Abstract
We construct an exact solution to the revised small-x orbital angular momentum (OAM) evolution equations derived in [1], based on an earlier work [2]. These equations are derived in the double logarithmic approximation (summing powers of αs ln2(1/x) with αs the strong coupling constant and x the Bjorken x variable) and the large-Nc limit, with Nc the number of quark colors. From our solution, we extract the small-x, large-Nc expressions of the quark and gluon OAM distributions. Additionally, we determine the large-Nc small-x asymptotics of the OAM distributions to be
with the intercept αh the same as obtained in the small-x helicity evolution [3], which can be approximated as αh ≈ \( 3.66074\sqrt{\frac{\alpha_s{N}_c}{2\pi }} \). This result is in complete agreement with [4]. Additionally, we calculate the ratio of the quark and gluon OAM distributions to the flavor-singlet quark and gluon helicity parton distribution functions respectively in the small-x region.
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Acknowledgments
The author would like to thank Yuri Kovchegov, Jeremy Borden and Yoshitaka Hatta for extensive advice and helpful discussions.
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award Number DE-SC0004286 and is performed within the framework of the Saturated Glue (SURGE) Topical Theory Collaboration.
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Manley, B. Orbital angular momentum small-x evolution: exact results in the large-Nc limit. J. High Energ. Phys. 2024, 55 (2024). https://doi.org/10.1007/JHEP04(2024)055
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DOI: https://doi.org/10.1007/JHEP04(2024)055