The differential multiplicity of dileptons in a hot and magnetized quark-gluon plasma, ∆ B ≡ dN B /d 4 xd 4 q, is derived from first principles. The constant magnetic field B is assumed to be aligned in a fixed spatial direction. It is shown that the anisotropy induced by the B field is mainly reflected in the general structure of photon spectral density function. This is related to the imaginary part of the vacuum polarization tensor, Im[Π µν ], which is derived in a first order perturbative approximation. As expected, the final analytical expression for ∆ B includes a trace over the product of a photonic part, Im[Π µν ], and a leptonic part, L µν . It is shown that ∆ B consists of two parts, ∆ B and ∆ ⊥ B , arising from the components (µ, ν) = ( , ) and (µ, ν) = (⊥, ⊥) of Im[Π µν ] and L µν . Here, the transverse and longitudinal directions are defined with respect to the direction of the B field. Combining ∆ B and ∆ ⊥ B , a novel anisotropy factor ν B is introduced. Using the final analytical expression of ∆ B , the possible interplay between the temperature T and the magnetic field strength eB on the ratio ∆ B /∆ 0 and ν B is numerically studied. Here, ∆ 0 is the Born approximated dilepton multiplicity in the absence of external magnetic fields. It is, in particular, shown that for each fixed T and B, in the vicinity of certain threshold energies of virtual photons, ∆ B ≫ ∆ 0 and ∆ ⊥ B ≫ ∆ B . The latter anisotropy may be interpreted as one of the microscopic sources of the macroscopic anisotropies, reflecting themselves, e.g., in the elliptic asymmetry factor v 2 of dileptons. 1 eB = 1 GeV 2 corresponds to B ≃ 1.7 × 10 20 Gauß. 2 See, e.g. [12,13] for a complete analysis of the effect of strong magnetic fields on various phases of quark matters, including chiral and color superconducting phases. See also [14] for the most recent review of the effects induced by magnetic catalysis [15,16] and inverse magnetic catalysis [17] on QCD phase diagram. 3 Studying the effect of hot magnetized plasminos on DPR is rather involved, and will be postponed to our future works.
We argue that in order to study the magneto-transport in a relativistic Weyl fluid, it is needed to take into account the associated quantum corrections, namely the side-jump effect, at least to second order. To this end, we impose Lorentz invariance to a system of free Weyl fermions in the presence of the magnetic field and find the second order correction to the energy dispersion. By developing a scheme to compute the integrals in the phase space, we show that the mentioned correction has non-trivial effects on the thermodynamics of the system. Specifically, we compute the expression of the negative magnetoresistivity in the system from the enthalpy density in equilibrium. Then in analogy with Weyl semimetal, in the framework of the chiral kinetic theory and under the relaxation time approximation, we explicitly compute the magneto-conductivities, at low temperature limit (T ≪ µ). We show that the conductivities obey a set of Ward identities which follow from the generating functional including the Chern-Simons part. * abbasi@ipm.ir † ftaghinavaz@ipm.ir ‡ omid.
The complete quasi-particle spectrum of a magnetized electromagnetic plasma is systematically explored at zero and nonzero temperatures. To this purpose, the general structure of the one-loop corrected propagator of magnetized fermions is determined, and the dispersion relations arising from the pole of this propagator are numerically solved. It turns out that in the lowest Landau level, where only one spin direction is allowed, the spectrum consists of one positively (negatively) charged fermionic mode with positive (negative) spin. In contrast, in higher Landau levels, as an indirect consequence of the double spin degeneracy of fermions, the spectrum consists of two massless collective modes with left-and right-chiralities. The mechanism through which these new collective excitations are created in a uniform magnetic field is similar to the production mechanism of dynamical holes (plasminos) at finite temperature and zero magnetic fields. Whereas cold magnetized plasminos appear for moderate magnetic fields and for all positive momenta of propagating fermions, hot magnetized plasminos appear only in the limit of weak magnetic fields and soft momenta.
We consider a fluid with weakly broken time and translation symmetries. We assume the fluid also possesses a U (1) symmetry which is not only weakly broken, but is anomalous. We use the second order chiral quasi-hydrodynamics to compute the magneto conductivities of this fluid in the presence of a weak magnetic field. Analogous to the electrical and thermoelectric conductivities, it turns out that the thermal conductivity depends on the coefficient of mixed gauge-gravitational anomaly. Our results can be applied to the hydrodynamic regime of every arbitrary system, once the thermodynamics of that system is known. By applying them to a free system of Weyl fermions at low temperature limit T ≪ µ, we find that our fluid is Onsager reciprocal if the relaxation in all energy, momentum and charge channels occurs at the same rate. In the high temperature limit T ≫ µ, we consider a strongly coupled SU (N c ) gauge theory with N c ≫ 1. Its holographic dual in thermal equilibrium is a magnetized charged brane from which, we compute the thermodynamic quantities and subsequently evaluate the conductivities in gauge theory. On the way, we show that analogous to the weak regime in the system of Weyl fermions, an energy cutoff emerges to regulate the thermodynamic quantities in the strong regime of boundary gauge theory. From this gravity background we also find the coefficients of chiral magnetic effect in agreement with the well-known result of Son-Surowka. * abbasi@ipm.ir † armin.ghazi@physics.
In the framework of chiral kinetic theory (CKT), we consider a system of right-and left-handed Weyl fermions out of thermal equilibrium in a homogeneous weak magnetic field. We show that the Lorentz invariance implies a modification in the definition of the momentum current in the phase space, compared to the case in which the system is in global equilibrium. Using this modified momentum current, we derive the linearized conservation equations from the kinetic equation up to second order in the derivative expansion. It turns out that the eigenmodes of these equations, namely the hydrodynamic modes, differ from those obtained from the hydrodynamic in the Landau-Lifshitz (LL) frame at the same order. We show that the modes of the former case may be transformed to the corresponding modes in the latter case by a global boost. The velocity of the boost is proportional to the magnetic field as well as the difference between the right-and left-handed charges susceptibility.We then compute the chiral transport coefficients in a system of non-Abelian chiral fermions in the no-drag frame and by making the above boost, obtain the well-known transport coeffiecients of the system in the LL frame. Finally by using the idea of boost, we reproduce the AdS/CFT result for the chiral drag force exerted on a quark at rest in the rest frame of the fluid, without performing any holographic computations.
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