Analysis of scheme transformations in the vicinity of an infrared fixed point

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 86, Issue 8, 2012, Pages

  Ryttov, Thomas A ^a   Shrock, Robert ^b  

^a HARVARD UNIVERSITY   (United States)

^b STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84867065371     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.86.085005     Document Type: Article

References (90)

1. C.G. Callan, Phys. Rev. D 2, 1541 (1970); PRVDAQ 0556-2821 10.1103/PhysRevD.2.1541
2. K. Symanzik, Commun. Math. Phys. 18, 227 (1970); CMPHAY 0010-3616 10.1007/BF01649434
3. Earlier related work includes M. Gell-Mann and F. Low, Phys. Rev. 95, 1300 (1954); PHRVAO 0031-899X 10.1103/PhysRev.95.1300
4. N.N. Bogolubov and D.V. Shirkov, Dokl. Akad. Nauk SSSR 103, 391 (1955); DASBAQ 0002-3264
5. See also K. Wilson, Phys. Rev. D 3, 1818 (1971). PRVDAQ 0556-2821 10.1103/PhysRevD.3.1818
6. T.A. Ryttov and R. Shrock, arXiv:1206.2366 [Phys. Rev. D (to be published)].
7. T. Appelquist and J. Carazzone, Phys. Rev. D 11, 2856 (1975). PRVDAQ 0556-2821 10.1103/PhysRevD.11.2856
8. T.A. Ryttov and R. Shrock, Phys. Rev. D 83, 056011 (2011). PRVDAQ 1550-7998 10.1103/PhysRevD.83.056011
9. C. Pica and F. Sannino, Phys. Rev. D 83, 035013 (2011). PRVDAQ 1550-7998 10.1103/PhysRevD.83.035013
10. D.J. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973); PRLTAO 0031-9007 10.1103/PhysRevLett.30.1343
11. H.D. Politzer, Phys. Rev. Lett. 30, 1346 (1973); PRLTAO 0031-9007 10.1103/PhysRevLett.30.1346
12. G. 't Hooft (unpublished).
13. W.E. Caswell, Phys. Rev. Lett. 33, 244 (1974); PRLTAO 0031-9007 10.1103/PhysRevLett.33.244
14. D.R.T. Jones, Nucl. Phys. B75, 531 (1974). NUPBBO 0550-3213 10.1016/0550-3213(74)90093-5
15. D.J. Gross, in Methods in Field Theory, Les Houches 1975, edited by, R. Balian, and, J. Zinn-Justin, (North Holland, Amsterdam, 1976).
16. G. 't Hooft and M. Veltman, Nucl. Phys. B44, 189 (1972). NUPBBO 0550-3213 10.1016/0550-3213(72)90279-9
17. G. 't Hooft, Nucl. Phys. B61, 455 (1973). NUPBBO 0550-3213 10.1016/0550-3213(73)90376-3
18. 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
19. 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
20. S.A. Larin and J.A.M. Vermaseren, Phys. Lett. B 303, 334 (1993). PYLBAJ 0370-2693 10.1016/0370-2693(93)91441-O
21. T. van Ritbergen, J.A.M. Vermaseren, and S.A. Larin, Phys. Lett. B 400, 379 (1997). PYLBAJ 0370-2693 10.1016/S0370-2693(97)00370-5
22. D.J. Gross and F. Wilczek, Phys. Rev. D 8, 3633 (1973); PRVDAQ 0556-2821 10.1103/PhysRevD.8.3633
23. D.J. Gross F. Wilczek Phys. Rev. D 9, 980 (1974); PRVDAQ 0556-2821 10.1103/PhysRevD.9.980
24. H.D. Politzer, Phys. Rep. 14, 124 (1974). PRPLCM 0370-1573
25. S. Bethke, Eur. Phys. J. C 64, 689 (2009). EPCFFB 1434-6044 10.1140/epjc/s10052-009-1173-1
26. Instanton effects on β were estimated in QCD in C.G. Callan, R.F. Dashen, and D.J. Gross, Phys. Rev. D 17, 2717 (1978); PRVDAQ 0556-2821 10.1103/PhysRevD.17.2717
27. C.G. Callan R.F. Dashen D.J. Gross Phys. Rev. D 20, 3279 (1979) and were found to increase the magnitude of β. PRVDAQ 0556-2821 10.1103/PhysRevD.20. 3279
28. G. 't Hooft, in The Whys of Subnuclear Physics, Proc. 1977 Erice Summer School, edited by A. Zichichi (Plenum, New York, 1979), p.943.
29. P.M. Stevenson, Phys. Rev. D 23, 2916 (1981); PRVDAQ 0556-2821 10.1103/PhysRevD.23.2916
30. P.M. Stevenson Nucl. Phys. B203, 472 (1982); NUPBBO 0550-3213 10.1016/0550-3213(82)90325-X
31. P.M. Stevenson Nucl. Phys. B231, 65 (1984). NUPBBO 0550-3213 10.1016/0550-3213(84)90307-9
32. E. Braaten and J.P. Leveille, Phys. Rev. D 24, 1369 (1981). PRVDAQ 0556-2821 10.1103/PhysRevD.24.1369
33. S.J. Brodsky, G.P. Lepage, and P.B. MacKenzie, Phys. Rev. D 28, 228 (1983); PRVDAQ 0556-2821 10.1103/PhysRevD.28.228
34. S.J. Brodsky and H.J. Lu, Phys. Rev. D 51, 3652 (1995); PRVDAQ 0556-2821 10.1103/PhysRevD.51.3652
35. S.J. Brodsky and P. Huet, Phys. Lett. B 417, 145 (1998). PYLBAJ 0370-2693 10.1016/S0370-2693(97)01209-4
36. S.J. Brodsky and X.-G. Wu, Phys. Rev. D 85, 034038 (2012); PRVDAQ 1550-7998 10.1103/PhysRevD.85.034038
37. S.J. Brodsky X.-G. Wu Phys. Rev. Lett. 109, 042002 (2012); PRLTAO 0031-9007 10.1103/PhysRevLett.109.042002
38. S.J. Brodsky X.-G. Wu Phys. Rev. D 86, 014021 (2012). PRVDAQ 1550-7998 10.1103/PhysRevD.86.014021
39. A.V. Garkusha and A.L. Kataev, Phys. Lett. B 705, 400 (2011). PYLBAJ 0370-2693 10.1016/j.physletb.2011.10.036
40. We focus here on an IR zero of the perturbative β function. A nonperturbative zero in β has been discussed in S.J. Brodsky, G.F. de Téramond, and A. Deur, Phys. Rev. D 81, 096010 (2010); PRVDAQ 1550-7998 10.1103/PhysRevD.81.096010
41. M. Creutz, Acta Phys. Slovaca 61, 1 (2011). APSVCO 0323-0465 10.2478/v10155-011-0001-y
42. T. Banks and A. Zaks, Nucl. Phys. B196, 189 (1982). NUPBBO 0550-3213 10.1016/0550-3213(82)90035-9
43. For a chiral gauge theory with requisite fermion content, there is also the alternate possibility that the theory may confine and produce massless composite fermions, as discussed in G. 't Hooft, Recent Developments in Gauge Theories, Cargése Summer Institute, 1979 (Plenum, New York, 1980), p.135;
44. recent studies include T. Appelquist, A. Cohen, M. Schmaltz, and R. Shrock, Phys. Lett. B 459, 235 (1999); PYLBAJ 0370-2693 10.1016/S0370-2693(99) 00616-4
45. T. Appelquist and F. Sannino, Phys. Rev. D 61, 125009 (2000), and references therein. PRVDAQ 0556-2821 10.1103/PhysRevD.61.125009
46. B. Holdom, Phys. Lett. 150B, 301 (1985); PYLBAJ 0370-2693 10.1016/0370-2693(85)91015-9
47. K. Yamawaki, M. Bando, and K. Matumoto, Phys. Rev. Lett. 56, 1335 (1986); PRLTAO 0031-9007 10.1103/PhysRevLett.56.1335
48. T. Appelquist, D. Karabali, and L.C.R. Wijewardhana, Phys. Rev. Lett. 57, 957 (1986); PRLTAO 0031-9007 10.1103/PhysRevLett.57.957
49. T. Appelquist and L.C.R. Wijewardhana, Phys. Rev. D 35, 774 (1987); PRVDAQ 0556-2821 10.1103/PhysRevD.35.774
50. T. Appelquist L.C.R. Wijewardhana Phys. Rev. D 36, 568 (1987). PRVDAQ 0556-2821 10.1103/PhysRevD.36.568
51. T. Appelquist, K.D. Lane, and U. Mahanta, Phys. Rev. Lett. 61, 1553 (1988); PRLTAO 0031-9007 10.1103/PhysRevLett.61.1553
52. T. Appelquist and S. Selipsky, Phys. Lett. B 400, 364 (1997); PYLBAJ 0370-2693 10.1016/S0370-2693(97)00369-9
53. C.D. Roberts and A.G. Williams, Prog. Part. Nucl. Phys. 33, 477 (1994); PPNPDB 0146-6410 10.1016/0146-6410(94)90049-3
54. P. Maris and P.C. Tandy, Phys. Rev. C 60, 055214 (1999); PRVCAN 0556-2813 10.1103/PhysRevC.60.055214
55. C.S. Fischer and R. Alkofer, Phys. Rev. D 67, 094020 (2003); PRVDAQ 0556-2821 10.1103/PhysRevD.67.094020
56. S.J. Brodsky and R. Shrock, Phys. Lett. B 666, 95 (2008). PYLBAJ 0370-2693 10.1016/j.physletb.2008.06.054
57. The latter is the case in QCD and technicolor theories: S. Weinberg, Phys. Rev. D 19, 1277 (1979); PRVDAQ 0556-2821 10.1103/PhysRevD.19.1277
58. L. Susskind, Phys. Rev. D 20, 2619 (1979). PRVDAQ 0556-2821 10.1103/PhysRevD.20.2619
59. M. Harada, M. Kurachi, and K. Yamawaki, Phys. Rev. D 68, 076001 (2003); PRVDAQ 0556-2821 10.1103/PhysRevD.68.076001
60. M. Harada M. Kurachi K. Yamawaki Phys. Rev. D 70, 033009 (2004). PRVDAQ 1550-7998 10.1103/PhysRevD.70.033009
61. M. Kurachi and R. Shrock, J. High Energy Phys. 12 (2006) 034; JHEPFG 1029-8479 10.1088/1126-6708/2006/12/034
62. M. Kurachi R. Shrock M. Kurachi Phys. Rev. D 74, 056003 (2006). PRVDAQ 1550-7998 10.1103/PhysRevD.74.056003
63. T. Appelquist, G. Fleming, and E. Neil, Phys. Rev. Lett. 100, 171607 (2008); PRLTAO 0031-9007 10.1103/PhysRevLett.100.171607
64. T. Appelquist G. Fleming E. Neil Phys. Rev. D 79, 076010 (2009); PRVDAQ 1550-7998 10.1103/PhysRevD.79.076010
65. T. Appelquist, Phys. Rev. Lett. 104, 071601 (2010); PRLTAO 0031-9007 10.1103/PhysRevLett.104.071601
66. T. Appelquist Phys. Rev. D 84, 054501 (2011); PRVDAQ 1550-7998 10.1103/PhysRevD.84.054501
67. A. Deuzeman, M.P. Lombardo, and E. Pallante, Phys. Lett. B 670, 41 (2008); PYLBAJ 0370-2693 10.1016/j.physletb.2008.10.039
68. A. Deuzeman M.P. Lombardo E. Pallante Phys. Rev. D 82, 074503 (2010); PRVDAQ 1550-7998 10.1103/PhysRevD.82.074503
69. A. Hasenfratz, Phys. Rev. Lett. 108, 061601 (2012); PRLTAO 0031-9007 10.1103/PhysRevLett.108.061601
70. Y. Aoki, arXiv:1202.4916;
71. Z. Fodor, K. Holland, J. Kuti, D. Nógrádi, and C. Schroeder, Phys. Lett. B 681, 353 (2009); PYLBAJ 0370-2693 10.1016/j.physletb. 2009.10.040
72. M. Hayakawa, K.-I. Ishikawa, Y. Osaki, S. Takeda, S. Uno, and N. Yamada, Phys. Rev. D 83, 074509 (2011); PRVDAQ 1550-7998 10.1103/PhysRevD.83.074509
73. X.-Y. Jin and R.D. Mawhinney, arXiv:1203.5855.
74. For recent reviews of this and other gauge theories on the lattice, see talks in https://latt11.llnl.gov;
75. http://lqcd.fnal.gov/(tilde)eneil/lat-exp-2011;
76. http://www.kmi.nagoya-u.ac.jp/workshop/SCGT12Mini.
77. See, e.g., T. Appelquist and J. Terning, Phys. Rev. D 50, 2116 (1994); PRVDAQ 0556-2821 10.1103/PhysRevD.50.2116
78. T. Appelquist and R. Shrock, Phys. Lett. B 548, 204 (2002); PYLBAJ 0370-2693 10.1016/S0370-2693(02)02854-X
79. T. Appelquist R. Shrock Phys. Rev. Lett. 90, 201801 (2003); PRLTAO 0031-9007 10.1103/PhysRevLett.90.201801
80. T. Appelquist, M. Piai, and R. Shrock, Phys. Rev. D 69, 015002 (2004); PRVDAQ 0556-2821 10.1103/PhysRevD.69.015002
81. N.D. Christensen and R. Shrock, Phys. Rev. Lett. 94, 241801 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.241801
82. An analogous study of the effect of higher-loop terms in the β function on the UV to IR evolution of a supersymmetric gauge theory has been carried out in T.A. Ryttov and R. Shrock, Phys. Rev. D 85, 076009 (2012); PRVDAQ 1550-7998 10.1103/PhysRevD.85.076009
83. See also T.A. Ryttov and F. Sannino, Phys. Rev. D 78, 065001 (2008); PRVDAQ 1550-7998 10.1103/PhysRevD.78.065001
84. C. Pica and F. Sannino, Phys. Rev. D 83, 116001 (2011). PRVDAQ 1550-7998 10.1103/PhysRevD.83.116001
85. W. Celmaster and R.J. Gonsalves, Phys. Rev. D 20, 1420 (1979); PRVDAQ 0556-2821 10.1103/PhysRevD.20.1420
86. A recent study is J.A. Gracey, Phys. Rev. D 84, 085011 (2011). PRVDAQ 1550-7998 10.1103/PhysRevD.84.085011
87. E. Gardi, G. Grunberg, and M. Karliner, J. High Energy Phys. 07 (1998) 007. JHEPFG 1029-8479 10.1088/1126-6708/1998/07/007
88. D.D. Dietrich, F. Sannino, and K. Tuominen, Phys. Rev. D 72, 055001 (2005); PRVDAQ 1550-7998 10.1103/PhysRevD.72.055001
89. R. Foadi, M.T. Frandsen, T.A. Ryttov, and F. Sannino, Phys. Rev. D 76, 055005 (2007); PRVDAQ 1550-7998 10.1103/PhysRevD.76.055005
90. F. Sannino, Acta Phys. Pol. B 40, 3533 (2009). APOBBB 0587-4254