-
1
-
-
84897774700
-
-
1a Some early studies on this and related renormalization-group functions include, 499 (); HPACAK 0018-0238 1b, Phys. Rev. 95, 1300 (1954); PHRVAO 0031-899X 10.1103/PhysRev.95.1300 1c, Dokl. Akad. Nauk SSSR 103, 391 (1955); 1d, Phys. Rev. D 2, 1541 (1970); PRVDAQ 0556-2821 10.1103/PhysRevD.2.1541 1e, Commun. Math. Phys. 18, 227 (1970); CMPHAY 0010-3616 10.1007/BF01649434 1f See also, Phys. Rev. D 3, 1818 (1971). PRVDAQ 0556-2821 10.1103/PhysRevD.3.1818
-
Some early studies on this and related renormalization-group functions include E. C. G. Stueckelberg and A. Peterman, Helv. Phys. Acta 26, 499 (1953); HPACAK 0018-0238 1b M. Gell-Mann and F. Low, Phys. Rev. 95, 1300 (1954); PHRVAO 0031-899X 10.1103/PhysRev.95.1300 1c N. N. Bogolubov and D. V. Shirkov, Dokl. Akad. Nauk SSSR 103, 391 (1955); 1d C. G. Callan, Phys. Rev. D 2, 1541 (1970); PRVDAQ 0556-2821 10.1103/PhysRevD.2.1541 1e K. Symanzik, Commun. Math. Phys. 18, 227 (1970); CMPHAY 0010-3616 10.1007/BF01649434 1f See also K. Wilson, Phys. Rev. D 3, 1818 (1971). PRVDAQ 0556-2821 10.1103/PhysRevD.3.1818
-
(1953)
Helv. Phys. Acta
, vol.26
-
-
Stueckelberg, E.C.G.1
Peterman, A.2
Gell-Mann, M.3
Low, F.4
Bogolubov, N.N.5
Shirkov, D.V.6
Callan, C.G.7
Symanzik, K.8
Wilson, K.9
-
2
-
-
84883478533
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.88.036003
-
R. Shrock, Phys. Rev. D 88, 036003 (2013). PRVDAQ 1550-7998 10.1103/PhysRevD.88.036003
-
(2013)
Phys. Rev. D
, vol.88
, pp. 036003
-
-
Shrock, R.1
-
3
-
-
84867017338
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.86.065032 3b, Phys. Rev. D 86, 085005 (2012). PRVDAQ 1550-7998 10.1103/PhysRevD.86.085005
-
T. A. Ryttov and R. Shrock, Phys. Rev. D 86, 065032 (2012); PRVDAQ 1550-7998 10.1103/PhysRevD.86.065032 3b T. A. Ryttov and R. Shrock, Phys. Rev. D 86, 085005 (2012). PRVDAQ 1550-7998 10.1103/PhysRevD.86.085005
-
(2012)
Phys. Rev. D
, vol.86
, pp. 065032
-
-
Ryttov, T.A.1
Shrock, R.2
Ryttov, T.A.3
Shrock, R.4
-
4
-
-
0001241483
-
-
PRVDAQ 0556-2821 10.1103/PhysRevD.14.985 4b, Phys. Rev. B 14, 3110 (1976); PLRBAQ 0556-2805 10.1103/PhysRevB.14.3110 4c see also A. Polyakov, Phys. Lett. B 59, 79 (1975). PYLBAJ 0370-2693 10.1016/0370-2693(75)90161-6
-
W. A. Bardeen, B. W. Lee, and R. E. Shrock, Phys. Rev. D 14, 985 (1976); PRVDAQ 0556-2821 10.1103/PhysRevD.14.985 4b E. Brézin and J. Zinn-Justin, Phys. Rev. B 14, 3110 (1976); PLRBAQ 0556-2805 10.1103/PhysRevB.14.3110 4c see also A. Polyakov, Phys. Lett. B 59, 79 (1975). PYLBAJ 0370-2693 10.1016/0370-2693(75)90161-6
-
(1976)
Phys. Rev. D
, vol.14
, pp. 985
-
-
Bardeen, W.A.1
Lee, B.W.2
Shrock, R.E.3
Brézin, E.4
Zinn-Justin, J.5
-
7
-
-
0040503919
-
-
APNYA6 0003-4916 10.1016/0003-4916(74)90118-3
-
E. de Rafael and J. L. Rosner, Ann. Phys. (N.Y.) 82, 369 (1974). APNYA6 0003-4916 10.1016/0003-4916(74)90118-3
-
(1974)
Ann. Phys. (N.Y.)
, vol.82
, pp. 369
-
-
De Rafael, E.1
Rosner, J.L.2
-
8
-
-
0347623473
-
-
TMPHAH 0040-5779 10.1007/BF01018394 8b, Nucl. Phys. B 174, 345 (1980). NUPBBO 0550-3213 10.1016/0550-3213(80)90289-8
-
A. A. Vladimirov, Theor. Math. Phys. 43, 417 (1980); TMPHAH 0040-5779 10.1007/BF01018394 8b K. G. Chetyrkin, A. L. Kataev, and F. V. Tkachov, Nucl. Phys. B 174, 345 (1980). NUPBBO 0550-3213 10.1016/0550-3213(80)90289-8
-
(1980)
Theor. Math. Phys.
, vol.43
, pp. 417
-
-
Vladimirov, A.A.1
Chetyrkin, K.G.2
Kataev, A.L.3
Tkachov, F.V.4
-
9
-
-
0001968685
-
-
PYLBAJ 0370-2693 10.1016/0370-2693(91)90222-C
-
S. G. Gorishny, A. L. Kataev, S. A. Larin, and L. R. Surguladze, Phys. Lett. B 256, 81 (1991). PYLBAJ 0370-2693 10.1016/0370-2693(91)90222-C
-
(1991)
Phys. Lett. B
, vol.256
, pp. 81
-
-
Gorishny, S.G.1
Kataev, A.L.2
Larin, S.A.3
Surguladze, L.R.4
-
10
-
-
84867029893
-
-
PZETAB 0370-274X 10b [, JETP Lett. 96, 61 (2012)]. JTPLA2 0021-3640 10.1134/S0021364012130073
-
A. L. Kataev and S. A. Larin, Pis'ma Zh. Eksp. Teor. Fiz. 96, 64 (2012); PZETAB 0370-274X 10b [A. L. Kataev and S. A. Larin, JETP Lett. 96, 61 (2012)]. JTPLA2 0021-3640 10.1134/S0021364012130073
-
(2012)
Pis'Ma Zh. Eksp. Teor. Fiz.
, vol.96
, pp. 64
-
-
Kataev, A.L.1
Larin, S.A.2
Kataev, A.L.3
Larin, S.A.4
-
11
-
-
84864464280
-
-
() 017; JHEPFG 1029-8479 10.1007/JHEP07(2012)017 11b, Nucl. Phys. B 867, 182. NUPBBO 0550-3213 10.1016/j.nuclphysb.2012.09.018
-
P. A. Baikov, K. G. Chetyrkin, J. H. Kühn, and J. Rittinger, J. High Energy Phys. 07 (2012) 017; JHEPFG 1029-8479 10.1007/JHEP07(2012)017 11b P. A. Baikov, K. G. Chetyrkin, J. H. Kühn, and C. Sturm, Nucl. Phys. B 867, 182 (2013). NUPBBO 0550-3213 10.1016/j.nuclphysb.2012.09.018
-
(2013)
J. High Energy Phys.
, vol.2012
, Issue.7
-
-
Baikov, P.A.1
Chetyrkin, K.G.2
Kühn, J.H.3
Rittinger, J.4
Baikov, P.A.5
Chetyrkin, K.G.6
Kühn, J.H.7
Sturm, C.8
-
12
-
-
36049059570
-
-
PHRVAO 0031-899X 10.1103/PhysRev.163.1699
-
K. Johnson, R. Willey, and M. Baker, Phys. Rev. 163, 1699 (1967). PHRVAO 0031-899X 10.1103/PhysRev.163.1699
-
(1967)
Phys. Rev.
, vol.163
, pp. 1699
-
-
Johnson, K.1
Willey, R.2
Baker, M.3
-
13
-
-
0000918826
-
-
PRVDAQ 0556-2821 10.1103/PhysRevD.5.3021
-
S. L. Adler, Phys. Rev. D 5, 3021 (1972). PRVDAQ 0556-2821 10.1103/PhysRevD.5.3021
-
(1972)
Phys. Rev. D
, vol.5
, pp. 3021
-
-
Adler, S.L.1
-
14
-
-
84897774697
-
-
For a review, see, e.g., edited by (World Scientific, Singapore)
-
For a review, see, e.g., Proceedings of the 1990 International Workshop on Strong Coupling Gauge Theories and Beyond, SCGT90, edited by T. Muta and K. Yamawaki (World Scientific, Singapore, 1991).
-
(1991)
Proceedings of the 1990 International Workshop on Strong Coupling Gauge Theories and Beyond, SCGT90
-
-
Muta, T.1
Yamawaki, K.2
-
15
-
-
0001541598
-
-
NUPBBO 0550-3213 10.1016/0550-3213(90)90490-5 15b, Phys. Rev. D 53, 1508 (1996); PRVDAQ 0556-2821 10.1103/PhysRevD.53.1508 15c, Phys. Rev. Lett. 80, 4119 (1998). PRLTAO 0031-9007 10.1103/PhysRevLett.80.4119
-
M. Göckeler, R. Horsley, E. Laermann, P. Rakow, G. Schierholz, R. Sommer, and U.-J. Wiese, Nucl. Phys. B 334, 527 (1990); NUPBBO 0550-3213 10.1016/0550-3213(90)90490-5 15b M. Göckeler, R. Horsley, P. Rakow, and G. Schierholz, Phys. Rev. D 53, 1508 (1996); PRVDAQ 0556-2821 10.1103/PhysRevD.53. 1508 15c M. Göckeler, R. Horsley, V. Linke, P. Rakow, G. Schierholz, and H. Stüben, Phys. Rev. Lett. 80, 4119 (1998). PRLTAO 0031-9007 10.1103/PhysRevLett.80.4119
-
(1990)
Nucl. Phys. B
, vol.334
, pp. 527
-
-
Göckeler, M.1
Horsley, R.2
Laermann, E.3
Rakow, P.4
Schierholz, G.5
Sommer, R.6
Wiese, U.-J.7
Göckeler, M.8
Horsley, R.9
Rakow, P.10
Schierholz, G.11
Göckeler, M.12
Horsley, R.13
Linke, V.14
Rakow, P.15
Schierholz, G.16
Stüben, H.17
-
16
-
-
0001589455
-
-
NUPBBO 0550-3213 10.1016/0550-3213(93)90115-6 16b, Phys. Rev. D 65, 054015 (2002); PRVDAQ 0556-2821 10.1103/PhysRevD.65.054015, Phys. Rev. D 71, 094012 (2005). PRVDAQ 1550-7998 10.1103/PhysRevD.71.094012
-
A. Kocić, J. B. Kogut, and M.-P. Lombardo, Nucl. Phys. B 398, 376 (1993); NUPBBO 0550-3213 10.1016/0550-3213(93)90115-6 16b S. Kim, J. B. Kogut, and M.-P. Lombardo, Phys. Rev. D 65, 054015 (2002); PRVDAQ 0556-2821 10.1103/PhysRevD.65.054015 J. B. Kogut and C. G. Strouthos, Phys. Rev. D 71, 094012 (2005). PRVDAQ 1550-7998 10.1103/PhysRevD.71.094012
-
(1993)
Nucl. Phys. B
, vol.398
, pp. 376
-
-
Kocić, A.1
Kogut, J.B.2
Lombardo, M.-P.3
Kim, S.4
Kogut, J.B.5
Lombardo, M.-P.6
Kogut, J.B.7
Strouthos, C.G.8
-
17
-
-
19644381876
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.93.110405
-
H. Gies and J. Jaeckel, Phys. Rev. Lett. 93, 110405 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.110405
-
(2004)
Phys. Rev. Lett.
, vol.93
, pp. 110405
-
-
Gies, H.1
Jaeckel, J.2
-
18
-
-
0001588906
-
-
These authors' variable K is equal to 4 y and their coefficient β n is equal to b n + 2, n + 1 / 4 n + 1 in terms of the notation used here. CMPHAY 0010-3616 10.1007/BF01212398
-
A. Palanques-Mestre and P. Pascual, Commun. Math. Phys. 95, 277 (1984). These authors' variable K is equal to 4 y and their coefficient β n is equal to b n + 2, n + 1 / 4 n + 1 in terms of the notation used here. CMPHAY 0010-3616 10.1007/BF01212398
-
(1984)
Commun. Math. Phys.
, vol.95
, pp. 277
-
-
Palanques-Mestre, A.1
Pascual, P.2
-
20
-
-
0001710088
-
-
PYLBAJ 0370-2693 10.1016/0370-2693(93)91017-H 20b, Phys. Lett. B 458, 117 (1999). PYLBAJ 0370-2693 10.1016/S0370-2693(99)00573-0
-
J. A. Gracey, Phys. Lett. B 317, 415 (1993); PYLBAJ 0370-2693 10.1016/0370-2693(93)91017-H 20b M. Ciuchini, S. E. Derkachov, J. A. Gracey, and A. N. Manashov, Phys. Lett. B 458, 117 (1999). PYLBAJ 0370-2693 10.1016/S0370-2693(99)00573-0
-
(1993)
Phys. Lett. B
, vol.317
, pp. 415
-
-
Gracey, J.A.1
Ciuchini, M.2
Derkachov, S.E.3
Gracey, J.A.4
Manashov, A.N.5
-
21
-
-
77957749744
-
-
Note that the variable A in this paper is equal to 4 y in terms of the notation used here. PYLBAJ 0370-2693 10.1016/j.physletb.2010.09.037
-
B. Holdom, Phys. Lett. B 694, 74 (2010). Note that the variable A in this paper is equal to 4 y in terms of the notation used here. PYLBAJ 0370-2693 10.1016/j.physletb.2010.09.037
-
(2010)
Phys. Lett. B
, vol.694
, pp. 74
-
-
Holdom, B.1
-
22
-
-
79952239996
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.83.035013
-
C. Pica and F. Sannino, Phys. Rev. D 83, 035013 (2011). PRVDAQ 1550-7998 10.1103/PhysRevD.83.035013
-
(2011)
Phys. Rev. D
, vol.83
, pp. 035013
-
-
Pica, C.1
Sannino, F.2
-
23
-
-
4243869616
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.30.1343 23b, Phys. Rev. Lett. 30, 1346 (1973); PRLTAO 0031-9007 10.1103/PhysRevLett.30.1346 (unpublished)
-
D. J. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973); PRLTAO 0031-9007 10.1103/PhysRevLett.30.1343 23b H. D. Politzer, Phys. Rev. Lett. 30, 1346 (1973); PRLTAO 0031-9007 10.1103/PhysRevLett.30.1346 G. 't Hooft (unpublished).
-
(1973)
Phys. Rev. Lett.
, vol.30
, pp. 1343
-
-
Gross, D.J.1
Wilczek, F.2
Politzer, H.D.3
'T Hooft, G.4
-
24
-
-
25544467102
-
-
PRVDAQ 0556-2821 10.1103/PhysRevD.8.3633
-
D. J. Gross and F. Wilczek, Phys. Rev. D 8, 3633 (1973). PRVDAQ 0556-2821 10.1103/PhysRevD.8.3633
-
(1973)
Phys. Rev. D
, vol.8
, pp. 3633
-
-
Gross, D.J.1
Wilczek, F.2
-
25
-
-
4244091327
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.33.244 25b, Nucl. Phys. B 75, 531 (1974). NUPBBO 0550-3213 10.1016/0550-3213(74)90093-5
-
W. E. Caswell, Phys. Rev. Lett. 33, 244 (1974); PRLTAO 0031-9007 10.1103/PhysRevLett.33.244 25b D. R. T. Jones, Nucl. Phys. B 75, 531 (1974). NUPBBO 0550-3213 10.1016/0550-3213(74)90093-5
-
(1974)
Phys. Rev. Lett.
, vol.33
, pp. 244
-
-
Caswell, W.E.1
Jones, D.R.T.2
-
26
-
-
26344466565
-
-
PYLBAJ 0370-2693 10.1016/0370-2693(80)90358-5, Phys. Lett. B 303, 334 (1993). PYLBAJ 0370-2693 10.1016/0370-2693(93)91441-O
-
O. V. Tarasov, A. A. Vladimirov, and A. Yu. Zharkov, Phys. Lett. B 93, 429 (1980); PYLBAJ 0370-2693 10.1016/0370-2693(80)90358-5 S. A. Larin and J. A. M. Vermaseren, Phys. Lett. B 303, 334 (1993). PYLBAJ 0370-2693 10.1016/0370-2693(93)91441-O
-
(1980)
Phys. Lett. B
, vol.93
, pp. 429
-
-
Tarasov, O.V.1
Vladimirov, A.A.2
Yu. Zharkov, A.3
Larin, S.A.4
Vermaseren, J.A.M.5
-
28
-
-
0003917354
-
-
in, edited by (North-Holland, Amsterdam)
-
D. J. Gross, in Proceedings of the Les Houches Summer School 1975, edited by R. Balian and J. Zinn-Justin (North-Holland, Amsterdam, 1976), p. 141.
-
(1976)
Proceedings of the les Houches Summer School 1975
, pp. 141
-
-
Gross, D.J.1
Balian, R.2
Zinn-Justin, J.3
-
29
-
-
28844508625
-
-
NUPBBO 0550-3213 10.1016/0550-3213(73)90376-3
-
G. 't Hooft, Nucl. Phys. B 61, 455 (1973). NUPBBO 0550-3213 10.1016/0550-3213(73)90376-3
-
(1973)
Nucl. Phys. B
, vol.61
, pp. 455
-
-
'T Hooft, G.1
-
30
-
-
0000487603
-
-
PRVDAQ 0556-2821 10.1103/PhysRevD.18.3998
-
W. A. Bardeen, A. J. Buras, D. W. Duke, and T. Muta, Phys. Rev. D 18, 3998 (1978). PRVDAQ 0556-2821 10.1103/PhysRevD.18.3998
-
(1978)
Phys. Rev. D
, vol.18
, pp. 3998
-
-
Bardeen, W.A.1
Buras, A.J.2
Duke, D.W.3
Muta, T.4
-
31
-
-
71249114666
-
-
A recent review is, 689. EPCFFB 1434-6044 10.1140/epjc/s10052-009-1173-1
-
A recent review is S. Bethke, Eur. Phys. J. C 64, 689 (2009). EPCFFB 1434-6044 10.1140/epjc/s10052-009-1173-1
-
(2009)
Eur. Phys. J. C
, vol.64
-
-
Bethke, S.1
-
32
-
-
33750379961
-
-
NUPBBO 0550-3213 10.1016/0550-3213(82)90035-9
-
T. Banks and A. Zaks, Nucl. Phys. B 196, 189 (1982). NUPBBO 0550-3213 10.1016/0550-3213(82)90035-9
-
(1982)
Nucl. Phys. B
, vol.196
, pp. 189
-
-
Banks, T.1
Zaks, A.2
-
33
-
-
0032575840
-
-
NUPBBO 0550-3213 10.1016/S0550-3213(98)00392-7 33b, J. High Energy Phys. (1998) 007. JHEPFG 1029-8479 10.1088/1126-6708/1998/07/007
-
E. Gardi and M. Karliner, Nucl. Phys. B 529, 383 (1998); NUPBBO 0550-3213 10.1016/S0550-3213(98)00392-7 33b E. Gardi, G. Grunberg, and M. Karliner, J. High Energy Phys. 07 (1998) 007. JHEPFG 1029-8479 10.1088/1126-6708/1998/07/007
-
(1998)
Nucl. Phys. B
, vol.529
, Issue.7
, pp. 383
-
-
Gardi, E.1
Karliner, M.2
Gardi, E.3
Grunberg, G.4
Karliner, M.5
-
34
-
-
79960714107
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.83.056011, Phys. Rev. D 85, 076009 (2012). PRVDAQ 1550-7998 10.1103/PhysRevD.85.076009
-
T. A. Ryttov and R. Shrock, Phys. Rev. D 83, 056011 (2011); PRVDAQ 1550-7998 10.1103/PhysRevD.83.056011 T. A. Ryttov and R. Shrock, Phys. Rev. D 85, 076009 (2012). PRVDAQ 1550-7998 10.1103/PhysRevD.85.076009
-
(2011)
Phys. Rev. D
, vol.83
, pp. 056011
-
-
Ryttov, T.A.1
Shrock, R.2
Ryttov, T.A.3
Shrock, R.4
-
35
-
-
84877931319
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.87.105005
-
R. Shrock, Phys. Rev. D 87, 105005 (2013). PRVDAQ 1550-7998 10.1103/PhysRevD.87.105005
-
(2013)
Phys. Rev. D
, vol.87
, pp. 105005
-
-
Shrock, R.1
-
36
-
-
84879487092
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.87.116007
-
R. Shrock, Phys. Rev. D 87, 116007 (2013). PRVDAQ 1550-7998 10.1103/PhysRevD.87.116007
-
(2013)
Phys. Rev. D
, vol.87
, pp. 116007
-
-
Shrock, R.1
-
37
-
-
84894505563
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.89.016013, arXiv:1311.0848
-
T. A. Ryttov, Phys. Rev. D 89, 016013 (2014); PRVDAQ 1550-7998 10.1103/PhysRevD.89.016013 T. A. Ryttov, arXiv:1311.0848.
-
(2014)
Phys. Rev. D
, vol.89
, pp. 016013
-
-
Ryttov, T.A.1
Ryttov, T.A.2
-
38
-
-
84878120864
-
-
JPAMB5 1751-8113 10.1088/1751-8113/46/22/225403
-
J. A. Gracey, J. Phys. A 46, 225403 (2013). JPAMB5 1751-8113 10.1088/1751-8113/46/22/225403
-
(2013)
J. Phys. A
, vol.46
, pp. 225403
-
-
Gracey, J.A.1
-
39
-
-
0037033394
-
-
Our expansions agree with, and extend to higher order, the results in [21] except for the A 4 term in Eq. (5) of [21] that term was derived from an earlier partial calculation of b 5 in P. A. Baikov, K. G. Chetyrkin, and J. H. Kühn, Phys. Rev. Lett. 88, 012001 (2001) which was superseded by the full calculation in [11]. PRLTAO 0031-9007 10.1103/PhysRevLett.88.012001
-
(2001)
Phys. Rev. Lett.
, vol.88
-
-
Baikov, P.A.1
Chetyrkin, K.G.2
Kühn, J.H.3
-
40
-
-
0003498504
-
-
(Academic, New York), Eqs. (8.321); 46b, Theory of the Riemann Zeta Function (Oxford Press, Oxford, 1951)
-
I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 1980), Eqs. (8.321); 46b E. C. Titchmarsh, Theory of the Riemann Zeta Function (Oxford Press, Oxford, 1951).
-
(1980)
Tables of Integrals, Series, and Products
-
-
Gradshteyn, I.S.1
Ryzhik, I.M.2
Titchmarsh, E.C.3
|