An Impact Parameter Dipole Saturation Model

TL;DR

This work develops an Impact Parameter dependent dipole saturation model that embeds unitarity via the Glauber–Mueller cross section and uses a proton transverse profile to connect saturation to diffractive observables. By combining LO DGLAP evolution of the gluon density with photon and vector-meson light-cone wave-functions, the model fits HERA DIS data and predicts diffractive $J/\psi$ features, including potential $t$-distribution dips that signal saturation. Extending the framework to nuclei and employing a lumpy nucleon distribution reproduces nuclear shadowing data and provides a quantitative estimate of the nuclear saturation scale, showing saturation effects persist but grow more slowly than naive $A^{1/3}$ expectations. Overall, the results advocate for saturation/CGC physics at HERA scales and offer a coherent path to exploring high-density QCD in nuclear DIS.

Abstract

We develop a dipole model for HERA DIS data which incorporates the impact parameter distribution of the proton. The model describes the inclusive total $γ^*p$ cross-sections as well as the diffractive $J/ψ$ differential cross-sections. We compare the model with previous approaches and show that the $t$-distributions are sensitive to saturation phenomena. We estimate the boundary of the saturation region and show that it dominates the data in the low-$Q^2$ region where the total $γ^*p$ cross-section exhibits the same universal rise as hadronic cross-sections. The model is then extended to nuclei and shows good agreement with the nuclear shadowing data at small-$x$. Finally, we estimate the saturation scale in nuclei.

Figures (25)

• Figure 1: The interaction of a quark anti-quark dipole with a proton.
• Figure 2: The dipole cross-section as a function of the impact parameter $b$ for various dipole sizes evaluated at two $x$-values.
• Figure 3: The differential cross-section for exclusive diffractive $J/\psi$ production as a function of $t$ for representative bins in $W$ref.ZEUSJP. The solid (dashed) lines show the results of the IP saturation model assuming $T_{GY}$ ($T_{G}$) for the proton shape.
• Figure 4: The gluon structure function for various dipole sizes. The dipole size determines the evolution scale $\mu^2$. The dashed lines shows the GRV results GRV.
• Figure 5: The logarithmic rate of rise of the gluon structure function as a function $x$, $\lambda_{eff} = \frac{d \log(xg(x,\mu^2))}{d\log(1/x)}$. $\lambda_{eff}$ is a measure of the strength of the gluon emission process.