Transition from soft to hard Pomeron in the structure functions of hadrons at small<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>x</mml:mi></mml:math>from holography

Abstract

We study the nucleon and pion structure functions at the small Bjorken-$x$ region in the framework of holographic QCD with a special emphasis on the roles of anti-de Sitter (AdS) space wave functions. Using the Brower-Polchinski-Strassler-Tan kernel for the Pomeron exchange and calculating its coupling to target hadrons in the AdS space, we obtain ${F}_{2}$ structure functions at the small $x$. Results for the proton ${F}_{2}^{p}$ as well as the pion ${F}_{2}^{\ensuremath{\pi}}$ are consistent with experimental data of the deep inelastic scattering and the forward electroproduction of a neutron. Observed ${Q}^{2}$ dependence of the Pomeron intercept is well reproduced from soft nonperturbative $({Q}^{2}\ensuremath{\sim}0)$ to hard perturbative $({Q}^{2}\ensuremath{\gg}1\text{ }\text{ }{\mathrm{GeV}}^{2})$ region. We find the interplay between soft and hard Pomerons is closely related with behavior of AdS wave functions of hadrons and the virtual photon.