 298
160. Yu.L. Dokshitzer Sov. Phys. JETP 46 1977 641
161. S.J. Brodsky, and Guy F. de Teramond arXiv:1112.4212
162. Guy F. de Teramond, and S.J. Brodsky arXiv:1203.4025
163. G. Curci, W. Furmanski, and R. Petronzio Nuclear Phys. B 175 1980 27
164. A. Vogt, S. Moch, and J.A.M. Vermaseren Nuclear Phys. B 691 2004 129
165. P.N. Burrows, and H. Masuda Z. Phys. C 63 1994 235
166. P. Nason, s. Dawson, and R.K. Ellis Nuclear Phys. B 303 1988 607
167. P. Nason, s. Dawson, and R.K. Ellis Nuclear Phys. B 327 1989 49
168. M. Cacciari, M. Czakon, M. Mangano, A. Mitov, and P. Nason Phys. Lett. B 710 2012 612
169. W. Beenakker, H. Kuijf, W.L. Van Neerven, and J. Smith Phys. Rev. D 40 1989 54
170. W. Beenakker, W.L. Van Neerven, R. Meng, and G.A. Schuler Phys. Rev. D 351 1991 507
171. M. Czakon, and A. Mitov Nuclear Phys. B 824 2010 111
172. M. Czakon, A. Mitov, and G. Sterman Phys. Rev. D 80 2009 074017
173. S. Moch, and P. Uwer Nuclear Phys. B 78 2008 034003
174. S. Moch, and P. Uwer Nuclear Phys. Proc. Suppl. 183 2008 75
175. U. Langenfeld, S. Moch, and P. Uwer Phys. Rev. D 80 2009 054009
176. M. Beneke, P. Falgari, and C. Schwinn Nuclear Phys. B 828 2010 69
177. M. Beneke, P. Falgari, S. Klein, and C. Schwinn arXiv:1112.4606
178. V. Ahrens, A. Ferroglia, M. Neubert, Ben D. Pecjak, and L.L. Yang J. High Energy Phys. 1009 2010 097
179. N. Kidonakis, and R. Vogt Phys. Rev. D 78 2008 074005
180. N. Kidonakis arXiv:0909.0037
181. M. Aliev, H. Lacker, U. Langenfeld, S. Moch, P. Uwer, and M. Wiedermann Comput. Phys. Commun. 182 2011 1034
182. P. Baernreuther, M. Czakon, and A. Mitov Phys. Rev. Lett. 109 2012 132001
183. N. Kidonakis Phys. Rev. D 82 2010 114030
184. G.P. Lepage J. Comput. Phys. 27 1978 192
185. C.H. Chang, C. Driouich, P. Eerola, and X.G. Wu Comput. Phys. Commun. 159 2004 192
186. C.H. Chang, J.X. Wang, and X.G. Wu Comput. Phys. Commun. 174 2006 241
187. C.H. Chang, J.X. Wang, and X.G. Wu Comput. Phys. Commun. 175 2006 624
188. X.Y. Wang, and X.G. Wu Comput. Phys. Commun. 183 2012 442
189. C.H. Chang, J.X. Wang, and X.G. Wu Comput. Phys. Commun. 177 2007 467
190. C.H. Chang, J.X. Wang, and X.G. Wu Comput. Phys. Commun. 181 2010 1144
191. X.Y. Wang, and X.G. Wu Comput. Phys. Commun. 184 2013 1070
192. K. Hagiwara, Y. Sumino, and H. Yokoya Phys. Lett. B 666 2008 71
193. Y. Kiyo, J.H. Kühn, S. Moch, M. Steinhauser, and P. Uwer Eur. Phys. J. C 60 2009 375
194. S.J. Brodsky, A.H. Hoang, J.H. Kuhn, and T. Teubner Phys. Lett. B 359 1995 355
195. G. Gamow Z. Phys. 51 1928 204
196. A. Sommerfeld Atombau und Spektrallinien vol. II 1939 Vieweg Braunschweig
197. A.D. Sakharov Sov. Phys. JETP 18 1948 631
198. H.L. Lai Phys. Rev. D 82 2010 074024
199. J. Gao arXiv:1302.6246
200. F. Halzen, P. Hoyer, and C.S. Kim Phys. Lett. B 195 1987 74
201. J.H. Kuhn, and G. Rodrigo Phys. Rev. Lett. 81 1998 49 Phys. Rev. D 59 1999 054017
202. T. Aaltonen CDF Collaboration Phys. Rev. D 83 2011 112003
203. V.M. Abazov D0 Collaboration Phys. Rev. D 84 2011 112005
204. W. Bernreuther, and Z.G. Si Nuclear Phys. B 837 2010 90
205. V. Ahrens, A. Ferroglia, M. Neubert, B.D. Pecjak, and L.L. Yang J. High Energy Phys. 1109 2011 070
206. K. Melnikov, and M. Schulze Nuclear Phys. B 840 2010 129
207. L.G. Almeida, G.F. Sterman, and W. Vogelsang Phys. Rev. D 78 2008 014008
208. N. Kidonakis Phys. Rev. D 84 2011 011504
209. J.M. Campbell, and R.K. Ellis Nuclear Phys. B 60 1999 113006
210. J.H. Kuhn, and G. Rodrigo J. High Energy Phys. 1201 2012 063
211. W. Hollik, and D. Pagani Phys. Rev. D 84 2011 093003
212. CMS Collaboration, CMS-PAS-TOP-10-010.
213. ATLAS Collaboration, ATLAS-CONF-2011-106.
214. A. Martin, R. Roberts, W. Stirling, and R. Thorne Eur. Phys. J. C 39 2005 155
215. S.L. Adler Phys. Rev. 143 1966 1144
216. J.D. Bjorken Phys. Rev. 163 1967 1767
217. D.J. Gross, and C.H. Llewellyn Smith Nuclear Phys. B 14 1969 337
218. J.D. Bjorken Phys. Rev. D 1 1970 1376
219. S.B. Gerasimov Yad. Fiz. 2 1965 598
220. S.D. Drell, and A.C. Hearn Phys. Rev. Lett. 16 1966 908
221. H. Burkhardt, and W.N. Cottingham Ann. Physics 56 1970 453
222. A.V. Efremov, O.V. Teryaev, and E. Leader Phys. Rev. D 55 1997 4307
223. J.R. Ellis, and R.L. Jaffe Phys. Rev. D 9 1974 1444
224. K. Gottfried Phys. Rev. Lett. 18 1967 1174
225. O. Blumlein Prog. Part. Nucl. Phys. 69 2013 28
226. P.A. Baikov, K.G. Chetyrkin, and J.H. Kuhn Phys. Rev. Lett. 104 2010 132004
227. P.A. Baikov, K.G. Chetyrkin, J.H. Kuhn, and J. Rittinger Phys. Lett. B 714 2012 62
228. G.T. Gabadadze, and A.L. Kataev JETP Lett. 61 1995 448
229. R.J. Crewther Phys. Lett. B 397 1997 137
230. V.M. Braun, G.P. Korchemsky, and D. Mueller Prog. Part. Nucl. Phys. 51 2003 311
231. K.G. Chetyrkin, J.H. Kuhn, and A. Kwiatkowski Phys. Rep. 277 1996 189
232. P.A. Baikov, K.G. Chetyrkin, J.H. Kuhn, and J. Rittinger J. High Energy Phys. 1207 2012 017
233. S.A. Larin arXiv:1303.4021
234. S.Q. Wang, X.G. Wu, X.C. Zheng, J.M. Shen, and Q.L. Zhang arXiv:1301.2992