Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 024, 14 pages      arXiv:0802.3193      http://dx.doi.org/10.3842/SIGMA.2008.024
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Effects of Quark Interactions on Dynamical Chiral Symmetry Breaking by a Magnetic Field

Brigitte Hiller a, Alexander A. Osipov b, Alex H. Blin a and João da Providência a
a) Centro de Física Teórica, Departamento de Física da Universidade de Coimbra, 3004-516 Coimbra, Portugal
b) Joint Institute for Nuclear Research, Laboratory of Nuclear Problems, 141980 Dubna, Moscow region, Russia

Received November 14, 2007, in final form February 07, 2008; Published online February 22, 2008

Abstract
It is shown how the strong interaction dynamics of a multi-quark Lagrangian affects the catalysis of dynamical symmetry breaking by a constant magnetic field in (3+1) dimensions. Attention is drawn to the local minima structure of the theory.

Key words: dynamical chiral symmetry breaking; catalysis; field theoretical model of multi-quark interactions.

pdf (349 kb)   ps (314 kb)   tex (222 kb)

References

  1. Jackiw R., Fractional charges and zero modes for planar systems in a magnetic field, Phys. Rev. D 29 (1984), 2375-2377.
    Barducci A., Casalbuoni R., Lusanna L., Supersymmetries and the pseudoclassical relativistic electron, Nuovo Cimento A 35 (1976), 377-399.
  2. Klevansky S.P., Lemmer R.H., Chiral symmetry restoration in the Nambu-Jona-Lasinio model with a constant electromagnetic field, Phys. Rev. D 39 (1989), 3478-3489.
  3. Klimenko K.G., Three-dimensional Gross-Neveu model in an external magnetic field, Theoret. and Math. Phys. 89 (1992), 1161-1168.
    Vshivtsev A.S., Klimenko K.G., Magnitsky B.V., Vacuum structure of the (y-`y)2 model, accounting for the magnetic field and chemical potential, Theoret. and Math. Phys. 106 (1996), 319-327.
  4. Krive I.V., Naftulin S.A., Electrodynamics of systems with dynamical generation of mass in (2+1)-dimensional space-time, Sov. J. Nuclear Phys. 54 (1991), 897-902.
    Krive I.V., Naftulin S.A., Dynamical symmetry breaking and phase transitions in a three-dimensional Gross-Neveu model in a strong magnetic field, Phys. Rev. D 46 (1992), 2737-2740.
  5. Gusynin V.P., Miransky V.A., Shovkovy I.A., Catalysis of dynamical flavor symmetry breaking by a magnetic field in (2+1)-dimensions, Phys. Rev. Lett. 73 (1994), 3499-3502, hep-ph/9405262.
  6. Gusynin V.P., Miransky V.A., Shovkovy I.A., Dimensional reduction and dynamical chiral symmetry breaking by a magnetic field in (3+1)-dimensions, Phys. Lett. B 349 (1995), 477-483, hep-ph/9412257.
    Gusynin V.P., Miransky V.A., Shovkovy I.A., Dynamical flavor symmetry breaking by a magnetic field in (2+1)-dimensions, Phys. Rev. D 52 (1995), 4718-4735, hep-th/9407168.
  7. Gusynin V.P., Miransky V.A., Shovkovy I.A., Dimensional reduction and catalysis of dynamical symmetry breaking by a magnetic field, Nuclear Phys. B 462 (1996), 249-290, hep-ph/9509320.
  8. Bardeen J., Cooper L.N., Schrieffer J.R., Theory of superconductivity, Phys. Rev. 108 (1957), 1175-1204.
  9. Ragazzon R., The Nambu-Jona-Lasinio in simple configurations of strong and non-homogeneous magnetic configuartions, Phys. Lett. B 334 (1994), 427-430.
    Dunne G., Hall T., Inhomogeneous condensates in planar QED, Phys. Rev. D 53 (1996), 2220-2226, hep-th/9511192.
  10. Ragazzon R., Nambu-Jona-Lasinio model in a magnetic field with variable direction, Phys. Rev. D 59 (1999), 065006, 5 pages.
  11. Nambu Y., Jona-Lasinio G., Dynamical model of elementary particles based on an analogy with superconductivity. I, Phys. Rev. 122 (1961), 345-358.
    Nambu Y., Jona-Lasinio G., Dynamical model of elementary particles based on an analogy with superconductivity. II, Phys. Rev. 124 (1961), 246-254.
    Vaks V.G., Larkin A.I., On the application of the methods of superconductivity theory to the problem of the masses of elementary particles, Zh. Éksp. Teor. Fiz. 40 (1961), 282-285 (English transl.: Sov. Phys. JETP 13 (1961), 192-193).
    Arbuzov B.A., Tavkhelidze A.N., Faustov R.N., On the fermion mass in the g5-invariant model of the quantum field theory, Dokl. Akad. Nauk. SSSR 139 (1961), 345-347 (English transl.: Sov. Phys. Dokl. 6 (1962), 598-600).
  12. Osipov A.A., Hiller B., da Providência J., Multi-quark interactions with a globally stable vacuum, Phys. Lett. B 634 (2006), 48-54, hep-ph/0508058.
  13. 't Hooft G., Computation of the quantum effects due to a four-dimensional pseudoparticle, Phys. Rev. D 14 (1976), 3432-3450, Erratum, Phys. Rev. D 18 (1978), 2199.
  14. Osipov A.A., Hiller B., Bernard V., Blin A.H., Aspects of UA(1) breaking in the Nambu and Jona-Lasinio model, Ann. Phys. 321 (2006), 2504-2534, hep-ph/0507226.
  15. Hiller B., Osipov A.A., Bernard V., Blin A.H., Functional integral approaches to the bosonization of effective multi-quark interactions with UA(1) breaking, SIGMA 2 (2006), 026, 18 pages, hep-ph/0602165.
  16. Zwanziger D., Private communication.
  17. Simonov Yu.A., Chiral Lagrangian with confinement from the QCD Lagrangian, Phys. Rev. D 65 (2002), 094018, 10 pages, hep-ph/0201170.
  18. Bali G.S., QCD forces and heavy quark bound states, Phys. Rep. 343 (2001), 1-136, hep-ph/0001312.
  19. Osipov A.A., Hiller B., Blin A.H., da Providência J., Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons, Ann. Phys. 332 (2007), 2021-2054, hep-ph/0607066.
  20. Osipov A.A., Hiller B., Moreira J., Blin A.H., da Providência J., Lowering the critical temperature with eight-quark interactions, Phys. Lett. B 646 (2007), 91-94, hep-ph/0612082.
    Osipov A.A., Hiller B., Moreira J., Blin A.H., OZI violating eight-quark interactions as a thermometer for chiral transitions, Phys. Lett. B 659 (2008), 270-274, arXiv:0709.3507.
  21. Kashiwa K., Kouno H., Sakaguchi T., Matsuzaki M., Yahiro M., Chiral phase transition in an extended NJL model with higher-order multi-quark interactions, Phys. Lett. B 647 (2007), 446-451, nucl-th/0608078.
    Kashiwa K., Kouno H., Matsuzaki M., Yahiro M., Critical endpoint in the Polyakov-loop extended NJL model, arXiv:0710.2180.
  22. Osipov A.A., Hiller B., Blin A.H., da Providência J., Dynamical chiral symmetry breaking by a magnetic field and multi-quark interactions, Phys. Lett. B 650 (2007), 262-267, hep-ph/0701090.
  23. Okubo S., Phi meson and unitary symmetry model, Phys. Lett. B 5 (1963), 165-168.
    Zweig G., An SU(3) model for strong interaction symmetry and its breaking. 2, CERN Report No. 8419/TH412, 1964.
    Iizuka I., A systematics and phenomenology of meson family, Progr. Theoret. Phys. Suppl. 37-38 (1966), 21-34.
  24. Eguchi T., New approach to collective phenomena in superconductivity models, Phys. Rev. D 14 (1976), 2755-2763.
    Kikkawa K., Quantum corrections in superconductor models, Progr. Theoret. Phys. 56 (1976), 947-955.
  25. Volkov M.K., Ebert D., Four-quark interactions as a common dynamical basis of the s model and the vector dominance model, Sov. J. Nuclear Phys. 36 (1982), 736-742.
    Ebert D., Volkov M.K., Composite meson model with vector dominance based on U(2) invariant four quark interactions, Z. Phys. C 16 (1983), 205-210.
  26. Dhar A., Wadia S., The Nambu-Jona-Lasinio model: an effective Lagrangian for quantum chromodynamics at intermediate length scales, Phys. Rev. Lett. 52 (1984), 959-962.
    Dhar A., Shankar R., Wadia S., Nambu-Jona-Lasinio type effective Lagrangian: anomalies and nonlinear Lagrangian of low-energy, large-N QCD, Phys. Rev. D 31 (1985), 3256-3267.
    Ebert D., Reinhardt H., Effective chiral hadron Lagrangian with anomalies and Skyrme terms from quark flavour dynamics, Nuclear Phys. B 271 (1986), 188-226.
    Schüren C., Arriola E.R., Goeke K., Explicit chiral symmetry breaking in the Nambu-Jona-Lasinio model, Nuclear Phys. A 547 (1992), 612-632.
    Bijnens J., Bruno C., de Rafael E., Nambu-Jona-Lasinio like models and the low energy effective action of QCD, Nuclear Phys. B 390 (1993), 501-541, hep-ph/9206236.
    Bernard V., Osipov A.A., Meißner U.-G., The momentum-space bosonization of the Nambu-Jona-Lasinio model with vector and axial-vector mesons Phys. Lett. B 324 (1994), 201-208, hep-ph/9312203.
    Bernard V., Blin A.H., Hiller B., Ivanov Yu.P., Osipov A.A., Meißner U.-G., Pion observables in the extended NJL model with vector and axial-vector mesons Ann. Phys. 249 (1996), 499-531, hep-ph/9506309.
    Osipov A.A., Hiller B., Effective chiral meson Lagrangian for the extended Nambu-Jona-Lasinio model, Phys. Rev. D 62 (2000), 114013, 10 pages, hep-ph/0007102.
    Osipov A.A., Sampaio M., Hiller B., Implications of a new effective chiral meson Lagrangian, Nuclear Phys. A 703 (2000), 378-392, hep-ph/0110285.
    Osipov A.A., Hiller B., Generalized proper time approach for the case of broken isospin symmetry, Phys. Rev. D 63 (2001), 094009, 10 pages, hep-ph/0012294.
  27. Bernard V., Jaffe R.L., Meißner U.-G., Flavor mixing via dynamical chiral symmetry breaking, Phys. Lett. B 198 (1987), 92-98.
    Bernard V., Jaffe R.L., Meißner U.-G., Strangeness mixing and quenching in the Nambu-Jona-Lasinio model, Nuclear Phys. B 308 (1988), 753-790.
  28. Reinhardt H., Alkofer R., Instanton induced flavour mixing in mesons, Phys. Lett. B 207 (1988), 482-488.
  29. Klimt S, Lutz M., Vogl U., Weise W., Generalized SU(3) Nambu-Jona-Lasinio model. Part 1. Mesonic modes, Nuclear Phys A 516 (1990), 429-468.
    Vogl U., Lutz M., Klimt S., Weise W., Generalized SU(3) Nambu-Jona-Lasinio model. Part 2. From current to constituent quarks, Nuclear Phys A 516 (1990), 469-495.
  30. Bernard V., Blin A.H., Hiller B., Meißner U.-G., Ruivo M.C., Strong and radiative meson decays in a generalized Nambu-Jona-Lasinio model, Phys. Lett. B 305 (1993), 163-167, hep-ph/9302245.
    Dmitrasinovic V., UA(1) symmetry breaking, scalar mesons and the nucleon spin problem in an effective chiral field theory, Nuclear Phys. A 686 (2001), 379-392, hep-ph/0010047.
  31. Klevansky S.P., The Nambu-Jona-Lasinio model of quantum chromodynamics, Rev. Modern Phys. 64 (1992), 649-708.
    Hatsuda T., Kunihiro T., QCD Phenomenology based on a chiral effective Lagrangian, Phys. Rep. 247 (1994), 221-367, hep-ph/9401310.
  32. Schwinger J., On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951), 664-679.
  33. Bateman H., Erdelyi A., Higher transcendental functions, Mc Graw-Hill Book Company, Inc., 1953.
  34. Duncan R.C., Thompson C., Formation of very strongly magnetized neutron stars - implications for gamma-ray bursts, Astrophys. J. Lett. 392 (1992), L9-L13.
    Thompson C., Duncan R.C., Neutron star dynamos and the origins of pulsar magnetism, Astrophys. J. 408 (1993), 194-203.
    Thompson C., Duncan R.C., The soft gamma repeaters as very strongly magnetized neutron stars. II. Quiescent neutrino, X-ray, and Alfven wave emission, Astrophys. J. 473 (1996), 322-342.
    Kouveliotou C. et al., An X-ray pulsar with a superstrong magnetic field in the soft gamma-ray repeater SGR 1806-20, Nature 393 (1998), 235-237.
    Kouveliotou C. et al., Discovery of a magnetar associated with the soft gamma repeater SGR 1900+14, Astrophys. J. 510 (1999), L115-L118, astro-ph/9809140.
    Woods P.M. et al., Discovery of a new soft gamma repeater, SGR 1627-41, Astrophys. J. Lett. 519 (1999), L139-L142, astro-ph/9903267.
  35. Vachaspati T., Magnetic fields from cosmological phase transitions, Phys. Lett. B 265 (1991), 258-261.
    Olesen P., On the possible creation of a background W condensate in the electroweak phase transition, Phys. Lett. B 281 (1992), 300-302.
  36. Yamazaki D.G., Ichiki K., Kajino T., Mathews G.J., Magnetic field constrained from CMB anisotropies,and its generation and evolution before, during and after the BBN, in Proceedings of the International Symposium on Nuclear Astrophysics "Nuclei in the Cosmos-IX" (June 25-30, 2006, CERN, Geneva), Proceedings of Science, PoS(NIC-IX), 2006, 194-199, astro-ph/0610234.
    Kernan P.J., Starkman G.D., Vachaspati T., Big bang nucleosynthesis constraints on primordial magnetic fields, Phys. Rev. D 54 (1996), 7207-7214, astro-ph/9509126.
    Cheng B., Olinto A.V., Schramm D.N., Truran J.W., Constraints on the strength of primordial magnetic fields from big bang nucleosynthesis revisited, Phys.Rev. D 54 (1996), 4714-4718, astro-ph/9606163.

Previous article   Next article   Contents of Volume 4 (2008)