Orbital Angular Momentum at Small $x$ Revisited
| Title: | Orbital Angular Momentum at Small $x$ Revisited |
|---|---|
| Authors: | Kovchegov, Yuri V., Manley, Brandon |
| Publication Year: | 2023 |
| Collection: | High Energy Physics - Experiment High Energy Physics - Phenomenology Nuclear Experiment Nuclear Theory |
| Subject Terms: | High Energy Physics - Phenomenology, High Energy Physics - Experiment, Nuclear Experiment, Nuclear Theory |
| More Details: | 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. 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 $\alpha_s \ln^2(1/x)$ with $\alpha_s$ 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 \begin{align} L_{q+\bar{q}}(x, Q^2) \sim L_{G}(x,Q^2) \sim \Delta \Sigma(x, Q^2) \sim \Delta G(x,Q^2) \sim \left(\frac{1}{x}\right)^{3.66 \, \sqrt{\frac{\alpha_s N_c}{2\pi}}}, \notag \end{align} in agreement with the existing results in the literature 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. Comment: 36 pages, 6 figures; v2: typos corrected, references added; v3: several signs corrected |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2310.18404 |
| Accession Number: | edsarx.2310.18404 |
| Database: | arXiv |
| Description not available. |