论文标题

半Quark-gluon等离子体中的实时硬圈gluon自我能源

Real-time hard-thermal-loop gluon self-energy in a semiquark-gluon plasma

论文作者

Wang, Yubiao, Du, Qianqian, Guo, Yun

论文摘要

在有限温度野外理论的实时形式主义中,我们计算了半夸克 - 格鲁恩等离子体(QGP)中的单环gluon自能源,在该血浆中,在该背景中引入了$ {\ cal q} $的矢量潜力$ {\ cal q} $,从而导致对polyakov earper的非主导期望值。在硬热环近似中,GLUON自我强度的明确结果至次临近领先顺序。我们发现,对于智障/高级的gluon自我能源,近代领先顺序的相应贡献与$ {\ cal q} = 0 $的众所周知的结果正式类似,其中Debye质量上的背景字段修改完全由第二个Bernoulli Polynomials编码。在对称的Gluon自能源中,主要的阶贡献共享相同的特征,在对称的Gluon自能源中,背景场的修饰变得更加复杂,包括三角函数和Bernoulli多项式。这些贡献是非逐渐播放的,并将正确的限制重现为$ {\ cal q} \ rightarrow 0 $。此外,对智障/高级Gluon自我能源的领先命令贡献以及对对称Gluon自我能源的临时订单贡献是全新的,因为它们仅在$ {\ cal Q} \ neq0 $中生存。鉴于上述结果,我们明确验证了在具有非零背景字段的半QGP中可以满足Kubo-Martin-Schinginger条件。

In the real time formalism of the finite-temperature field theory, we compute the one-loop gluon self-energy in a semi-quark-gluon plasma (QGP) where a background filed ${\cal Q}$ has been introduced for the vector potential, leading to a non-trivial expectation value for the Polyakov loop in the deconfined phase. Explicit results of the gluon self-energies up to the next-to-leading order in the hard-thermal-loop approximation are obtained. We find that for the retarded/advanced gluon self-energy, the corresponding contributions at next-to-leading order are formally analogous to the well-known result at ${\cal Q}=0$ where the background field modification on the Debye mass is entirely encoded in the second Bernoulli polynomials. The same feature is shared by the leading order contributions in the symmetric gluon self-energy where the background field modification becomes more complicated, including both trigonometric functions and the Bernoulli polynomials. These contributions are non-vanishing and reproduce the correct limit as ${\cal Q} \rightarrow 0$. In addition, the leading order contributions to the retarded/advanced gluon self-energy and the next-to-leading order contributions to the symmetric gluon self-energy are completely new as they only survive at ${\cal Q}\neq0$. Given the above results, we explicitly verify that the Kubo-Martin-Schwinger condition can be satisfied in a semi-QGP with non-zero background field.

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