Measurement of elastic electroproduction of phi mesons at HERA

TL;DR

This paper reports a detailed measurement of elastic $\phi$ meson electroproduction at HERA with the H1 detector in the kinematic range $1 < Q^2 < 15$ GeV$^2$ and $40 < W < 130$ GeV. By analyzing the $Q^2$ and $t$ dependences, the $\,\phi$ cross section is compared to lighter and heavier vector mesons after SU(5) scaling, and a comprehensive polarization study yields the full set of spin-density matrix elements. A small but significant violation of s-channel helicity conservation is observed, while the ratio of longitudinal to transverse cross sections rises with $Q^2$ and exhibits a universal pattern when expressed in terms of $Q^2/M_V^2$, consistent with perturbative QCD expectations. The results reinforce a diffraction-based description of vector-meson production and provide stringent tests of pQCD models across multiple vector mesons.

Abstract

The elastic electroproduction of phi mesons is studied at HERA with the H1 detector for photon virtualities 1 < Q^2 < 15 GeV^2 and hadronic centre of mass energies 40 < W < 130 GeV. The Q^2 and t dependences of the cross section are extracted (t being the square of the four-momentum transfer to the target proton). When plotted as function of (Q^2 + M_V^2) and scaled by the appropriate SU(5) quark charge factor, the phi meson cross section agrees within errors with the cross sections of the vector mesons V = rho, omega and J/psi. A detailed analysis is performed of the phi meson polarisation state and the ratio of the production cross sections for longitudinally and transversely polarised phi mesons is determined. A small but significant violation of s-channel helicity conservation (SCHC) is observed.

Figures (7)

• Figure 1: (a) and (b): distribution of $m_{KK}$ for $m_{KK}$$<$ 1.12 GeV and $m_{KK}$$<$ 2.00 GeV, respectively; (c) distribution of $m_{\pi\pi}$ after removing the $\phi$ signal ($m_{KK}$$<$ 1.04 GeV). The points represent the data and the full lines the prediction of a simulation, which includes contributions from elastic $\rho$ (dashed lines), $\omega$ (dotted lines) and $\phi$ (dash-dotted lines) meson production. The errors on the data points are statistical only.
• Figure 2: Ratio of the cross sections for elastic $\phi$ and $\rho$ production, as a function of $Q^2$, together with previous H1 h1_phi_94 and ZEUS zeus_phi_hqzeus_phi_gp measurements. The inner error bars are statistical and the full error bars include the systematic errors added in quadrature. The dashed line corresponds to the ratio $2/9$.
• Figure 3: H1 and ZEUS measurements h1_rho_96zeus_rho_jpsi_hqh1_jpsi_gph1_jpsi_hqzeus_jpsi_gph1_phi_94zeus_phi_gpzeus_phi_hqzeus_rho_gpzeus_ome_gph1_ups_gpzeus_ups_gp of the total cross sections $\sigma (\gamma^{\star}p \rightarrow V p)$ as a function of ($Q^2$ + $M^2_V$) for elastic $\rho$, $\omega$, $\phi$, $J/\psi$ and $\Upsilon$ meson production, at the fixed value $W$ = 75 GeV. The cross sections were scaled by SU(5) factors, according to the quark charge content of the vector meson. For the error bars statistical and systematic errors have been added in quadrature. The curve corresponds to a fit to the H1 and ZEUS $\rho$ data, and the ratio $D$ of the scaled $\omega$, $\phi$ and $J/\psi$ cross sections to this parametrisation is presented in the insert.
• Figure 4: Corrected $t$ distributions for elastic $\phi$ meson production, in the range 2.5 $<$$Q^2$$<$ 15 ${\rm GeV}^2$. The full curve presents the result of the fit to the sum of three exponentials (see text), the dotted line showing the elastic contribution. The errors on the data points are statistical only.
• Figure 5: The full set of spin density matrix elements for elastic electroproduction of $\phi$ mesons, for two ranges of $Q^2$. The inner bars are statistical, the full error bars include the systematic errors added in quadrature. Where indicated the dotted lines show the expectation of zero for $s$-channel helicity conservation (SCHC). The five elements predicted to be non-zero under SCHC are $r_{00}^{04}$, $r_{1-1}^{1}$, Im $r_{1-1}^{2}$, Re $r_{10}^{5}$ and Im $r_{10}^{6}$. The full, dashed and dash-dotted lines represent respectively predictions of the models of Royen and Cudell isa, Ivanov and Kirschner ivanov and Akushevich, Ivanov and Nikolaev kolya.