The amplitude for multiple soft gluon emissions, ordered in their relative softness, can be written as a product of infrared (IR) divergent loop-expanded soft gluon currents and the matrix elements. In a more recent work, Angeles-Martinez, Forshaw and Seymour \cite{Angeles-Martinez:2016dph} (AMFS) showed that the result for this amplitude can in fact be re-expressed in an ordered evolution approach, involving \textit{IR finite} one-loop insertions where the virtual loop momentum is constrained in a highly non-trivial way by the $k_T$ of the adjacent real emissions. The result thus exhibits a novel amplitude level QCD coherence where the IR divergences originating only from the very last, softest, gluon emission remain, and the rest cancel. The proof of the AMFS result at one-loop in QCD, however, involves many diagrams, and only after carefully grouping and summing over all the diagrams does the correct ordering variable emerge, making the higher order extension a challenging task. Moreover, the compact, Markovian nature of the final AMFS result is suggestive of a deeper underlying physics that is obscured in the derivation using traditional diagrammatic QCD. By considering a (recursive) sequence of effective field theories (EFTs) with Glauber-SCET operators, we present an elegant derivation of this result involving only a handful of diagrams. The SCET derivation offers clean physical insights, and makes a higher order extension of the AMFS result tractable. We also show that the grouping of QCD graphs necessary to derive the AMFS result in full theory is already implicit in the Feynman rules of Glauber-SCET operators such that the same result can alternatively be derived with significantly less effort in a single EFT with multiple ordered soft gluon emissions.
Glauber Gluon Effects in Soft Collinear Factorization
在软共线有效理论（SCET）框架下，研究了Glauber胶子效应对不同喷注间弹性散射过程的影响。在积分前将Glauber模加入到拉格朗日量中，这有助于明确地研究共线粒子和软粒子的Glauber耦合。证明了硬碰撞后的相互作用在足够包容的过程中相互抵消。与光锥坐标Sx^{+} $ and $ x^{-}$的相互作用也大于硬碰撞的相互作用。讨论了活性粒子Glauber耦合的Eikonalization以及活性-活性、活性-软和活性-旁观Glauber交换被共线软Wilson线吸收的问题，这与Glauber胶子的圈能级定义有关。在观众-观众和观众-软性Glauber交流的包容性总和上，主动-观众连贯被证明是无害的。基于这一结果，观众观众和观众软芒硝交换被证明在这里考虑的过程中抵消。为了解释在微扰QCD框架下Glauber胶子的图形相消与算符水平技巧之间的关系，本文还讨论了这种相消的图形方面。
Institut für Theoretische Physik & AEC, Universität Bern（伯尔尼大学理论物理研究所与AEC）；CERN, Theoretical Physics Department（欧洲核子研究中心理论物理部）；PRISMA ++ Cluster of Excellence & MITP, Johannes Gutenberg University（约翰内斯·古腾堡大学PRISMA++卓越集群与MITP）；Department of Physics, LEPP, Cornell University（康奈尔大学LEPP物理系）
