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The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange

Description: The resummation of soft gluon exchange for QCD hard scattering requires a matrix of anomalous dimensions. We compute this matrix directly for arbitrary 2 {yields} 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 {yields} 2 amplitudes in the literature, and it predicts all poles at next-to-leading order in any 2 {yields} 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 {yields} n processes.
Date: June 27, 2006
Creator: Aybat, S.Mert; Dixon, Lance J. & Sterman, George
Partner: UNT Libraries Government Documents Department

Factorization and resummation for collinear poles in QCD amplitudes

Description: We study the origin of subleading soft and collinear poles of form factors and amplitudes in dimensionally-regulated massless gauge theories. In the case of form factors of fundamental fields, these poles originate from a single function of the coupling, denoted G({alpha}{sub s}), depending on both the spin and gauge quantum numbers of the field. We relate G({alpha}{sub s}) to gauge-theory matrix elements involving the gluon field strength. We then show that G({alpha}{sub s}) is the sum of three terms: a universal eikonal anomalous dimension, a universal non-eikonal contribution, given by the coefficient B{sub {delta}}({alpha}{sub s}) of {delta}(1-z) in the collinear evolution kernel, and a process-dependent short-distance coefficient function, which does not contribute to infrared poles. Using general results on the factorization of soft and collinear singularities in fixed-angle massless gauge theory amplitudes, we conclude that all such singularities are captured by the eikonal approximation, supplemented only by the knowledge of B{sub {delta}}({alpha}{sub s}). We explore the consequences of our results for conformal gauge theories, where in particular we find a simple exact relation between the form factor and the cusp anomalous dimension.
Date: May 28, 2008
Creator: Dixon, Lance J.; Magnea, Lorenzo & Sterman, George
Partner: UNT Libraries Government Documents Department

The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole

Description: We extend the resummation of dimensionally-regulated amplitudes to next-to-next-to-leading poles. This requires the calculation of two-loop anomalous dimension matrices for color mixing through soft gluon exchange. Remarkably, we find that they are proportional to the corresponding one-loop matrices. Using the color generator notation, we reproduce the two-loop single-pole quantities H{sup (2)} introduced by Catani for quark and gluon elastic scattering. Our results also make possible threshold and a variety of other resummations at next-to-next-to leading logarithm. All of these considerations apply to 2 {yields} n processes with massless external lines.
Date: September 8, 2006
Creator: Mert Aybat, S.; /SUNY, Stony Brook; Dixon, Lance J.; /SLAC; Sterman, George & /SUNY, Stony Brook
Partner: UNT Libraries Government Documents Department