Two-Loop Anomalous-Dimension Matrix for Soft-Gluon Exchange

Stanford University, Palo Alto, California, United States
Physical Review Letters (Impact Factor: 7.51). 08/2006; 97(7):072001. DOI: 10.1103/PhysRevLett.97.072001
Source: arXiv


The resummation of soft-gluon exchange for QCD hard scattering requires a matrix of anomalous dimensions. We compute this matrix directly for arbitrary 2-->n massless processes for the first time at two loops. Using color-generator notation, we show that it is proportional to the one-loop matrix. This result reproduces all pole terms in dimensional regularization of the explicit calculations of massless 2-->2 amplitudes in the literature, and it predicts all poles at next-to-next-to-leading order in any 2-->n process that has been computed at next-to-leading order. The proportionality of the one- and two-loop matrices makes possible the resummation in closed form of the next-to-next-to-leading logarithms and poles in dimensional regularization for the 2-->n processes.

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    • "One must finally divide each jet by its eikonal counterpart J i , to correct for the fact that soft and collinear divergences have been double-counted. The factorization in Eq. (1.2) leads to exponentiation of soft and collinear factors in terms of a restricted set of anomalous dimensions: color singlet anomalous dimensions are known to three loops, since they can be extracted from the poles of partonic form factors [14] [15]; the soft anomalous dimension matrix, on the other hand, is known at two loops for both massless and massive partons [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]; the development of the necessary techniques to extend these results to the three-loop order and beyond is under way [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39]. The factorization of leading-power infrared enhancements at amplitude level, embodied by Eq. (1.2), ultimately leads to the resummation of LP threshold logarithms for a large class of infrared-safe observables, under mild assumptions concerning the behavior of the associated real radiation [40]. "
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    • "Whilst much is known about the case of two Wilson lines meeting at a cusp [72] [73] [74], the general case of more than two Wilson lines has been studied only recently. The anomalous dimension has been calculated up to two-loop order for both massless [75] [76] and massive [77] [78] [79] particles, where in the former case it was found to have the same colour structure as the one-loop result. This was later explained by constraints on the structure of infrared singularities in massless scattering amplitudes which follow from factorisation and rescalaing symmetry, leading to the formulation of the dipole formula [80] [81] [82]), a minimal all-order ansatz for the anomalous dimension. "
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    ABSTRACT: Journal article
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