Saturation effects in exclusive vector meson production in DIS

TL;DR

This paper investigates saturation effects in exclusive vector meson production in DIS within a CGC-based dipole framework, employing a localized color-hotspot model for the proton to study both coherent and incoherent diffractive cross sections. It derives cross-section formulas in the Good-Walker picture, implements the dipole amplitude with dense and dilute limits, and includes event-by-event geometric fluctuations through a hotspot model, computing observables via Monte Carlo integration. The results show saturation effects are generally mild at the studied energies but become more pronounced with higher color-charge densities, and they highlight the relative roles of hotspot and color fluctuations in shaping the t-dependence of the diffractive spectra; a sizable normalization factor is needed to match incoherent data, pointing to the importance of refining the vector-meson wave-function and relativistic corrections. The study provides a unified, microscopic treatment of fluctuations and non-linear QCD dynamics in exclusive vector meson production, with implications for interpreting data at HERA, UPCs, and future Electron-Ion Colliders.

Abstract

We investigate saturation effects in exclusive vector meson production in deep inelastic scattering (DIS), where we model fluctuations within the target protons as localized color-charge hotspots. Based on the Color Glass Condensate (CGC) framework and the dipole picture for vector meson production, we examine the dependencies of coherent and incoherent scattering cross sections on the momentum transfer. We draw conclusions on the effectiveness of our hot spot model and the strength of the suppression of the scattering cross sections caused by saturation effects. We find that saturation has mild effects in the given energy and charge-density ranges, but can also show that suppression becomes more prominent as the color-charge density inside the proton increases.

Figures (13)

• Figure 1: The process of exclusive vector meson production. Displayed are the incoming interaction particles (electron, which scatters off the virtual photon $\gamma^*$, with virtuality $Q^2$, and the proton) and the outgoing products (the vector meson and the proton p' or dissociated proton p$^*$).
• Figure 2: Illustration of the hotspot proton model, which shows an arbitrary configuration of $N_\mathrm{h}=3$ hotspots. The hotspots are not confined to the proton and radiate some color charge beyond the size of the proton. The passing dipole with quarks at positions $\mathbf{x}$ and $\mathbf{y}$ is also drawn.
• Figure 3: Coherent cross sections in the dense and dilute limits. Data labeled "Analytical" refers to results from previous work Demirci:2021kya, where the hotspot average was calculated analytically in the dilute limit and no numerical sampling was performed. H1 data is from H1:2013okq. The bands correspond to statistical error coming from the MC sampling of geometrical fluctuations in the proton.
• Figure 4: Incoherent cross sections in the dense and dilute limits. Also shown are the color and hotspot fluctuations making up the total cross section. H1 data is from H1:2013okq for small-$t$ and H1:2003ksk for large-$t$. The standard error is shown as bands.
• Figure 5: Coherent cross sections for different color-charge amounts $g^2\mu_0^2$. The standard error is shown as bands. The smaller diagram shows the ratio of dense to dilute model scattering cross sections.