-
2
-
-
84867017338
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.86.065032
-
T.A. Ryttov and R. Shrock, Phys. Rev. D 86, 065032 (2012); PRVDAQ 1550-7998 10.1103/PhysRevD.86.065032
-
(2012)
Phys. Rev. D
, vol.86
, pp. 065032
-
-
Ryttov, T.A.1
Shrock, R.2
-
3
-
-
84867065371
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.86.085005
-
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. 085005
-
-
Ryttov, T.A.1
Shrock, R.2
-
4
-
-
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
-
5
-
-
4243869616
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.30.1343
-
D.J. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973); PRLTAO 0031-9007 10.1103/PhysRevLett.30.1343
-
(1973)
Phys. Rev. Lett.
, vol.30
, pp. 1343
-
-
Gross, D.J.1
Wilczek, F.2
-
6
-
-
17544378111
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.30.1346
-
H.D. Politzer, Phys. Rev. Lett. 30, 1346 (1973); PRLTAO 0031-9007 10.1103/PhysRevLett.30.1346
-
(1973)
Phys. Rev. Lett.
, vol.30
, pp. 1346
-
-
Politzer, H.D.1
-
7
-
-
84940339974
-
-
(unpublished).
-
G.Hooft (unpublished).
-
-
-
Hooft, G.1
-
8
-
-
4244091327
-
-
PRLTAO 0031-9007 10.1103/PhysRevLett.33.244
-
W.E. Caswell, Phys. Rev. Lett. 33, 244 (1974). PRLTAO 0031-9007 10.1103/PhysRevLett.33.244
-
(1974)
Phys. Rev. Lett.
, vol.33
, pp. 244
-
-
Caswell, W.E.1
-
9
-
-
0001336464
-
-
NUPBBO 0550-3213 10.1016/0550-3213(74)90093-5
-
D.R.T. Jones, Nucl. Phys. B75, 531 (1974). NUPBBO 0550-3213 10.1016/0550-3213(74)90093-5
-
(1974)
Nucl. Phys.
, vol.B75
, pp. 531
-
-
Jones, D.R.T.1
-
10
-
-
84940347661
-
-
in, Proceedings of Les Houches 1975, edited by R. Balian and J. Zinn-Justin (North Holland, Amsterdam).
-
D.J. Gross, in Methods in Field Theory, Proceedings of Les Houches 1975, edited by R. Balian and J. Zinn-Justin (North Holland, Amsterdam, 1976).
-
(1976)
Methods in Field Theory
-
-
Gross, D.J.1
-
11
-
-
9344244565
-
-
PRVDAQ 0556-2821 10.1103/PhysRevD.20.881
-
N.N. Khuri and O.A. McBryan, Phys. Rev. D 20, 881 (1979). PRVDAQ 0556-2821 10.1103/PhysRevD.20.881
-
(1979)
Phys. Rev. D
, vol.20
, pp. 881
-
-
Khuri, N.N.1
McBryan, O.A.2
-
12
-
-
26344466565
-
-
PYLBAJ 0370-2693 10.1016/0370-2693(80)90358-5
-
O.V. Tarasov, A.A. Vladimirov, and A. Yu. Zharkov, Phys. Lett. 93B, 429 (1980); PYLBAJ 0370-2693 10.1016/0370-2693(80)90358-5
-
(1980)
Phys. Lett.
, vol.93
, Issue.B
, pp. 429
-
-
Tarasov, O.V.1
Vladimirov, A.A.2
Yu. Zharkov, A.3
-
13
-
-
0000310610
-
-
PYLBAJ 0370-2693 10.1016/0370-2693(93)91441-O
-
S.A. Larin and J.A.M. Vermaseren, Phys. Lett. B 303, 334 (1993). PYLBAJ 0370-2693 10.1016/0370-2693(93)91441-O
-
(1993)
Phys. Lett. B
, vol.303
, pp. 334
-
-
Larin, S.A.1
Vermaseren, J.A.M.2
-
15
-
-
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
-
16
-
-
28844508625
-
-
NUPBBO 0550-3213 10.1016/0550-3213(73)90376-3
-
G. 't Hooft, Nucl. Phys. B61, 455 (1973). NUPBBO 0550-3213 10.1016/0550-3213(73)90376-3
-
(1973)
Nucl. Phys.
, vol.B61
, pp. 455
-
-
Hooft, T.G.1
-
17
-
-
84940330915
-
-
The Casimir invariants CR and TR are defined as a=1o (G) j=1dim (R) DR (Ta)ij DR (Ta)jk = CR δik and i,j=1dim (R) DR (Ta)ij DR (Tb)ji = TR δab, where R is the representation and Ta are the generators of G, so that for SU (Nc), CA = Nc for the adjoint (A) and Tfund =1 /2 for the fundamental representation, etc. Cf denotes CR for the fermion representation.
-
The Casimir invariants CR and TR are defined as a=1o (G) =1dim (R) DR (Ta)ij DR (Ta)jk = CR δik and i,j=1dim (R) DR (Ta)ij DR (Tb)ji = TR δab, where R is the representation and Ta are the generators of G, so that for SU (Nc), CA = Nc for the adjoint (A) and Tfund =1 /2 for the fundamental representation, etc. Cf denotes CR for the fermion representation.
-
-
-
-
18
-
-
33750379961
-
-
NUPBBO 0550-3213 10.1016/0550-3213(82)90035-9
-
T. Banks and A. Zaks, Nucl. Phys. B196, 189 (1982). NUPBBO 0550-3213 10.1016/0550-3213(82)90035-9
-
(1982)
Nucl. Phys.
, vol.B196
, pp. 189
-
-
Banks, T.1
Zaks, A.2
-
19
-
-
33751327732
-
-
Early discussions include, (); PYLBAJ 0370-2693 10.1016/0370-2693(85) 91015-9
-
Early discussions include B. Holdom, Phys. Lett. 150B, 301 (1985); PYLBAJ 0370-2693 10.1016/0370-2693(85)91015-9
-
(1985)
Phys. Lett.
, vol.150 B
, pp. 301
-
-
Holdom, B.1
-
22
-
-
84940355853
-
-
For some recent discussions on continuum and lattice studies, see, edited by Y. Aoki, T. Maskawa, and K. Yamawaki (World Scientific, Singapore); CP3-Origins Workshop on the Origin of Mass at; Lattice Meets Experiment 2013 at http://www.bnl.gov/lme2013; and Workshop on Strong Coupling Gauge Theories Beyond the Standard Model, SCGT14Mini, at http://www.kmi.nagoya-u.ac.jp/ workshop/SCGT14Mini.
-
For some recent discussions on continuum and lattice studies, see Proceedings of SCGT12-Strong Coupling Gauge Theories in the LHC Perspective, 2012, edited by Y. Aoki, T. Maskawa, and K. Yamawaki (World Scientific, Singapore, 2014); CP3-Origins Workshop on the Origin of Mass at http://cp3-origins.dk/events/meetings/mass2013; Lattice Meets Experiment 2013 at http://www.bnl.gov/lme2013; and Workshop on Strong Coupling Gauge Theories Beyond the Standard Model, SCGT14Mini, at http://www.kmi.nagoya-u.ac.jp/ workshop/SCGT14Mini.
-
(2014)
Proceedings of SCGT12-Strong Coupling Gauge Theories in the LHC Perspective, 2012
-
-
-
23
-
-
0032575840
-
-
NUPBBO 0550-3213 10.1016/S0550-3213(98)00392-7
-
E. Gardi and M. Karliner, Nucl. Phys. B529, 383 (1998); NUPBBO 0550-3213 10.1016/S0550-3213(98)00392-7
-
(1998)
Nucl. Phys.
, vol.B529
, pp. 383
-
-
Gardi, E.1
Karliner, M.2
-
24
-
-
4243222885
-
-
JHEPFG 1029-8479 10.1088/1126-6708/1999/03/024
-
E. Gardi and G. Grunberg, J. High Energy Phys. 03 (1999) 024. JHEPFG 1029-8479 10.1088/1126-6708/1999/03/024
-
J. High Energy Phys.
, vol.1999
, Issue.3
, pp. 024
-
-
Gardi, E.1
Grunberg, G.2
-
25
-
-
79960714107
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.83.056011
-
T.A. Ryttov and R. Shrock, Phys. Rev. D 83, 056011 (2011). PRVDAQ 1550-7998 10.1103/PhysRevD.83.056011
-
(2011)
Phys. Rev. D
, vol.83
, pp. 056011
-
-
Ryttov, T.A.1
Shrock, R.2
-
26
-
-
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
-
27
-
-
84860168377
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.85.076009
-
T.A. Ryttov and R. Shrock, Phys. Rev. D 85, 076009 (2012). PRVDAQ 1550-7998 10.1103/PhysRevD.85.076009
-
(2012)
Phys. Rev. D
, vol.85
, pp. 076009
-
-
Ryttov, T.A.1
Shrock, R.2
-
28
-
-
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
-
29
-
-
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
-
30
-
-
70349850395
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.80.065032
-
D.D. Dietrich, Phys. Rev. D 80, 065032 (2009). PRVDAQ 1550-7998 10.1103/PhysRevD.80.065032
-
(2009)
Phys. Rev. D
, vol.80
, pp. 065032
-
-
Dietrich, D.D.1
-
31
-
-
79960872505
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.83.116001
-
C. Pica and F. Sannino, Phys. Rev. D 83, 116001 (2011). PRVDAQ 1550-7998 10.1103/PhysRevD.83.116001
-
(2011)
Phys. Rev. D
, vol.83
, pp. 116001
-
-
Pica, C.1
Sannino, F.2
-
32
-
-
82555186103
-
-
PYLBAJ 0370-2693 10.1016/j.physletb.2011.10.036
-
A.V. Garkusha and A.L. Kataev, Phys. Lett. B 705, 400 (2011). PYLBAJ 0370-2693 10.1016/j.physletb.2011.10.036
-
(2011)
Phys. Lett. B
, vol.705
, pp. 400
-
-
Garkusha, A.V.1
Kataev, A.L.2
-
33
-
-
84894505563
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.89.016013
-
T.A. Ryttov, Phys. Rev. D 89, 016013 (2014); PRVDAQ 1550-7998 10.1103/PhysRevD.89.016013
-
(2014)
Phys. Rev. D
, vol.89
, pp. 016013
-
-
Ryttov, T.A.1
-
34
-
-
84897011612
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.89.056001
-
T.A. Ryttov Phys. Rev. D 89, 056001 (2014). PRVDAQ 1550-7998 10.1103/PhysRevD.89.056001
-
(2014)
Phys. Rev. D
, vol.89
, pp. 056001
-
-
Ryttov, T.A.1
-
35
-
-
84897775829
-
-
PRVDAQ 1550-7998 10.1103/PhysRevD.89.045019
-
R. Shrock, Phys. Rev. D 89, 045019 (2014). PRVDAQ 1550-7998 10.1103/PhysRevD.89.045019
-
(2014)
Phys. Rev. D
, vol.89
, pp. 045019
-
-
Shrock, R.1
-
36
-
-
84940322600
-
-
As was observed in (endnote [26] of the first paper of) Ref. [2], this is consistent with the fact that (2.6), in general, maps a′=- b1 / b2 to a≠- b1 / b2, since (2.6) is an exact result, whereas the equality of two-loop IR zero values holds for the truncations of βα and βα′ to two-loop order.
-
As was observed in (endnote [26] of the first paper of) Ref. [2], this is consistent with the fact that (2.6), in general, maps a′=- b1 / b2 to a≠- b1 / b2, since (2.6) is an exact result, whereas the equality of two-loop IR zero values holds for the truncations of βα and βα′ to two-loop order.
-
-
-
-
37
-
-
84880315166
-
-
A recent review is,. PPNPDB 0146-6410 10.1016/j.ppnp.2013.06.001
-
A recent review is X.-G. Wu, S.J. Brodsky, and M. Mojaza, Prog. Part. Nucl. Phys. 72, 44 (2013). PPNPDB 0146-6410 10.1016/j.ppnp.2013.06.001
-
(2013)
Prog. Part. Nucl. Phys.
, vol.72
, pp. 44
-
-
Wu, X.-G.1
Brodsky, S.J.2
Mojaza, M.3
-
38
-
-
33744543538
-
-
NUPBBO 0550-3213 10.1016/0550-3213(74)90154-0
-
G. 't Hooft, Nucl. Phys. B72, 461 (1974); NUPBBO 0550-3213 10.1016/0550-3213(74)90154-0
-
(1974)
Nucl. Phys.
, vol.B72
, pp. 461
-
-
Hooft, T.G.1
-
39
-
-
33744618636
-
-
NUPBBO 0550-3213 10.1016/0550-3213(74)90088-1
-
G. 't Hooft Nucl. Phys. B75, 461 (1974); NUPBBO 0550-3213 10.1016/0550-3213(74)90088-1
-
(1974)
Nucl. Phys.
, vol.B75
, pp. 461
-
-
Hooft, T.G.1
-
40
-
-
0039731124
-
-
NUPBBO 0550-3213 10.1016/0550-3213(76)90412-0
-
G. Veneziano, Nucl. Phys. B117, 519 (1976). NUPBBO 0550-3213 10.1016/0550-3213(76)90412-0
-
(1976)
Nucl. Phys.
, vol.B117
, pp. 519
-
-
Veneziano, G.1
-
41
-
-
84940304083
-
-
Here and elsewhere, when an analytic expression is given for Nf that evaluates to a nonintegral real value, it is understood implicitly that one infers an appropriate neighboring integral value of Nf from it.
-
Here and elsewhere, when an analytic expression is given for Nf that evaluates to a nonintegral real value, it is understood implicitly that one infers an appropriate neighboring integral value of Nf from it.
-
-
-
|