Vladimirov Alexey A
Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany.
Phys Rev Lett. 2017 Feb 10;118(6):062001. doi: 10.1103/PhysRevLett.118.062001. Epub 2017 Feb 8.
We establish a correspondence between ultraviolet singularities of soft factors for multiparticle production and rapidity singularities of soft factors for multiparton scattering. This correspondence is a consequence of the conformal mapping between scattering geometries. The correspondence is valid to all orders of perturbation theory and in this way, provides one with a proof of rapidity renormalization procedure for multiparton scattering [including the transverse momentum dependent (TMD) factorization as a special case]. As a by-product, we obtain an exact relation between the rapidity anomalous dimension and the well-known soft anomalous dimension. The three-loop expressions for TMD and a general multiparton scattering rapidity anomalous dimension are derived.
我们建立了多粒子产生软因子的紫外奇点与多部分子散射软因子的快度奇点之间的对应关系。这种对应关系是散射几何之间共形映射的结果。该对应关系在微扰理论的所有阶数下均有效，并且以此方式为多部分子散射的快度重整化程序（包括作为特殊情况的横向动量依赖（TMD）因子分解）提供了一种证明。作为一个副产品，我们得到了快度反常维度与著名的软反常维度之间的精确关系。推导了TMD的三圈表达式以及一般多部分子散射快度反常维度的表达式。
