Semi-inclusive Deep Inelastic Scattering at small x

Abstract

We study the semi-inclusive hadron production in deep inelastic scattering at small $x$. A transverse momentum dependent factorization is found consistent with the results calculated in the small-$x$ approaches, such as the color-dipole framework and the color glass condensate, in the appropriate kinematic region at the lowest order. The transverse momentum dependent quark distribution can be studied in this process as a probe for the small-$x$ saturation physics. Especially, the ratio of quark distributions as a function of transverse momentum at different $x$ demonstrates strong dependence on the saturation scale. The $Q^2$ dependence of the same ratio is also studied by applying the Collins-Soper-Sterman resummation method.

Figures (3)

• Figure 1: Semi-inclusive DIS at small-x, where the cross represents the quark fragmenting into the final-state hadron. The quark carries the momentum fraction $\hat{\xi}$ of the virtual photon, and transverse momentum $k_\perp$.
• Figure 2: Transverse-momentum-dependent quark distribution calculated from small-x gluon splitting. The double line represents the gauge link contribution from the TMD quark distribution definition.
• Figure 3: The transverse-momentum-dependent quark distributions at small-$x$: (left) at $x=10^{-4}$ and $10^{-3}$ as ratios relative to that at $x=10^{-2}$ for fixed $Q^2=Q_0^2=10GeV^2$ where the transverse momentum resummation effect is not important; (right) at different $Q^2$ relative to that at $Q^2=10GeV^2$ for fixed $x=3\cdot 10^{-4}$ with $Q_s^2=1GeV^2$ in the GBW model.