Orbital Angular Momentum at Small $x$ Revisited
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911964421160960 |
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| author | Kovchegov, Yuri V. Manley, Brandon |
| author_facet | Kovchegov, Yuri V. Manley, Brandon |
| contents | 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 $α_s \ln^2(1/x)$ 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
\begin{align}
L_{q+\bar{q}}(x, Q^2) \sim L_{G}(x,Q^2) \sim ΔΣ(x, Q^2) \sim ΔG(x,Q^2) \sim \left(\frac{1}{x}\right)^{3.66 \, \sqrt{\frac{α_s N_c}{2π}}}, \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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18404 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Orbital Angular Momentum at Small $x$ Revisited Kovchegov, Yuri V. Manley, Brandon High Energy Physics - Phenomenology High Energy Physics - Experiment Nuclear Experiment Nuclear Theory 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 $α_s \ln^2(1/x)$ 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 \begin{align} L_{q+\bar{q}}(x, Q^2) \sim L_{G}(x,Q^2) \sim ΔΣ(x, Q^2) \sim ΔG(x,Q^2) \sim \left(\frac{1}{x}\right)^{3.66 \, \sqrt{\frac{α_s N_c}{2π}}}, \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. |
| title | Orbital Angular Momentum at Small $x$ Revisited |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment Nuclear Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2310.18404 |