Exclusive electroproduction of $φ$ mesons at HERA

TL;DR

This study measures exclusive $\phi$ electroproduction in $e^{\pm}p$ collisions at HERA over $2<Q^2<70\,\text{GeV}^2$ and $35<W<145\,\text{GeV}$, with $|t|<0.6\,\text{GeV}^2$. By combining a dipole-model framework with precise angular analyses, the authors extract the total and differential $\gamma^*p\rightarrow\phi p$ cross sections, determine the ratio $R=\sigma_L/\sigma_T$, and study the $W$ and $Q^2$ dependences as well as the $t$-slope. The data show a moderate $W$-rise and a growing longitudinal component with $Q^2$, consistent with gluon-dominated dynamics in the dipole picture, and provide substantive tests for the FS04 and MRT vector-meson production models. Model comparisons indicate FS04 better describes the longitudinal part while MRT captures the $W$-dependence, constraining the behavior of the gluon density and dipole–proton interactions in the transition from soft to hard QCD.

Abstract

Exclusive electroproduction of $φ$ mesons has been studied in $e^\pm p$ collisions at $\sqrt{s}=318 \gev$ with the ZEUS detector at HERA using an integrated luminosity of 65.1 pb$^{-1}$. The $γ^*p$ cross section is presented in the kinematic range $2<Q^2<70 \gev^2$, $35<W<145 \gev$ and ${|t|}<0.6 \gev^2$. The cross sections as functions of $Q^2$, $W$, $t$ and helicity angle $θ_h$ are compared to cross sections for other vector mesons. The ratios $R$ of the cross sections for longitudinally and transversely polarized virtual photons are presented as functions of $Q^2$ and $W$. The data are also compared to predictions from theoretical models.

Figures (10)

• Figure 1: The distribution of the events in the kinematic plane of Bjorken x and $Q^2$. The open grey dots represent all reconstructed events while the solid black dots are events in the accepted kinematic range (Section \ref{['sec-eventsel']}).
• Figure 2: Invariant mass distribution of the $K^+K^-$ candidate pairs. The solid line shows the result of a fit including signal+background, while the dashed line shows the background component only. The shaded region indicates the mass range used for cross-section calculations. The error bars indicate the statistical uncertainties.
• Figure 3: (a) Exclusive $\phi$ cross section as a function of $W$ for four values of $Q^2$. The solid lines are the results of a fit to the form $\sigma \propto W^{\delta}$. The overall normalization uncertainty of $^{+4.1}_{-5.3}$ % is not included in the error bar. (b) The extracted values of $\delta$ compared with results from other vector mesons. The error bars represent the quadratic sum of the statistical and systematic uncertainties. Note that the ZEUS $\rho$ data point at $Q^2+M_V^2$ near $8{\,\text{Ge}\text{V}}^2$ has been shifted down by $0.3{\,\text{Ge}\text{V}}^2$ for clarity of presentation.
• Figure 4: Exclusive $\phi$ cross section as a function of $Q^2+M_{\phi}^2$ for $W=75 {\,\text{Ge}\text{V}}$. (a) The total cross section compared with previous measurements. (b) The separate longitudinal and transverse contributions to the cross section. The curves represent the results of the fits to the total cross section as described in the text. The error bars represent the quadratic sum of the statistical and systematic uncertainties. The overall normalization uncertainty of $^{+4.1}_{-5.3}$ % is not shown.
• Figure 5: (a) Exclusive $\phi$ cross section as a function of $W$ for three values of $Q^2$ compared with predictions from the MRT and FS04 model. Different gluon densities (ZEUS-S, MRST99, CTEQ6M) were employed in the MRT predictions as indicated in the figure. Note that the data at $Q^2=3.8$ GeV$^2$ are not shown in the figure for clarity. (b) Exclusive $\phi$ cross section as a function of $Q^2+M_{\phi}^2$ for $W=75 {\,\text{Ge}\text{V}}$. The data are compared to the MRT and FS04 predictions. The ZEUS-S gluon density was used in the MRT model.