Orbital Angular Momentum Small-x Evolution: Exact Results in the Large Nc Limit

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Date

2024-03

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Abstract

We construct an exact solution to the revised small-x orbital angular momentum (OAM) evolution equations derived in an earlier work. These equations are derived in the double logarithmic approximation (summing powers of the strong coupling constant with two logarithms of 1/x, with 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 a power law growth in 1/x with the intercept the same as obtained in the small-x helicity evolution, which can be approximated as 3.66074. This result is in complete agreement with the literature. 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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Mathematical and Physical Sciences: 3rd Place (The Ohio State University Edward F. Hayes Advanced Research Forum)

Keywords

Physics, Quantum Chromodynamics, High Energy Physics, Spin physics

Citation

Manley, Brandon. ‘Orbital Angular Momentum Small-x Evolution: Exact Results in the Large-N_c Limit’. arXiv [Hep-Ph], 2024. https://doi.org/10.48550/arXiv.2401.05508