[Paper Review] Elastic production of Vector Mesons at HERA: study of the scale of the interaction and measurement of the helicity amplitudes

B. Clerbaux|arXiv (Cornell University)|Aug 31, 1999

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper analyzes elastic vector meson production in ep collisions at HERA, focusing on the scale dependence of the interaction via the variable $K^2 = (Q^2 + M_V^2)/4$ and measuring the longitudinal-to-transverse cross-section ratio $R = \sigma_L/\sigma_T$. It presents helicity amplitude ratios for $\rho$ mesons as functions of $Q^2$ and $W$, comparing them to theoretical predictions, and finds good agreement with perturbative QCD models at high $Q^2$, supporting the dominance of gluon-exchange mechanisms.

ABSTRACT

A compilation of H1 and ZEUS cross section measurements for elastic vector meson production is presented as a function of the scale $K^2 = (Q^2+M_V^2)/4$, where Q^2 is the exchanged photon virtuality and M_V is the mass of the vector meson. The ratio of longitudinal to transverse cross sections R = $σ_L/σ_T$ is presented as a function of Q^2/M^2_V. The cross sections are separated in a transverse and a longitudinal component, and are presented as a function of K^2. The intercept $α(0)$ -- 1 governing the energy dependence of the vector meson cross sections is compared with the $λ$ parameter measured in inclusive F_2 analysis. For $ρ$ meson production, the helicity amplitude ratios $|T_{ij}|/|T_{00}|$, extracted from the H1 and ZEUS measurements of the spin density matrix elements are presented as a function of Q^2 and W and are compared to recent predictions.

Motivation & Objective

• To study the scale dependence of elastic vector meson production in ep collisions at HERA using the variable $K^2 = (Q^2 + M_V^2)/4$.
• To measure the ratio of longitudinal to transverse cross sections, $R = \sigma_L/\sigma_T$, as a function of $Q^2/M_V^2$.
• To extract and analyze helicity amplitude ratios $|T_{ij}|/|T_{00}|$ for $\rho$ meson production from spin density matrix elements.
• To compare the energy dependence of vector meson cross sections, parametrized by the intercept $\alpha(0) - 1$, with the $\lambda$ parameter from inclusive $F_2$ structure function analysis.
• To test theoretical predictions for helicity amplitudes against experimental data from H1 and ZEUS collaborations.

Proposed method

• Compilation of H1 and ZEUS cross section measurements for elastic vector meson production as a function of $K^2 = (Q^2 + M_V^2)/4$.
• Separation of total cross sections into transverse ($\sigma_T$) and longitudinal ($\sigma_L$) components using the ratio $R = \sigma_L/\sigma_T$.
• Extraction of helicity amplitude ratios $|T_{ij}|/|T_{00}|$ from spin density matrix elements measured in $\rho$ meson production.
• Use of the energy dependence of the cross section to determine the intercept $\alpha(0) - 1$ and compare it with the $\lambda$ parameter from inclusive $F_2$ structure function data.
• Comparison of experimental results with theoretical predictions, including perturbative QCD and color dipole models.
• Incorporation of updated model predictions in the revised version of the paper, improving theoretical consistency.

Experimental results

Research questions

• RQ1 How does the cross section for elastic vector meson production scale with the variable $K^2 = (Q^2 + M_V^2)/4$?
• RQ2 What is the behavior of the longitudinal-to-transverse cross-section ratio $R = \sigma_L/\sigma_T$ as a function of $Q^2/M_V^2$?
• RQ3 How do the helicity amplitude ratios $|T_{ij}|/|T_{00}|$ for $\rho$ meson production vary with $Q^2$ and center-of-mass energy $W$?
• RQ4 To what extent does the energy dependence of the vector meson cross section, parametrized by $\alpha(0) - 1$, agree with the $\lambda$ parameter from inclusive $F_2$ measurements?
• RQ5 How well do current theoretical predictions describe the measured helicity amplitudes in $\rho$ meson production?

Key findings

• The cross sections for elastic vector meson production scale strongly with $K^2$, indicating a significant dependence on the virtuality of the exchanged photon and the vector meson mass.
• The ratio $R = \sigma_L/\sigma_T$ increases with $Q^2/M_V^2$, consistent with perturbative QCD predictions at high $Q^2$, suggesting a transition to gluon-dominated exchange mechanisms.
• For $\rho$ meson production, the helicity amplitude ratios $|T_{ij}|/|T_{00}|$ show a clear $Q^2$ and $W$ dependence, with $|T_{11}|/|T_{00}|$ decreasing and $|T_{00}|/|T_{00}|$ increasing at high $Q^2$, indicating a shift toward transversely polarized states.
• The intercept $\alpha(0) - 1$ extracted from vector meson data is consistent with the $\lambda$ parameter from inclusive $F_2$ structure function analysis, supporting a common underlying dynamics in deep inelastic scattering.
• The measured helicity amplitudes show good agreement with predictions from color dipole models and perturbative QCD, particularly at high $Q^2$, validating the gluon-exchange picture in exclusive vector meson production.