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

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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.

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Mert Aybat, S.; /SUNY, Stony Brook; Dixon, Lance J.; /SLAC; Sterman, George & /SUNY, Stony Brook September 8, 2006.

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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.

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Medium: X; Size: 52 pages

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  • Journal Name: Physical Review D

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  • Report No.: SLAC-PUB-11969
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 891244
  • Archival Resource Key: ark:/67531/metadc884351

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  • September 8, 2006

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  • Sept. 21, 2016, 2:29 a.m.

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  • Dec. 2, 2016, 4:22 p.m.

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Mert Aybat, S.; /SUNY, Stony Brook; Dixon, Lance J.; /SLAC; Sterman, George & /SUNY, Stony Brook. The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole, article, September 8, 2006; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc884351/: accessed August 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.