XXVIII International Workshop on Deep Inelastic Scattering and Related Subjects

Proton Orbital Angular Momentum at Small 𝑥

24 Mar 2020, 14:48

18m

Brooklyn, NY

Contributed Talk Small-x, Diffraction and Vector Mesons Joint Session: WG2+WG5

Speaker

Yuri Kovchegov (The Ohio State University)

Description

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:
$L_{q+\overline{q}}(x,Q^2)=-\mathrm{\Delta }\mathrm{\Sigma }(x,Q^2)\sim {\left(\frac{1}{x}\right)}^{\frac{4}{\sqrt{3}}\sqrt{\frac{{\alpha }_s{N}_c}{2\pi }}}$ ,
$L_G(x,Q^2)\sim \mathrm{\Delta }G(x,Q^2)\sim {\left(\frac{1}{x}\right)}^{\frac{13}{4\sqrt{3}}\sqrt{\frac{{\alpha }_s{N}_c}{2\pi }}}$.