Inelastic Leptoproduction of J/psi Mesons at HERA

'Heavy' quarks, like the charm quark c, can be produced in electron proton scatterings at HERA by the process of photon gluon fusion: Here a gluon out of the proton splits into a charm/anti-charm pair that reacts with a photon emitted by the incoming electron. After this production process the heavy charm/anti-charm pair can transform into a bound state, the J/psi meson, which we observe in the detector.

Gluons carry colour, and when the charm/anti-charm pair is produced it keeps this colour, it is in a colour octet state. Now, observable free particles are colourless, i.e. in colour singlet states as predicted in the theory of the strong force, Quantum Chromo-Dynamics QCD, and as verified by experiments. Thus, also the J/psi meson is expected to be colourless. For this reason there must be some mechanism in the production of the bound charm/anticharm state, to get rid of the colour.

Several theoretical approaches exist to describe J/psi production. Here only two are explained in more detail:

• 'Non-relativistic Quantum Chromo-Dynamics' (NRQCD) In this approach the charm/anti-charm pair may be produced in a colour singlet state or in a colour octet state. The colour is then carried away later during the formation of the J/psi meson by 'soft' gluons that do not change anything but the colour. Due to these soft gluons the theory can at the moment not calculate how large the contributions from colour octet state are. These absolute and relative normalisations have to be taken from experimental measurements such as p/anti-p scattering where a similar mechanism is thought to take place.
• 'Colour Singlet Model' (CS): Here only the contributions due to colourless charm/anti-charm states are taken into account. This means that another 'hard' gluon has to be emitted in the production of the charm/anti-charm pair. This hard gluon changes not only the colour but also the kinematics of the quark pair, e.g. the momentum.
  The colour singlet model is a special case of the more general NRQCD. It was however developed independently before the calculations within NRQCD were carried out.

In the following figure on the left hand side the data are compared with the calculations as a function of the photon virtuality Q². The yellow band of the CS prediction falls below the data by a factor of three. On the other hand the full NRQCD calculation (blue band), containing both colour singlet and colour octet contributions (therefore labeled with CS+CO) is in agreement with the data in normalisation and shape at high values of Q².

On the right hand side the squared transverse momentum p_t^*2 of the J/psi meson calculated in the photon-proton system for Q² > 2 GeV² is shown. Again we see, that the CS+CO calculation describes the shape of the data well at large values of p_t^*2 while the CS model tends to predict a dependence which is too steep.

This pattern, that better agreement between data and theory is found at larger values of Q² or p_t^*2 is quite interesting because in this region the theory is more reliable and theoretical uncertainties decrease. On the other hand the experimental results show larger uncertainties here due to lower statistics.

A study on inelastic J/psi production in the range of photoproduction (this means we have a quasi-real photon emitted from the electron - Q²=0) can be found here.