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2009

The Massive Soft Anomalous Dimension Matrix at Two Loops

Mitov, Alexander, Sterman, George, Sung, Ilmo

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We study two-loop anomalous dimension matrices in QCD and related gauge theories for products of Wilson lines coupled at a point.

We verify by an analysis in Euclidean space that the contributions to these matrices from diagrams that link three massive Wilson lines do not vanish in general.
We show, however, that for two-to-two processes the two-loop anomalous dimension matrix is diagonal in the same color-exchange basis as the one-loop matrix for arbitrary masses at absolute threshold and for scattering at ninety degrees in the center of mass.
This result is important for applications of threshold resummation in heavy quark production.

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This observation has also been made by E. Gardi, using a similar representation in x x -space. We thank E. Gardi for this private communication
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Then

S. Mert Aybat, L. J. Dixon and G. Sterman, Phys. Rev. Lett. 97
2006
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A. Mitov and S. Moch, JHEP 0705
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2007
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R. Bonciani, S. Catani, M. L. Mangano and P. Nason, Nucl. Phys. B 529
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We observe that the relations s = − t s=-t or s = − u s=-u do not correspond to equal invariants in the sense above

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