Orbital Angular Momentum at Small $x$

Abstract

We determine the small Bjorken $x$ asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton in the double-logarithmic approximation (DLA), which resums powers of ${\alpha }_s{\ln }^2(1/x)$ with ${\alpha }_s$ the strong coupling constant. Starting with the operator definitions for the quark and gluon OAM, we simplify them at small $x$, relating them, respectively, to the polarized dipole amplitudes for the quark and gluon helicities defined in our earlier works. Using the small-$x$ evolution equations derived for these polarized dipole amplitudes earlier we arrive at the following small-$x$ asymptotics of the quark and gluon OAM distributions in the large-$N_c$ limit: \begin{align} L_{q + \bar{q}} (x, Q^2) = - ΔΣ(x, Q^2) \sim \left(\frac{1}{x}\right)^{\frac{4}{\sqrt{3}} \, \sqrt{\frac{α_s \, N_c}{2 π}} }, \ \ \ \ \ L_G (x, Q^2) \sim ΔG (x, Q^2) \sim \left(\frac{1}{x}\right)^{\frac{13}{4 \sqrt{3}} \, \sqrt{\frac{α_s \, N_c}{2 π}}} . \end{align}

27 pages

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Cited by in corpus (18)

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• First analysis of world polarized DIS data with small-$x$ helicity evolution
• Probing the Sivers function with an unpolarized target: GTMD distributions and the Odderons
• Analytic Solution for the Revised Helicity Evolution at Small $x$ and Large $N_c$: New Resummed Gluon-Gluon Polarized Anomalous Dimension and Intercept
• T-odd Leading-Twist Quark TMDs at Small $x$
• Gluon-mediated inclusive Deep Inelastic Scattering from Regge to Bjorken kinematics
• Helicity Evolution at Small $x$: Revised Asymptotic Results at Large $N_c\&N_f$
• Lensing Mechanism Meets Small-$x$ Physics: Single Transverse Spin Asymmetry in $p^{\uparrow }+p$ and $p^{\uparrow }+A$ Collisions
• Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution
• Quark TMDs from back-to-back dijet production at forward rapidities in pA collisions beyond eikonal accuracy in the CGC
• Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$
• Energy-momentum tensor form factors and spin density distribution in the nucleon calculated in a quantized Skyrme model with vector mesons