Magnetic catalysis and anisotropic confinement in QCD

V. A. Miransky; I. A. Shovkovy

doi:10.1103/PhysRevD.66.045006

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Magnetic catalysis and anisotropic confinement in QCD

V. A. Miransky^*

I. A. Shovkovy^*

Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada N6A 5B7

School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455

^*On leave of absence from Bogolyubov Institute for Theoretical Physics, 252143, Kiev, Ukraine.

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Phys. Rev. D 66, 045006 – Published 15 August, 2002

DOI: https://doi.org/10.1103/PhysRevD.66.045006

Abstract

The expressions for dynamical masses of quarks in the chiral limit in QCD in a strong magnetic field are obtained. A low energy effective action for the corresponding Nambu-Goldstone bosons is derived and the values of their decay constants as well as the velocities are calculated. The existence of a threshold value of the number of colors $N_{c}^{thr},$ dividing the theories with essentially different dynamics, is established. For the number of colors $N_{c} ≪ N_{c}^{thr},$ an anisotropic dynamics of confinement with the confinement scale much less than $Λ_{QCD}$ and a rich spectrum of light glueballs is realized. For $N_{c}$ of order $N_{c}^{thr}$ or larger, a conventional confinement dynamics takes place. It is found that the threshold value $N_{c}^{thr}$ grows rapidly with the magnetic field $[N_{c}^{thr} ≳ 100$ for $| eB | ≳ (1 GeV)^{2}] .$ In contrast with QCD with a nonzero baryon density, there are no principal obstacles for examining these results and predictions in lattice computer simulations.

References (27)

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The fact that the pairing dynamics responsible for generating rather light quark masses (of order $Λ_{QCD}$ or less) decouples from the confinement dynamics may seem to be puzzling. As it will be shown in Sec. IV, the confinement scale $λ_{QCD}$ in QCD in a strong magnetic field is much less than $Λ_{QCD},$ i.e., the quark masses are large if expressed in units of the new confinement scale. This point implies that the pairing dynamics is indeed weakly coupled.
V.A. Miransky, Dynamical Symmetry Breaking in Quantum Field Theories (World Scientific, Singapore, 1993).
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V.A. Miransky, I.A. Shovkovy, and L.C.R. Wijewardhana, Phys. Rev. D 62, 085025 (2000); ibid.63, 056005 (2001).
D.T. Son and M.A. Stephanov, Phys. Rev. D 61, 074012 (2000); ibid.62, 059902(E) (2000); S.R. Beane, P.F. Bedaque, and M.J. Savage, Phys. Lett. B 483, 131 (2000); K. Zarembo, Phys. Rev. D 62, 054003 (2000).
M.G. Alford, K. Rajagopal, and F. Wilczek, Nucl. Phys. B537, 443 (1999).
D.H. Rischke, D.T. Son, and M.A. Stephanov, Phys. Rev. Lett. 87, 062001 (2001).

[c1] D.J. Gross, R.D. Pisarski, and L.G. Yaffe, Rev. Mod. Phys. 53, 43 (1981).

[c2] K. Rajagopal and F. Wilczek, in At the Frontier of Particle Physics, edited by M. Shifman (World Scientific, Singapore, 2002), Vol. 3, pp. 2061–2151.

[c3] S. Kawati, G. Konisi, and H. Miyata, Phys. Rev. D 28, 1537 (1983); ibid.S.P. Klevansky and R.H. Lemmer, 39, 3478 (1989); H. Suganuma and T. Tatsumi, Ann. Phys. (N.Y.) 208, 470 (1991).

[c4] S. Schramm, B. Muller, and A.J. Schramm, Mod. Phys. Lett. A 7, 973 (1992).

[c5] V.P. Gusynin, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. Lett. 73, 3499 (1994); Phys. Rev. D 52, 4718 (1995).

[c6] V.P. Gusynin, V.A. Miransky, and I.A. Shovkovy, Phys. Lett. B 349, 477 (1995).

[c7] K. Farakos, G. Koutsoumbas, and N.E. Mavromatos, Int. J. Mod. Phys. B 12, 2475 (1998); G.W. Semenoff, I.A. Shovkovy, and L.C.R. Wijewardhana, Mod. Phys. Lett. A 13, 1143 (1998); W.V. Liu, Nucl. Phys. B556, 563 (1999); E.J. Ferrer, V.P. Gusynin, and V. de la Incera, Mod. Phys. Lett. B 16, 107 (2002); cond-mat/0203217.

[c8] D.V. Khveshchenko, Phys. Rev. Lett. 87, 206401 (2001); E.V. Gorbar, V.P. Gusynin, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. B 66, 045108 (2002).

[c9] V.A. Miransky, Prog. Theor. Phys. Suppl. 123, 49 (1996); Y.J. Ng, hep-th/9803074; C.N. Leung, hep-th/9806208; V.P. Gusynin, Ukr. Phys. J. 45, 603 (2000).

[c10] V.P. Gusynin, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. D 52, 4747 (1995); Nucl. Phys. B462, 249 (1996).

[c11] V.P. Gusynin, V.A. Miransky, and I.A. Shovkovy, Phys. Rev. Lett. 83, 1291 (1999); Nucl. Phys. B563, 361 (1999).

[c12] C.N. Leung, Y.J. Ng, and A.W. Ackley, Phys. Rev. D 54, 4181 (1996); ibid.D.S. Lee, C.N. Leung, and Y.J. Ng, 55, 6504 (1997); ibid.57, 5224 (1998).

[c13] D.K. Hong, Y. Kim, and S.J. Sin, Phys. Rev. D 54, 7879 (1996).

[c14] V.P. Gusynin and A.V. Smilga, Phys. Lett. B 450, 267 (1999).

[c15] J. Alexandre, K. Farakos, and G. Koutsoumbas, Phys. Rev. D 64, 067702 (2001).

[c16] I.A. Shushpanov and A.V. Smilga, Phys. Lett. B 402, 351 (1997); ibid.N.O. Agasian and I.A. Shushpanov, 472, 143 (2000).

[c17] V.C. Zhukovsky, V.V. Khudyakov, K.G. Klimenko, and D. Ebert, Pis’ma Zh. Éksp. Teor. Fiz. 74, 595 (2001) [JETP Lett. 74, 523 (2001)]; D. Ebert, V.V. Khudyakov, V.C. Zhukovsky, and K.G. Klimenko, Phys. Rev. D 65, 054024 (2002).

[c18] D. Kabat, K. Lee, and E. Weinberg, Phys. Rev. D 66, 014004 (2002).

[c19] J. Schwinger, Phys. Rev. 125, 397 (1962); S.R. Coleman, R. Jackiw, and L. Susskind, Ann. Phys. (N.Y.) 93, 267 (1975); ibid.S.R. Coleman, 101, 239 (1976).

[c20] D.T. Son, Phys. Rev. D 59, 094019 (1999); ibid.T. Schafer and F. Wilczek, 60, 114033 (1999); ibid.D.K. Hong, V.A. Miransky, I.A. Shovkovy, and L.C. Wijewardhana, 61, 056001 (2000); ibid.R.D. Pisarski and D.H. Rischke, 61, 051501(R) (2000).

[c21] The fact that the pairing dynamics responsible for generating rather light quark masses (of order $Λ_{QCD}$ or less) decouples from the confinement dynamics may seem to be puzzling. As it will be shown in Sec. IV, the confinement scale $λ_{QCD}$ in QCD in a strong magnetic field is much less than $Λ_{QCD},$ i.e., the quark masses are large if expressed in units of the new confinement scale. This point implies that the pairing dynamics is indeed weakly coupled.

[c22] V.A. Miransky, Dynamical Symmetry Breaking in Quantum Field Theories (World Scientific, Singapore, 1993).

[c23] H. Pagels and S. Stokar, Phys. Rev. D 20, 2947 (1979).

[c24] V.A. Miransky, I.A. Shovkovy, and L.C.R. Wijewardhana, Phys. Rev. D 62, 085025 (2000); ibid.63, 056005 (2001).

[c25] D.T. Son and M.A. Stephanov, Phys. Rev. D 61, 074012 (2000); ibid.62, 059902(E) (2000); S.R. Beane, P.F. Bedaque, and M.J. Savage, Phys. Lett. B 483, 131 (2000); K. Zarembo, Phys. Rev. D 62, 054003 (2000).

[c26] M.G. Alford, K. Rajagopal, and F. Wilczek, Nucl. Phys. B537, 443 (1999).

[c27] D.H. Rischke, D.T. Son, and M.A. Stephanov, Phys. Rev. Lett. 87, 062001 (2001).

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