Vector Meson Production

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    Elastic vector meson production from ep collisions involve the exchange of a colour singlet object which is emitted by the proton. Of special interest are processes with a hard scale such as

    the mass M_V of a heavy vector meson, 

    the virtuality Q^2 of the photon in a deep inelastic scattering process, or 

    the squared four-momentum transfer t of the colour singlet exchange.

    Such processes allow perturbative QCD calculations to be compared with the measurements and therefore give new information on colour singlet exchange as well as on the proton and the vector meson. 
The figure shows a compilation of the measurements of the total photoproduction cross section sigma_gamma-p and elastic vector meson cross sections sigma_gamma-p^V up to the production of Upsilon as a function of the photon--proton center-of-mass energy W=root(s_gamma-p). 
    The measured total cross section is at large center-of-mass energies compatible with a slowly rising distribution as 

    sigma_gamma-p ~ s^epsilon

    with epsilon~0.095+- 0.002. The optical theorem relates the total cross section to the imaginary part of the amplitude of forward elastic scattering. Therefore, elastic vector meson cross sections should rise with approximately twice the power:

    sigma_gamma-p^V ~ s^2epsilon.

    Photoproduction of light vector mesons (rho, omega, phi) show an increase in the production that is compatible with this prediction. However, photoproduction of the heavy J/psi mesons exhibit a stronger dependence on the center-of-mass energy with epsilon~0.2. In the following results from processes involving a hard scale as defined above, are shown.  

Rho Meson

The figure shows the measurement of the rho meson production cross section as a function of Q2. In contrast to the parton density of virtual photons, the rho cross section falls steeply which implies that the time to develop a hadronic bound state from the quark-antiquark pair of the photon diminishes as Q2 increases.  
    At fixed Q2, the energy dependence of the rho cross section has been measured:  
In the figure the energy dependence of sigma_gamma-p^V measurements by the H1 and ZEUS Collaborations was expressed in terms of the fit parameter epsilon using the above equation and is shown as a function of the scale. The scale was here chosen to be the sum of the photon virtuality and the vector meson squared mass Q^2+M_V^2. The parameter epsilon is found to increase with increasing scale. 

J/Psi Meson

The figure shows the J/psi production cross section as a function of the photon--proton center-of-mass energy W= root(s_gamma*p). 
    The measurements can be described by perturbative QCD calculations which use existing parameterizations of the gluon distributions in the proton. The calculations use the square of the gluon density to account for the colour neutrality of the exchanged object. Therefore, the comparisons of the data with the calculations give a highly sensitive measure of the gluons in the proton. A further component of the calculations is the mechanism for formation of the vector meson such that the comparisons to the data will give new information also on this part of the process. 

b-parameter

    The t distribution at small momentum transfer from the proton gives a measure of the size of the interaction region which is quantified by exponential fits to the data:

    exp( - b t )  
In the figure, a compilation of the fitted b parameters is shown for the HERA data for rho, phi, and J/psi meson production as a function of the scale. The scale has been chosen to be the sum of the photon virtuality Q^2 and the vector meson squared mass M_V^2. 
    With increasing scale, the data tend to approach a constant value of b~4 GeV^-2 which corresponds to the size of the proton. The size of the quark-antiquark state is therefore small compared to that of the proton and probes the proton at small distances. Note that the b parameter measured for the photoproduction of J/psi mesons indicates the small size of the charm-anticharm object in the interaction with the proton. 
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last updated by H1 webmaster on 19/05/98