QCD phase diagram in the presence of electric and magnetic fields


  • Aftab Ahmad Institute of Physics,Gomal University




Schwinger Dysons Eqautions; chiral symmetry breaking; confinement; electric and magnetic fields; QCD phase diagram


In this contribution, We revisit the effect of electric eE and magnetic field eB and on the critical temperature T χ,C c of the chiral symmetry breaking/restoration and confinement/deconfinement phase transition in the QCD Phase diagram. In this context, we use the symmetrypreserving vector-vector contact interaction model of quarks, in the Schwinger-Dyson equations framework and in the proper time regularization scheme. We also describe the phenomenon of inverse electric catalysis in the pure electric case, magnetic catalysis (and inverse magnetic catalysis) in the pure magnetic case and inverse electromagnetic catalysis in the presence of both electric and magnetic background fields.


S. P. Klevansky and R. H. Lemmer, Chiral symmetry breaking at finite temperatures, Phys. Rev. D 38 (1988) 3559, https://doi.org/10.1103/PhysRevD.38.3559

H. Suganuma and T. Tatsumi, On the Behavior of Symmetry and Phase Transitions in a Strong Electromagnetic Field, Annals Phys. 208 (1991) 470, https://doi.org/10.1016/0003-4916(91)90304-Q

K. G. Klimenko, Three-dimensional Gross-Neveu model in an external magnetic field, Theor. Math. Phys. 89 (1992) 1161, https://doi.org/10.1007/BF01015908

S. P. Klevansky, The Nambu-Jona-Lasinio model of quantum chromodynamics, Rev. Mod. Phys. 64 (1992) 649, https://doi.org/10.1103/RevModPhys.64.649

I. V. Krive and S. A. Naftulin, Dynamical symmetry breaking and phase transitions in a three-dimensional Gross-Neveu model in a strong magnetic field, Phys. Rev. D 46 (1992) 2737, https://doi.org/10.1103/PhysRevD.46.2737

V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Catalysis of dynamical flavor symmetry breaking by a magnetic field in (2+1)-dimensions, Phys. Rev. Lett. 73 (1994) 3499, https://doi.org/10.1103/PhysRevLett.76.1005, https://doi.org/10.1103/PhysRevLett.73.3499

V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Dynamical flavor symmetry breaking by a magnetic field in (2+1)- dimensions, Phys. Rev. D 52 (1995) 4718, https://doi.org/10.1103/PhysRevD.52.4718

V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Dimensional reduction and dynamical chiral symmetry breaking by a magnetic field in (3+1)-dimensions, Phys. Lett. B 349 (1995) 477, https://doi.org/10.1016/0370-2693(95)00232-A

K. G. Klimenko, Three-dimensional Gross-Neveu model at nonzero temperature and in an external magnetic field, Theor. Math. Phys. 90 (1992) 1, https://doi.org/10.1007/BF01018812

G. S. Bali et al., The finite temperature QCD transition in external magnetic fields, PoS LATTICE 2011 (2011) 192, https://doi.org/10.22323/1.139.0192

G. S. Bali et al., Magnetic field-induced gluonic (inverse) catalysis and pressure (an)isotropy in QCD, JHEP 04 (2013) 130, https://doi.org/10.1007/JHEP04(2013)130

G. Endrodi et al., Magnetic catalysis and inverse catalysis for heavy pions, JHEP 07 (2019) 007, https://doi.org/10.1007/JHEP07(2019)007

R. L. S. Farias et al., Importance of asymptotic freedom for the pseudocritical temperature in magnetized quark matter, Phys. Rev. C 90 (2014) 025203, https://doi.org/10.1103/PhysRevC.90.025203

P. Costa et al., Influence of the inverse magnetic catalysis and the vector interaction in the location of the critical end point, Phys. Rev. D 92 (2015) 036012, https://doi.org/10.1103/PhysRevD.92.036012

E. J. Ferrer, V. de la Incera, and X. J. Wen, Quark Antiscreening at Strong Magnetic Field and Inverse Magnetic Catalysis, Phys. Rev. D 91 (2015) 054006, https://doi.org/10.1103/PhysRevD.91.054006

A. Ayala et al., Inverse magnetic catalysis from the properties of the QCD coupling in a magnetic field, Phys. Lett. B 759 (2016) 99, https://doi.org/10.1016/j.physletb.2016.05.058

A. Ahmad and A. Raya, Inverse magnetic catalysis and confinement within a contact interaction model for quarks, J. Phys. G 43 (2016) 065002, https://doi.org/10.1088/0954-3899/43/6/065002

A. Ahmad, Chiral symmetry restoration and deconfinement in the contact interaction model of quarks with parallel electric and magnetic fields, Chin. Phys. C 45 (2021) 073109, https://doi.org/10.1088/1674-1137/abfb5f

A. Ahmad et al., Flavor, temperature and magnetic field dependence of the QCD phase diagram: magnetic catalysis and its inverse, J. Phys. G 48 (2021) 075002, https://doi.org/10.1088/1361-6471/abd88f

G. Cao and X.-G. Huang, Chiral phase transition and Schwinger mechanism in a pure electric field, Phys. Rev. D 93 (2016) 016007, https://doi.org/10.1103/PhysRevD.93.016007

W. R. Tavares and S. S. Avancini, Schwinger mechanism in the SU(3) Nambu-Jona-Lasinio model with an electric field, Phys. Rev. D 97 (2018) 094001, https://doi.org/10.1103/PhysRevD.97.094001

M. Ruggieri and G. X. Peng, Quark matter in a parallel electric and magnetic field background: Chiral phase transition and equilibration of chiral density, Phys. Rev. D 93 (2016) 094021, https://doi.org/10.1103/PhysRevD.93.094021

A. Ahmad and A. Farooq, Schwinger Pair Production in QCD from Flavor-Dependent Contact Interaction Model of Quarks (2023)

L. Wang and G. Cao, Competition between magnetic catalysis effect and chiral rotation effect, Phys. Rev. D 97 (2018) 034014, https://doi.org/10.1103/PhysRevD.97.034014

W. R. Tavares, R. L. S. Farias, and S. S. Avancini, Deconfinement and chiral phase transitions in quark matter with a strong electric field, Phys. Rev. D 101 (2020) 016017, https://doi.org/10.1103/PhysRevD.101.016017

A. Bzdak and V. Skokov, Event-by-event fluctuations of magnetic and electric fields in heavy ion collisions, Phys. Lett. B 710 (2012) 171, https://doi.org/10.1016/j. physletb.2012.02.065

W.-T. Deng and X.-G. Huang, Event-by-event generation of electromagnetic fields in heavy-ion collisions, Phys. Rev. C 85 (2012) 044907, https://doi.org/10.1103/PhysRevC.85.044907

J. Bloczynski et al., Azimuthally fluctuating magnetic field and its impacts on observables in heavy-ion collisions, Phys. Lett. B 718 (2013) 1529, https://doi.org/10.1016/j.physletb.2012.12.030

J. Bloczynski et al., Charge-dependent azimuthal correlations from AuAu to UU collisions, Nucl. Phys. A 939 (2015) 85, https://doi.org/10.1016/j.nuclphysa.2015.03.012

L. Wang et al., Nambu-Jona-Lasinio model in a parallel electromagnetic field, Phys. Lett. B 780 (2018) 273, https://doi.org/10.1016/j.physletb.2018.03.018

G. Cao, Effects of a parallel electromagnetic field in the threeflavor Nambu-Jona-Lasinio model, Phys. Rev. D 101 (2020) 094027, https://doi.org/10.1103/PhysRevD.101.094027

H. L. L. Roberts et al., pi- and rho-mesons, and their diquark partners, from a contact interaction, Phys. Rev. C 83 (2011) 065206, https://doi.org/10.1103/PhysRevC.83. 065206

J. S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664, https://doi.org/10.1103/PhysRev.82.664

L. X. Gutierrez-Guerrero et al., Pion form factor from a contact interaction, Phys. Rev. C 81 (2010) 065202, https://doi.org/10.1103/PhysRevC.81.065202

P. Boucaud et al., The Infrared Behaviour of the Pure YangMills Green Functions, Few Body Syst. 53 (2012) 387, https://doi.org/10.1007/s00601-011-0301-2

A. Ahmad and A. Murad, Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram, Chin. Phys. C 46 (2022) 083109, https://doi.org/10.1088/1674-1137/ac6cd8

C. D. Roberts et al., Aspects of hadron physics, Eur. Phys. J. ST 140 (2007) 53, https://doi.org/10.1140/epjst/e2007-00003-5

J. C. Ward, An Identity in Quantum Electrodynamics, Phys. Rev. 78 (1950) 182, https://doi.org/10.1103/PhysRev.78.182

Y. Takahashi, On the generalized Ward identity, Nuovo Cim. 6 (1957) 371, https://doi.org/10.1007/BF02832514

D. Ebert, T. Feldmann, and H. Reinhardt, Extended NJL model for light and heavy mesons without q - anti-q thresholds, Phys. Lett. B 388 (1996) 154, https://doi.org/10.1016/0370-2693(96)01158-6

F. Marquez et al., The dual quark condensate in local and nonlocal NJL models: an order parameter for deconfinement?, Phys. Lett. B 747 (2015) 529, https://doi.org/10.1016/j.physletb.2015.06.031




How to Cite

Ahmad A. QCD phase diagram in the presence of electric and magnetic fields. Supl. Rev. Mex. Fis. [Internet]. 2023 Sep. 18 [cited 2023 Dec. 10];4(2):021102 1-. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/7027