Gluon radiation off hard quarks in a nuclear environment: opacity expansion
Gluon radiation off hard quarks in a nuclear environment: opacity expansion
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DOI：
10.1016/s0550-3213(00)00457-0
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发表时间：
2000-05
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影响因子：
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通讯作者：
U. Wiedemann
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作者：
U. Wiedemann
研究了硬夸克介质诱导胶子辐射的Baier-Dokshitzer-Mueller-Peigné-Schiff(BDMPS)和Zakharov公式与极少数散射中心辐射之间的关系。基于空间扩展色场中硬部子运动的非阿贝尔Furry近似，我们导出了k⊥微分胶子辐射截面N阶项在介质不透明度展开时的紧凑图解和显色平凡表达式。将这个量归结到不透明的所有阶，我们得到了扎哈罗夫的路径积分表达式(补充了一个正则化规定)。这为BDMPS形式和Zakharov形式的等价性提供了新的证明，从而将以前的结果推广到k⊥-微分截面。我们给出了自由入射和介质中产生的夸克的胶子辐射截面的三阶不透明度的显式解析结果。辐射截面的不透明度展开式中的N阶项是与N次再散射有关的辐射的卷积，以及在N个散射中心以下发生再散射的概率的重新调整。这两个信息都可以通过从辐射截面中分解出来来解缠，辐射截面项只取决于射弹的平均自由程。这使得可以推导出辐射截面的完全相干和完全非相干极限到不透明度的任意数量级的解析表达式。
We study the relation between the Baier–Dokshitzer–Mueller–Peigné–Schiff (BDMPS) and Zakharov formalisms for medium-induced gluon radiation off hard quarks, and the radiation off very few scattering centers. Based on the non-abelian Furry approximation for the motion of hard partons in a spatially extended colour field, we derive a compact diagrammatic and explicitly colour trivial expression for the N th order term of the k⊥-differential gluon radiation cross section in an expansion in the opacity of the medium. Resumming this quantity to all orders in opacity, we obtain Zakharov's path-integral expression (supplemented with a regularization prescription). This provides a new proof of the equivalence of the BDMPS and Zakharov formalisms which extends previous arguments to the k⊥-differential cross section. We give explicit analytical results up to third order in opacity for both the gluon radiation cross section of free incoming and of in-medium produced quarks. The N th order term in the opacity expansion of the radiation cross section is found to be a convolution of the radiation associated to N -fold rescattering and a readjustment of the probabilities that rescattering occurs with less than N scattering centers. Both informations can be disentangled by factorizing out of the radiation cross section a term which depends only on the mean free path of the projectile. This allows to infer analytical expressions for the totally coherent and totally incoherent limits of the radiation cross section to arbitrary orders in opacity.