The Two-loop soft anomalous dimension matrix and resummation at next-to-next-to leading pole

By S. Aybat, L. Dixon, G. Sterman. 2006

234 citations recorded by the source corpus.

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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/24b9d92103b6438f2b1bbdef85d5981612e2c53d

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In Nuclear and High Energy Physics

1. T. Becher
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Citations in the corpus

• Scattering amplitudes, Wilson loops and the string/gauge theory correspondence (2008, background): “The realization that soft and virtual collinear effects can be factorized in a universal way, together with the fact [41] that the soft radiation can be further factorized from the (harder) collinear one led to a three-factor structure for gauge theory scattering amplitudes [42, 43, 44]:”
• Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis) (2009, background): “e the functions contain no large logarithms, and then evolving them to the scale . This evolution is known analytically [94, 135, 151] and the required anomalous dimensions are already known to NNLL [92, 112, 127, 130, 146, 147], because we have inclusive jet and beam functions. NNLL also requires t”
• Introduction to Soft-Collinear Effective Theory (2014, background): “In a two-loop computation of the anomalous dimension of the soft function, it was observed that higher-order correlations do not appear at this order [82, 83].”
• Conformal properties of four-gluon planar amplitudes and Wilson loops (2007, background): “This anomalous dimension first emerged in the studies of ultraviolet cusp singularities of Wilson loops [11] (see also [12] and references therein) and its relation to infrared asymptotics in gauge theories was discovered in [5, 13, 14].”
• Calculation of the quark and gluon form factors to three loops in QCD (2010, background): “[ 47 , 48] which showed the colour matrix structure of the soft anomalous dimension at two loops is identical to that at one loop.”
• When does the gluon reggeize? (2013, unknown): “[91].”
• Erratum: On the structure of infrared singularities of gauge-theory amplitudes (2009, methodology): “agrees with the findings of [31] and confirms a conjecture for the form of H (2) R.”