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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2401.05508 |
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| _version_ | 1866910596782358528 |
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| author | Manley, Brandon |
| author_facet | Manley, Brandon |
| contents | We construct an exact solution to the revised small-$x$ orbital angular momentum (OAM) evolution equations derived recently, based on an earlier work. These equations are derived in the double logarithmic approximation (summing powers of $α_s \ln^2(1/x)$ with $α_s$ the strong coupling constant and $x$ the Bjorken $x$ variable) and the large-$N_c$ limit, with $N_c$ the number of quark colors. From our solution, we extract the small-$x$, large-$N_c$ expressions of the quark and gluon OAM distributions. Additionally, we determine the large-$N_c$ small-$x$ asymptotics of the OAM distributions to be
\begin{align}
\notag
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)^{α_h},
\end{align} with the intercept $α_h$ the same as obtained in the small-$x$ helicity evolution, which can be approximated as $α_h \approx 3.66074 \sqrt{\frac{α_s N_c}{2π}}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05508 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orbital Angular Momentum Small-$x$ Evolution: Exact Results in the Large-$N_c$ Limit Manley, Brandon High Energy Physics - Phenomenology High Energy Physics - Experiment Nuclear Experiment Nuclear Theory We construct an exact solution to the revised small-$x$ orbital angular momentum (OAM) evolution equations derived recently, based on an earlier work. These equations are derived in the double logarithmic approximation (summing powers of $α_s \ln^2(1/x)$ with $α_s$ the strong coupling constant and $x$ the Bjorken $x$ variable) and the large-$N_c$ limit, with $N_c$ the number of quark colors. From our solution, we extract the small-$x$, large-$N_c$ expressions of the quark and gluon OAM distributions. Additionally, we determine the large-$N_c$ small-$x$ asymptotics of the OAM distributions to be \begin{align} \notag 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)^{α_h}, \end{align} with the intercept $α_h$ the same as obtained in the small-$x$ helicity evolution, which can be approximated as $α_h \approx 3.66074 \sqrt{\frac{α_s N_c}{2π}}$. 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. |
| title | Orbital Angular Momentum Small-$x$ Evolution: Exact Results in the Large-$N_c$ Limit |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment Nuclear Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2401.05508 |