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Prog. Theor. Phys. Vol. 102 No. 6 (1999) pp. 1151-1162

[ Full Text PDF : FREE ACCESS (192K) ]

Wilson Renormalization Group Equations for the Critical Dynamics of Chiral Symmetry

Ken-Ichi Aoki, Keiichi Morikawa, Jun-Ichi Sumi,* Haruhiko Terao and Masashi Tomoyose

Institute for Theoretical Physics, Kanazawa University
Kanazawa 920-1192, Japan
*Department of Fundamental Sciences
Faculty of Integrated Human Studies, Kyoto University
Kyoto 606-8501, Japan

(Received August 10, 1999)

Abstract:

The critical dynamics of the chiral symmetry breaking induced by a gauge interaction is examined in the Wilson renormalization group framework in comparison with the Schwinger-Dyson approach. We derive the beta functions for the four-fermi couplings in the sharp cutoff renormalization group scheme, from which the critical couplings and the anomalous dimensions of the fermion composite operators near criticality are immediately obtained. It is also shown that the beta functions lead to the same critical behavior found by solving the so-called ladder Schwinger-Dyson equation, if we restrict the radiative corrections to a certain limited type.


URL : http://ptp.ipap.jp/link?PTP/102/1151/
DOI : 10.1143/PTP.102.1151

[ Full Text PDF : FREE ACCESS (192K) ] Citation:

References:

  1. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (1961), 345[APS].
  2. T. Maskawa and H. Nakajima, Prog. Theor. Phys. 52 (1974), 1326[PTP].
    R. Fukuda and T. Kugo, Nucl. Phys. B117 (1976), 250.
    V. A. Miransky, Nuovo Cim. 90A (1985), 149.
  3. K.-I. Kondo, H. Mino and K. Yamawaki, Phys. Rev. D39 (1989), 2430[APS].
    K. Yamawaki, in Proc. Johns Hopkins Workshop on Current Problems in Particle Theory 12, Baltimore, 1988, ed. G. Domokos and S. Kovesi-Domokos (World Scientific, Singapore, 1988).
    T. Appelquist, M. Soldate, T. Takeuchi and L. C. R. Wijewardhana, ibid.
    W. A. Bardeen, C. N. Leung and S. T. Love, Phys. Rev. Lett. 56 (1986), 1230[APS].
    C. N. Leung, S. T. Love and W. A. Bardeen, Nucl. Phys. B273 (1986), 649.
  4. K. Yamawaki, M. Bando and K. Matumoto, Phys. Rev. Lett. 56 (1986), 1335[APS].
    T. Akiba and T. Yanagida, Phys. Lett. B169 (1986), 432.
    B. Holdom, Phys. Rev. D24 (1981), 1441[APS].
  5. V. A. Miransky, M. Tanabashi and K. Yamawaki, Phys. Lett. B221 (1989), 177.
    W. A. Bardeen, C. T. Hill and M. Lindner, Phys. Rev. D41 (1990), 1647[APS].
    B. Holdom, Phys. Rev. D54 (1996), 1068[APS].
    K. Yamawaki, hep-ph/9603293[e-print arXiv], in the Proceedings of 14th Symposium on Theoretical Physics: Dynamical Symmetry Breaking and Effective Field Theory, Cheju, Korea, 21-26 Jul 1995.
  6. V. A. Miransky, Sov. J. Nucl. Phys. 38 (1984), 280.
    K. Higashijima, Phys. Rev. D29 (1984), 1228[APS].
  7. K-I. Aoki, T. Kugo and M. G. Mitchard, Phys. Lett. B266 (1991), 467.
    K-I. Aoki, M. Bando, T. Kugo, M. G. Mitchard and H. Nakatani, Prog. Theor. Phys. 84 (1990), 683[PTP].
  8. K-I. Aoki, M. Bando, T. Kugo, K. Hasebe and H. Nakatani, Prog. Theor. Phys. 81 (1989), 866[PTP].
  9. K.-I. Kondo and H. Nakatani, Nucl. Phys. B351 (1991), 236; Prog. Theor. Phys. 88 (1992), 7373[PTP].
    K.-I. Kondo, Int. J. Mod. Phys. A7 (1992), 7239.
  10. K. G. Wilson and I. G. Kogut, Phys. Rep. 12 (1974), 75[CrossRef].
  11. F. Wegner and A. Houghton, Phys. Rev. A8 (1973), 401[APS].
  12. J. Polchinski, Nucl. Phys. B231 (1984) 269.
    G. Keller, C. Kopper and M. Salmhofer, Helv. Phys. Acta 65 (1992), 32.
    C. Wetterich, Phys. Lett. B301 (1993), 90.
    M. Bonini, M. D'Attanasio and G. Marchesini, Nucl. Phys. B409 (1993), 441.
    T. R. Morris, Int. J. Mod. Phys. A9 (1994), 2411.
  13. D. U. Jungnickel and C. Wetterich, Phys. Lett. B389 (1996), 600; Eur. Phys. J. C2 (1998), 557.
    B. Bergerhoff and C. Wetterich, Phys. Rev.  D57 (1998), 1591[APS].
  14. M. Alford, Phys. Lett. B336 (1994), 237.
    N. Tetradis and C. Wetterich, Nucl. Phys. B422 (1994), 541.
    T. R. Morris, Phys. Lett. B329 (1994), 241.
  15. K-I. Aoki, K. Morikawa, W. Souma, J-I. Sumi and H. Terao, Prog. Theor. Phys. 95 (1996), 409[PTP].
  16. G. Benfatto and G. Gallavotti, J. Stat. Phys. 59 (1990), 541.
    R. Shankar, Rev. Mod. Phys. 66 (1993), 129[APS].
    J. Polchinski, in Proceedings of the 1992 TASI, ed. J. Harvey and J. Polcjinski (World Scientific, Singapore, 1993).
  17. N. Evans, S. D. H. Hsu and M. Schwetz, Nucl. Phys. B551 (1999), 275; Phys. Lett. B449 (1999), 281.
    T. Schäfer anf F. Wilczek, Phys. Lett. B450 (1999), 325.
  18. K-I. Aoki, K. Morikawa, W. Souma, J-I. Sumi and H. Terao, Prog. Theor. Phys. 97 (1997), 479[PTP].
  19. A. Hazenfratz and P. Hazenfratz, Nucl. Phys. B270 (1986), 269.
    T. R. Morris, Phys. Lett. B334 (1994), 355.
  20. M. Maggiore, Z. Phys. C41 (1989), 687.
    T. E. Clark, B. Haeri and S. T. Love, Nucl. Phys. B402 (1993), 628.
  21. C. Becchi, On the construction of renormalized quantum field theory using renormalization group techniques, in Elementary Particles, Field Theory and Statistical Mechanics, ed. M. Bonini, G. Marchesini and E. Onofri (Parma University, 1993).
    U. Ellwanger, Phys. Lett. B335 (1994), 364.
    U. Ellwanger, M. Hirsch and A. Weber, Z. Phys. C69 (1996), 687.
    M. Bonini, M. D'Attanasio and G. Marchesini, Nucl. Phys. B418 (1994), 81; B421 (1994), 429; B437 (1995), 163; Phys. Lett. B346 (1995), 87.
    M. D'Attanasio and T. R. Morris, Phys. Lett. B378 (1996), 213.
    F. Freire and C. Wetterich, Phys. Lett. B380 (1996), 337.
  22. K.-I. Kondo, S. Shuto and K. Yamawaki, Mod. Phys. Lett. A6 (1991), 3385.
    K.-I. Kondo, M. Tanabashi and K. Yamawaki, Prog. Thoer. Phys. 89 (1993), 1249.
  23. M. Harada, Y. Kikukawa, T. Kugo and H. Nakano, Prog. Theor. Phys. 92 (1994), 1161[PTP].
    N. V. Krasnikov, Mod. Phys. Lett. A8 (1993), 797.
  24. K-I. Kubota and H. Terao, hep-th/9908062[e-print arXiv], Prog. Theor. Phys. 102 (1999), 1163[PTP].
  25. K-I. Aoki, K. Morikawa, J-I. Sumi, H. Terao and M. Tomoyose, hep-th/9908043[e-print arXiv], to be published in Phys. Rev D.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 102 No. 6 (1999) pp. 1163-1179 :
    Non-Perturbative Renormalization Group and Renormalizability of Gauged NJL Model
    Ken-Ichi Kubota and Haruhiko Terao
  2. Progress of Theoretical Physics Vol. 103 No. 4 (2000) pp. 815-832 :
    Non-Ladder Extended Renormalization Group Analysis of the Dynamical Chiral Symmetry Breaking
    Ken-Ichi Aoki, Kaoru Takagi, Haruhiko Terao and Masashi Tomoyose
  3. Progress of Theoretical Physics Vol. 115 No. 1 (2006) pp. 165-188 :
    The Chiral Phase Transition of Hot QCD from the Exact Renormalization Group
    Dai Shimizube and Jun-Ichi Sumi
  4. Progress of Theoretical Physics Vol. 121 No. 4 (2009) pp. 875-884 :
    Evaluation of the Spontaneous Chiral Symmetry Breaking Scale in General Gauge Theories with Non-Perturbative Renormalization Group
    Ken-Ichi Aoki and Kazuhiro Miyashita
  5. Progress of Theoretical Physics Supplement No. 180 (2009) pp. 1-19 :
    Quest for the Dynamical Origin of Mass
    Koichi Yamawaki

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