Polarization tensor of magnetized quark-gluon plasma at nonzero baryon density
Xinyang Wang, I. A. Shovkovy
Abstract
Abstract We derive a general expression for the absorptive part of the one-loop photon polarization tensor in a strongly magnetized quark-gluon plasma at nonzero baryon chemical potential. To demonstrate the application of the main result in the context of heavy-ion collisions, we study the effect of a nonzero baryon chemical potential on the photon emission rate. The rate and the ellipticity of photon emission are studied numerically as a function the transverse momentum (energy) for several values of temperature and chemical potential. When the chemical potential is small compared to the temperature, the rates of the quark and antiquark splitting processes (i.e., $$q\rightarrow q +\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>→</mml:mo> <mml:mi>q</mml:mi> <mml:mo>+</mml:mo> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> and $${\bar{q}}\rightarrow {\bar{q}} +\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>→</mml:mo> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>+</mml:mo> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> , respectively) are approximately the same. However, the quark splitting gradually becomes the dominant process with increasing the chemical potential. We also find that increasing the chemical potential leads to a growing total photon production rate but has only a small effect on the ellipticity of photon emission. The quark-antiquark annihilation ( $$q+{\bar{q}}\rightarrow \gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>+</mml:mo> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>→</mml:mo> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> ) also contributes to the photon production, but its contribution remains relatively small for a wide range of temperatures and chemical potentials investigated.