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Physical Review D

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$C P$ -violating theta parameter in the domain model of the QCD vacuum

Alex C. Kalloniatis^*

Sergei N. Nedelko^†

Special Research Centre for the Subatomic Structure of Matter, University of Adelaide, South Australia 5005, Australia

Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia

^*Email address: akalloni@physics.adelaide.edu.au
^†Email address: nedelko@thsun1.jinr.ru

Phys. Rev. D 71, 054002 – Published 2 March, 2005

DOI: https://doi.org/10.1103/PhysRevD.71.054002

Abstract

A nonzero $C P$ -violating $θ$ parameter is treated in the domain model which assumes a clusterlike vacuum structure whose units are characterized, in particular, by a topological charge which is not necessarily an integer number. In the present paper we restrict consideration to rational values of the charge. The model has previously been shown to manifest confinement, spontaneous chiral symmetry breaking and the absence of an axial $U (1)$ Goldstone boson. We find that the specific structure of the minima of the free energy density of the domain ensemble forces a $2 π$ periodicity of observables in $θ$ for any number of light quarks, that vacuum doubling occurs at $θ = π$ for any $N_{f} > 1$ and any value of topological charge $q$ . These features are in agreement with expectations based on anomalous Ward identities and large $N_{c}$ effective theories. We find also additional values of $θ$ depending on $q$ for which vacuum doubling occurs.

Article Text

References (22)

R. Dashen, Phys. Rev. D 3, 1879 (1971).
K. F. Smith et al., Phys. Lett. B 234, 191 (1990); I. S. Altarev et al., 276, 242 (1992).
R. J. Crewther, P. di Vecchia, G. Veneziano, and E. Witten, Phys. Lett. 88B, 123 (1979); 91B, 487(E) (1980).
A. C. Kalloniatis and S. N. Nedelko, Phys. Rev. D 64, 114025 (2001).
R. J. Crewther, in Chiral Properties of Quantum Chromodynamics, NATO Advanced Study Institutes, Ser. B, Vol. 55 (Plenum Press, New York, 1980), p. 529.
E. Witten, Ann. Phys. (N.Y.) 128, 363 (1980); P. Di Vecchia and G. Veneziano, Nucl. Phys. B171, 253 (1980).
W. F. Palmer and S. S. Pinsky, Phys. Lett. 114B, 162 (1982).
R. J. Crewther, Nucl. Phys. B209, 413 (1982).
H. Leutwyler and A. Smilga, Phys. Rev. D 46, 5607 (1992).
G. Akemann, J. T. Lenaghan, and K. Splittorff, Phys. Rev. D 65, 085015 (2002), and references therein.
M. Creutz, Phys. Rev. Lett. 92, 201601 (2004); 92, 162003 (2004).
A. C. Kalloniatis and S. N. Nedelko, Phys. Rev. D 66, 074020 (2002).
A. C. Kalloniatis and S. N. Nedelko, Phys. Rev. D 69, 074029 (2004); 70, 119903(E) (2004).
N. K. Nielsen, Nucl. Phys. B120, 212 (1977).
P. Minkowski, Nucl. Phys. B177, 203 (1981).
I. Horvath et al., Phys. Rev. D 66, 034501 (2002).
R. G. Edwards and U. M. Heller, Phys. Rev. D 65, 014505 (2002); T. De Grand and A. Hasenfratz, 65, 014503 (2002); I. Hip et al., 65, 014506 (2002); T. Blum et al., 65, 014504 (2002).
A. Wipf and S. Duerr, Nucl. Phys. B443, 201 (1995).
K. Fujikawa, Phys. Rev. D 21, 2848 (1980); 22, 1499(E) (1980).
S. Deser, L. Griguolo, and D. Seminara, Phys. Rev. D 57, 7444 (1998).
L. Bergamin and P. Minkowski, hep-th/0003097; M. Leibundgut and P. Minkowski, Nucl. Phys. B531, 95 (1998).
A. Pich and E. de Rafael, Nucl. Phys. B367, 313 (1991).