Chiral phase dependence of the massive fermionic path integral

Hisashi Kikuchi

doi:10.1103/PhysRevD.46.4704

Access by Xinjiang University

Chiral phase dependence of the massive fermionic path integral

Hisashi Kikuchi

Department of Physics, University of California, Riverside, California 92521

PDF

Phys. Rev. D 46, 4704 – Published 15 November, 1992

DOI: https://doi.org/10.1103/PhysRevD.46.4704

Abstract

The Jacobian in the path-integral measure is evaluated for quarks in QCD with arbitrary complex mass matrix. The result clarifies, more transparently than the usual understanding, that the overall chiral U(1) phase of the mass matrix leads to an apparently $CP$ -violating $θ$ term in QCD.

References (19)

S. Weinberg, Phys. Rev. Lett. 31, 494 (1973) ibid.37, 657 (1976)
M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973)
G. 't Hooft, Phys. Rev. Lett. 37, 8 (1976) Phys. Rev. D 14, 3432 (1976)
R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37, 172 (1976) C. Callan, R. Dashen, and D. Gross, Phys. Lett. 63B, 334 (1976)
A. Belavin, A. Polyakov, A. Schwartz, and Y. Tyupkin, Phys. Lett. 59B, 85 (1975)
R. Peccei and H. Quinn, Phys. Rev. Lett. 38, 1440 (1977) Phys. Rev. D 16, 1791 (1977)
S. Weinberg, Phys. Rev. Lett. 40, 223 (1978)
F. Wilczek, Phys. Rev. Lett. 40, 279 (1978)
V. Baluni, Phys. Rev. D 19, 2227 (1979) R. Crewther, P. Di Vecchia, G. Veneziano, and E. Witten, Phys. Lett. 88B, 123 (1979) M. Shifman, A. Vainshtein, and V. Zakharov, Nucl. Phys. B166, 493 (1980)
K. Fujikawa, Phys. Rev. Lett. 42, 1195 (1979) Phys. Rev. D 21, 2848 (1980) ibid.22, 1499 (1980)
K. Fujikawa, Phys. Rev. D 29, 285 (1984)
K. Fujikawa, in Super Field Theories, Proceedings of the NATO Advanced Study Institute, Vancouver, Canada, 1986, edited by H. C. Lee , NATO ASI Series B: Physics, Vol. 160 (Plenum, New York, 1987)
S. Coleman, in The Whys of Subnuclear Physics, Proceedings of the International School, Erice, Italy, edited by A. Zichichi, Subnuclear Series Vol. 15 (Plenum, New York, 1979)
R. Jackiw and C. Rebbi, Phys. Rev. D 16, 1052 (1977)
T. D. Lee, Particle Physics and Introduction to Field Theory (Harwood, Chur, Switzerland, 1981), Chap. 1
E. Witten, Phys. Lett. 117B, 324 (1982)
J. Kiskis, Phys. Rev. D 15, 2329 (1977)
A. Niemi and G. Semenoff, Phys. Rev. D 30, 809 (1984) A. Niemi, Nucl. Phys. B253, 14 (1985) A. Niemi and G. Semenoff, Phys. Rep. 135, 99 (1986)
T. Eguchi, P. Gilkey, and A. Hanson, Phys. Rep. 66, 213 (1980)

[c1] S. Weinberg, Phys. Rev. Lett. 31, 494 (1973) ibid.37, 657 (1976)

[c2] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973)

[c3] G. 't Hooft, Phys. Rev. Lett. 37, 8 (1976) Phys. Rev. D 14, 3432 (1976)

[c4] R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37, 172 (1976) C. Callan, R. Dashen, and D. Gross, Phys. Lett. 63B, 334 (1976)

[c5] A. Belavin, A. Polyakov, A. Schwartz, and Y. Tyupkin, Phys. Lett. 59B, 85 (1975)

[c6] R. Peccei and H. Quinn, Phys. Rev. Lett. 38, 1440 (1977) Phys. Rev. D 16, 1791 (1977)

[c7] S. Weinberg, Phys. Rev. Lett. 40, 223 (1978)

[c8] F. Wilczek, Phys. Rev. Lett. 40, 279 (1978)

[c9] V. Baluni, Phys. Rev. D 19, 2227 (1979) R. Crewther, P. Di Vecchia, G. Veneziano, and E. Witten, Phys. Lett. 88B, 123 (1979) M. Shifman, A. Vainshtein, and V. Zakharov, Nucl. Phys. B166, 493 (1980)

[c10] K. Fujikawa, Phys. Rev. Lett. 42, 1195 (1979) Phys. Rev. D 21, 2848 (1980) ibid.22, 1499 (1980)

[c11] K. Fujikawa, Phys. Rev. D 29, 285 (1984)

[c12] K. Fujikawa, in Super Field Theories, Proceedings of the NATO Advanced Study Institute, Vancouver, Canada, 1986, edited by H. C. Lee , NATO ASI Series B: Physics, Vol. 160 (Plenum, New York, 1987)

[c13] S. Coleman, in The Whys of Subnuclear Physics, Proceedings of the International School, Erice, Italy, edited by A. Zichichi, Subnuclear Series Vol. 15 (Plenum, New York, 1979)

[c14] R. Jackiw and C. Rebbi, Phys. Rev. D 16, 1052 (1977)

[c15] T. D. Lee, Particle Physics and Introduction to Field Theory (Harwood, Chur, Switzerland, 1981), Chap. 1

[c16] E. Witten, Phys. Lett. 117B, 324 (1982)

[c17] J. Kiskis, Phys. Rev. D 15, 2329 (1977)

[c18] A. Niemi and G. Semenoff, Phys. Rev. D 30, 809 (1984) A. Niemi, Nucl. Phys. B253, 14 (1985) A. Niemi and G. Semenoff, Phys. Rep. 135, 99 (1986)

[c19] T. Eguchi, P. Gilkey, and A. Hanson, Phys. Rep. 66, 213 (1980)

Physical Review D

Export citation

Export citation

Chiral phase dependence of the massive fermionic path integral

Abstract

References (19)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation