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arXiv 1601.04887hep-phnucl-th
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高温磁化夸克-胶子等离子体中的双轻子产生率

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

N. Sadooghi, F. Taghinavaz

备注：
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)
发表信息：
Annals of Physics 376 (2017) 218
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摘要：

从第一性原理出发，导出了热的磁化夸克-胶子等离子体中双轻子的微分多重数$Δ_{B}\equiv dN_{B}/d^{4}xd^{4}q$。假设恒定磁场$B$在固定的空间方向上对齐。结果表明，$B$场引起的各向异性主要反映在光子谱密度函数的一般结构中。这与真空极化张量的虚部$\mbox{Im}[Π^{μν}]$有关，它是在一阶微扰近似下导出的。正如预期的那样，$Δ_{B}$的最终解析表达式包括光子部分$\mbox{Im}[Π^{μν}]$和轻子部分${\cal{L}}_{μν}$的乘积的迹线。结果表明，$Δ_{B}$由两部分组成，$Δ_{B}^{\|}$和$Δ_{B}^{\perp}$，产生的组件$(μ,ν)=(\|,\|)$和$(μ,ν)=(\perp,\perp)$的$\mbox{Im}[Π^{μν}]$和${\cal{L}}_{μν}$。这里，横向和纵向是相对于$B$场的方向定义的。结合$Δ_{B}^{\|}$和$Δ_{B}^{\perp}$，提出了一种新的各向异性因子$ν_{B}$。利用$Δ_{B}$的最终解析表达式，数值研究了温度$T$和磁场强度$eB$之间对比值$Δ_{B}/Δ_{0}$和$ν_{B}$的可能相互作用。在这里，$Δ_{0}$是在没有外部磁场的情况下玻恩近似的双轻子多重数。它是，特别是，示出，对于每个固定的$T$和$B$，在附近的某些阈值能量，$Δ_{B}\gg Δ_{0}$和$Δ_{B}^{\perp}\gg Δ_{B}^{\|}$。后一种各向异性可以解释为宏观各向异性的微观来源之一，反映了它们自身，例如，双轻子的椭圆不对称因子$v_{2}$。

英文摘要：

The differential multiplicity of dileptons in a hot and magnetized quark-gluon plasma, $Δ_{B}\equiv dN_{B}/d^{4}xd^{4}q$, 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, $\mbox{Im}[Π^{μν}]$, which is derived in a first order perturbative approximation. As expected, the final analytical expression for $Δ_{B}$ includes a trace over the product of a photonic part, $\mbox{Im}[Π^{μν}]$, and a leptonic part, ${\cal{L}}_{μν}$. It is shown that $Δ_{B}$ consists of two parts, $Δ_{B}^{\|}$ and $Δ_{B}^{\perp}$, arising from the components $(μ,ν)=(\|,\|)$ and $(μ,ν)=(\perp,\perp)$ of $\mbox{Im}[Π^{μν}]$ and ${\cal{L}}_{μν}$. Here, the transverse and longitudinal directions are defined with respect to the direction of the $B$ field. Combining $Δ_{B}^{\|}$ and $Δ_{B}^{\perp}$, a novel anisotropy factor $ν_{B}$ is introduced. Using the final analytical expression of $Δ_{B}$, the possible interplay between the temperature $T$ and the magnetic field strength $eB$ on the ratio $Δ_{B}/Δ_{0}$ and $ν_{B}$ is numerically studied. Here, $Δ_{0}$ 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, $Δ_{B}\gg Δ_{0}$ and $Δ_{B}^{\perp}\gg Δ_{B}^{\|}$. 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.

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