Constraining the proton transverse partonic distribution through coherent diffractive $J/ψ$ production at HERA within a static Gaussian hot spot model

TL;DR

The paper addresses constraining the proton's transverse partonic distribution at small $x$ by analyzing the $t$-dependence of coherent $J/ψ$ production in the dipole framework. It introduces a static Gaussian hot-spot model with three valence-quark centers, characterized by the hot-spot width $R_p$, quark distance from the center $b_0$, and azimuthal orientation $\theta$, and calibrates these against HERA data using an MV/GBW-inspired dipole amplitude and Boosted Gaussian vector-meson wave functions. The study finds that the $t$-slope is highly sensitive to the hot-spot geometry, especially the rotational degree of freedom which dominates at large $t$ (with amplitudes varying up to about two orders of magnitude for $t\approx1.2$ GeV$^2$), while small-$t$ behavior is less affected. Corrections for the real part and skewedness mainly adjust the normalization (up to ~55%), with limited impact on the slope, providing a practical handle to constrain the proton's transverse geometry and guiding future explorations of other vector mesons and incoherent processes.

Abstract

We investigate the transverse parton distribution of the proton through the t-dependence of the coherent J/psi differential cross section extracted from HERA measurements in the small-x regime. Employing a simple static Gaussian hot spot model inspired by the large-x three-valence-quark picture of the proton, we introduce three geometric degrees of freedom of each hot spot: the Gaussian width of each hot spot, the spatial distance of the valence quarks from the proton center, and their azimuthal orientation. In the simplest implementation, the valence quarks are assumed to form a symmetric triangular configuration. We find that variations in these geometric structures significantly influence the t-slope of the coherent cross section. In particular, the rotational degree of freedom strongly affects the cross section at t > 0.5 GeV^2, while the small-t region remains largely insensitive to variations in this parameter.

Figures (6)

• Figure 1: The configuration of three valence quarks in the proton, forming an equilateral triangle.
• Figure 2: Example contour plots of the transverse color-charge distribution at (a) $\theta=0$, (b) $\theta=\frac{\pi}{6}$, and (c) $\theta=\frac{\pi}{3}$ using $b_0=0.43$ fm and $R_p=0.165$ fm.
• Figure 3: The predicted value of differential cross section as a function of $\theta$, together with the comparison between each correction term applied in the small- and large-$t$, are shown for (a) $Q^2=0.05$ GeV$^2$ and (b) $Q^2=22.4$ GeV$^2$.
• Figure 4: (a) Model fit of the exclusive coherent $J/\psi$ productions as a function of $t$. The shaded bands represent the range of differential cross-section amplitudes obtained from all possible azimuthal rotation configurations of the valence quarks. The data are obtained from H1 H1:2005dtp and ZEUS ZEUS:2004yeh experiments. (b) The variable $R_{\text{corr}}$ represents the ratio between two schemes for calculating the differential cross section, as defined in Eq. \ref{['rcorr']}.
• Figure 5: The $W$ dependence of the model fit is compared with the H1 coherent $J/\psi$ productions data for (a) $Q^2=0.05$ GeV$^2$ and (b) $Q^2=8.9$ GeV$^2$ with the same parameters as in Fig. \ref{['modelfittdep']}. Bands corresponding to all rotational configurations are also included.