Abstract / Description of output
We compute a class of diagrams contributing to the multi-leg soft anomalous dimension through three loops, by renormalizing a product of semi-infinite non-lightlike Wilson lines in dimensional regularization. Using non-Abelian exponentiation we directly compute contributions to the exponent in terms of webs. We develop a general strategy to compute webs with multiple gluon exchanges between Wilson lines in configuration space, and explore their analytic structure in terms of $\alpha_{ij}$, the exponential of the Minkowski cusp angle formed between the lines $i$ and $j$. We show that beyond the obvious inversion symmetry $\alpha_{ij}\to 1/\alpha_{ij}$, at the level of the Symbol the result also admits a crossing symmetry $\alpha_{ij}\to -\alpha_{ij}$, relating spacelike and timelike kinematics, and hence argue that in this class of webs the Symbol alphabet is restricted to $\alpha_{ij}$ and $1-\alpha_{ij}^2$. We carry out the calculation up to three gluons connecting four Wilson lines, finding that the contributions to the soft anomalous dimension are remarkably simple: they involve pure functions of uniform weight, which are written as a sum of products of polylogarithms, each depending on a single cusp angle. We conjecture that this type of factorization extends to all multiple-gluon-exchange contributions to the anomalous dimension.
Original language | English |
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Article number | 44 |
Journal | Journal of High Energy Physics |
Volume | 14 |
Issue number | 04 |
DOIs | |
Publication status | Published - 7 Apr 2014 |
Keywords / Materials (for Non-textual outputs)
- hep-ph
- hep-th