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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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Not all that is β0 is β-function: the DGLAP resummation and the running coupling in NLO JIMWLK
A<sc>bstract</sc> We reanalyze the origin of the large transverse logarithms associated with the QCD one loopβfunction coefficient in the NLO JIMWLK Hamiltonian. We show that some of these terms are not associated with the running of the QCD coupling constant but rather with the DGLAP evolution. The DGLAP-like resummation of these logarithms is mandatory within the JIMWLK Hamiltonian, as long as the color correlation length in the projectile is larger than that in the target. This regime in fact covers the whole range of rapidities at which JIMWLK evolution is supposed to be applicable. We derive the RG equation that resums these logarithms to all orders inαsin the JIMWLK Hamiltonian. This is a nonlinear equation for the eikonal scattering matrixS(x). We solve this equation, and perform the DGLAP resummation in two simple cases: the dilute limit, where both the projectile and the target are far from saturation, and the saturated regime, where the target correlation length also determines its saturation momentum.
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- Award ID(s):
- 2208387
- PAR ID:
- 10529876
- Publisher / Repository:
- Journal of High Energy Physics
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2024
- Issue:
- 7
- 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/JHEP07(2024)148
