Magnetized effective QCD phase diagram

The QCD phase diagram in the temperature vs quark chemical potential plane is studied in the presence of a magnetic field, using the linear sigma model coupled to quarks. It is shown that the decrease of the couplings with increasing field strength obtained in this model leads to the critical temperature for the phase transition to decrease with increasing field intensity (inverse magnetic catalysis). This happens provided that plasma screening is properly accounted for. It is also found that with increasing field strength the location of the critical end point in the phase diagram moves toward lower values of the critical quark chemical potential and larger values of the critical temperature. In addition, the critical end point approaches the temperature axis for large values of the magnetic field. We argue that a similar behavior is to be expected in QCD, since the physical impact of the magnetic field, regardless of strength, is to produce a spatial dimension reduction, whereby virtual quark-antiquark pairs are closer on average and thus the strength of their interaction decreases due to asymptotic freedom.

Figure 1

One-loop Feynman diagrams that contribute to the thermal and magnetic correction to the coupling $\lambda$. The dashed line denotes the charged pion, the continuous line is the sigma, and the double line represents the neutral pion. Columns (a),(b),(c),(d),(e) and (f) contribute, respectively, to the correction to ${\sigma }^4$, $({\pi }^0{)}^4$, $({\pi }^{+}{)}^2({\pi }^{-}{)}^2$, ${\sigma }^2{\pi }^{+}{\pi }^{-}$, $({\pi }^0{)}^2{\pi }^{+}{\pi }^{-}$ and ${\sigma }^2({\pi }^0{)}^2$ terms of the interaction Lagrangian, respectively.

Figure 2

One-loop Feynman diagrams that contribute to the thermal and magnetic correction to the coupling $g$. The dashed line denotes the charged pion, the continuous line is the sigma, the double line represents the neutral pion, and the continuous line with arrows represents the quarks. Columns (a),(b) and (c) contribute to the correction to the quark-$\sigma$, quark-${\pi }^0$ and quark-${\pi }^{\pm }$ terms of the interaction Lagrangian, respectively.

Figure 3

Effective boson coupling ${\lambda }_{\mathrm{eff}}$ evaluated at the temperature $T=180\mathrm{MeV}$ with $\lambda =0.4$, $g=0.63$ as a function of the magnetic field strength for different values of $\mu$.

Figure 4

Effective boson-fermion coupling $g_{\mathrm{eff}}$ evaluated at the temperature $T=180\mathrm{MeV}$ with $\lambda =0.4$, $g=0.63$ as a function of the magnetic field strength for different values of $\mu$.

Figure 5

Critical temperature as a function of the magnetic field strength evaluated using effective couplings including thermo-magnetic corrections with the bare values of the couplings $\lambda =0.4$, $g=0.63$ for different values of $\mu$. Note that in all cases the critical temperature is a monotonically decreasing function of the magnetic field strength.

Figure 6

Critical temperature as a function of the magnetic field strength evaluated without effective couplings and instead with the bare values of the couplings $\lambda =0.4$, $g=0.63$ for different values of $\mu$. Note that in all cases the critical temperature is a monotonically increasing function of the magnetic field strength.

Figure 7

Critical temperature as a function of the magnetic field strength evaluated keeping $\lambda =0.4$ fixed and with the full magnetic field and temperature-dependence of the quark-meson coupling computed with $g=0.63$, for different values of $\mu$.

Figure 8

Critical temperature as a function of the magnetic field strength evaluated keeping $g=0.63$ fixed and with the full magnetic field and temperature dependence of the meson self-coupling computed with $\lambda =0.63$, for different values of $\mu$.

Figure 9

Phase diagram in the temperature quark chemical potential plane computed with thermo-magnetic corrections to the couplings using the bare values $\lambda =0.4$, $g=0.63$ corresponding to $a/T_c^0=0.77$ for different values of the magnetic field strength. The phase transitions to the left (right) of the CEP in each case are of second (first) order.

Figure 10

Phase diagram in the temperature quark chemical potential plane computed with thermo-magnetic corrections to the couplings using the bare values $\lambda =0.36$, $g=0.51$ corresponding to $a/T_c^0=0.66$ for different values of the magnetic field strength. The phase transitions to the left (right) of the CEP in each case are of second (first) order.

Figure 11

Diagrams contributing to the calculation of the fermion thermal mass.