Dilepton production rate in a hot and magnetized quark-gluon plasma

Abstract

The differential multiplicity of dileptons in a hot and magnetized quark-gluon plasma, ${\Delta }_B\equiv d{N}_B/d^{4}x{d}^{4}q$, 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, $\mbox{Im}[Π^{μν}]$, which is derived in a first order perturbative approximation. As expected, the final analytical expression for ${\Delta }_B$ includes a trace over the product of a photonic part, $\mbox{Im}[Π^{μν}]$, and a leptonic part, ${\mathcal{L}}_{\mu \nu }$. It is shown that ${\Delta }_B$ consists of two parts, ${\Delta }_B^{\Vert }$ and ${\Delta }_B^{\perp }$, arising from the components $(\mu ,\nu )=(\Vert ,\Vert )$ and $(\mu ,\nu )=(\perp ,\perp )$ of $\mbox{Im}[Π^{μν}]$ and ${\mathcal{L}}_{\mu \nu }$. Here, the transverse and longitudinal directions are defined with respect to the direction of the $B$ field. Combining ${\Delta }_B^{\Vert }$ and ${\Delta }_B^{\perp }$, a novel anisotropy factor ${\nu }_B$ is introduced. Using the final analytical expression of ${\Delta }_B$, the possible interplay between the temperature $T$ and the magnetic field strength $eB$ on the ratio ${\Delta }_B/{\Delta }_0$ and ${\nu }_B$ is numerically studied. Here, ${\Delta }_0$ 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, ${\Delta }_B\gg {\Delta }_0$ and ${\Delta }_B^{\perp }\gg {\Delta }_B^{\Vert }$. 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.

V1: 24 pages (two-column), 11 figures, 1 table; V2: 44 pages (one-column), 12 figures, 2 tables. Typos corrected, discussions improved, references updated, appendix B added; V3: 41 pages (one-column), 12 figures, 2 tables, discussions improved. Version accepted for publication in AOP (2017)

References in corpus (15)

• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• The QCD equation of state in background magnetic fields
• Heavy Quark Diffusion in Strong Magnetic Fields at Weak Coupling and Implications for Elliptic Flow
• Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization
• Electromagnetic radiation by quark-gluon plasma in magnetic field
• Electromagnetic spectral properties and Debye screening of a strongly magnetized hot medium
• Thermal Dileptons from Coarse-Grained Transport as Fireball Probes at SIS Energies
• Magnetic-field Induced Screening Effect and Collective Excitations
• The Magneto-Sono-Luminescence and its signatures in photon and dilepton production in heavy ion collisions
• Pair creation by a photon in a strong magnetic field
• Photon and dilepton production at the Facility for Antiproton and Ion Research and the beam energy scan program at the Relativistic Heavy-Ion Collider using coarse-grained microscopic transport simulations
• Low Mass Dilepton Rate from the Deconfined Phase
• Zeta Function Regularization of Photon Polarization Tensor for a Magnetized Vacuum
• Thermal photon production from gluon fusion induced by magnetic fields in relativistic heavy-ion collisions
• Recent developments in the theory of electromagnetic probes in relativistic heavy-ion collisions

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