Orbital angular momentum at small $x$ revisited

Kovchegov, Yuri V.; Manley, Brandon

doi:10.1007/jhep02(2024)060

Title: Orbital angular momentum at small $$x$$ revisited

Journal Article · 07 February 2024 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep02(2024)060 · OSTI ID:2322576

^[1];

^[2]

The Ohio State Univ., Columbus, OH (United States); The Ohio State University
The Ohio State Univ., Columbus, OH (United States)

We revisit the problem of the small Bjorken-x asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton utilizing the revised small-x helicity evolution derived recently in [1]. We relate the quark and gluon OAM distributions at small x to the polarized dipole amplitudes and their (first) impact-parameter moments. To obtain the OAM distributions, we derive novel small-x evolution equations for the impact-parameter moments of the polarized dipole amplitudes in the double-logarithmic approximation (summing powers of α_s ln²(1/x) with α_s the strong coupling constant). We solve these evolution equations numerically and extract the leading large-N_c, small-x asymptotics of the quark and gluon OAM distributions, which we determine to be $${L}_{q+\overline{q}}\left(x,{Q}^2\right)\sim {L}_G\left(x,{Q}^2\right)\sim \Delta \Sigma \left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {\left(\frac{1}{2}\right)}^{3.66\sqrt{\frac{\alpha_s{N}_c}{2_π}}}$$in agreement with [2] within the precision of our numerical evaluation. (Here N_c is the number of quark colors.) We also investigate the ratios of the quark and gluon OAM distributions to their helicity distribution counterparts in the small-x region.

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Research Organization:: The Ohio State Univ., Columbus, OH (United States). Office of Sponsored Programs

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0004286

OSTI ID:: 2322576

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2024; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Orbital angular momentum at small $$x$$ revisited

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