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A<sc>bstract</sc> We explore the recently derived equation that resums DGLAP corrections to the JIMWLK Hamiltonian in the simplified setting of the SU(2) gauge theory. We solve the equation numerically for the scattering matrix of a dressed gluon for a particular initial condition, that corresponds to a dipole initial state. We evolve theS-matrix of a single dressed gluon from the scaleQP, which is the inverse color correlation length in the projectile toQ≫QPwhich corresponds to the hard resolution scale provided by the target. As expected,Sceases to be unitary if evolved to significant ln$$ {Q}^2/{Q}_P^2 $$ . Our numerical results indicate an interesting universal (independent of the coupling constant) pattern for this deviation from unitarity.
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Reconstructing S-matrix Phases with Machine Learning
A<sc>bstract</sc> An important element of theS-matrix bootstrap program is the relationship between the modulus of anS-matrix element and its phase. Unitarity relates them by an integral equation. Even in the simplest case of elastic scattering, this integral equation cannot be solved analytically and numerical approaches are required. We apply modern machine learning techniques to studying the unitarity constraint. We find that for a given modulus, when a phase exists it can generally be reconstructed to good accuracy with machine learning. Moreover, the loss of the reconstruction algorithm provides a good proxy for whether a given modulus can be consistent with unitarity at all. In addition, we study the question of whether multiple phases can be consistent with a single modulus, finding novel phase-ambiguous solutions. In particular, we find a new phase-ambiguous solution which pushes the known limit on such solutions significantly beyond the previous bound.
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- Award ID(s):
- 2019786
- PAR ID:
- 10555690
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2024
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP05(2024)200
