Extracting the asymptotic behavior of S-matrix elements from their phases
The asymptotic kinematic limits of S-matrices are dominated by large logarithms which, roughly speaking, fall into two categories: those which are controlled by a renormalization group (RG) scale, which we may think of as logs involving ratios of invariant mass scales, and those which are functions of ratios of rapidities, so called “rapidity logs”. It has been pointed out by Caron-Huot and Wilhlem [1] that RG anomalous dimension can be extracted from the phase of the S-matrix, which can greatly simplify calculations via unitarity methods. In this paper we generalize the results of [1] to show that the phase can be used to reconstruct rapidity anomalous dimensions, by performing a special type of complex boost. The methodology introduced allows one to calculate without the need for a rapidity regulator which can lead to significant simplifications. We demonstrate the use of this method to derive the rapidity anomalous dimensions in the Sudakov form factor and the two parton soft function at two loops order.
- Research Organization:
- Carnegie Mellon University, Pittsburgh, PA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- Grant/Contract Number:
- SC0010118; SC0013528
- OSTI ID:
- 2483472
- Journal Information:
- Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 11 Vol. 2024; ISSN 1029-8479
- Publisher:
- Springer NatureCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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