Effective Hamiltonian for QCD evolution at high energy |
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| Affiliation: | 1. RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA;2. Service de Physique Theorique, Saclay, F-91191 Gif-sur-Yvette, France;3. Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA;4. Institute of Nuclear Physics PAN, Radzikowskiego 152, Kraków, Poland;1. Department of Mathematics, Kingʼs College London, The Strand, London WC2R 2LS, United Kingdom;2. Mathematical Institute, University of Oxford, 24-29 St Gilesʼ, Oxford OX1 3LB, United Kingdom;1. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China;2. School of Mathematics and Computer Science, Shaanxi Sci-Tech University, Hanzhong, Shaanxi 723000, China;3. Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, Hunan 410081, China;4. School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China |
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| Abstract: | ![]()
We construct the effective Hamiltonian which governs the renormalization group flow of the gluon distribution with increasing energy and in the leading logarithmic approximation. This Hamiltonian defines a two-dimensional field theory which involves two types of Wilson lines: longitudinal Wilson lines which describe gluon recombination (or merging) and temporal Wilson lines which account for gluon bremsstrahlung (or splitting). The Hamiltonian is self-dual, i.e., it is invariant under the exchange of the two types of Wilson lines. In the high density regime where one can neglect gluon number fluctuations, the general Hamiltonian reduces to that for the JIMWLK evolution. In the dilute regime where gluon recombination becomes unimportant, it reduces to the dual partner of the JIMWLK Hamiltonian, which describes bremsstrahlung. |
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