Charmonium Production

Future analyses of quarkonium production at HERA offer unique possibilities to test the theoretical framework of NRQCD factorization. The existing $J/\psi$ and $\psi(2S)$ measurements can be improved and extended into new kinematic regions, and other quarkonium final states, such as $\chi_c$, may become accessible.

The measurement of inelastic $\chi_c$ photoproduction is a particularly powerful way to discriminate between NRQCD and the color-evaporation model. The assumption of a single, universal long-distance factor in the color-evaporation model implies a universal $\sigma[\chi_c]/\sigma[J/\psi]$ ratio. A large $\chi_c$ cross section is predicted for photon-proton collisions. The ratio of $\chi_c$ production to $J/\psi$ production is expected to be similar to that at hadron colliders, for which $\sigma[\chi_c] / \sigma[J/\psi] \approx 0.5$ [192]. In NRQCD, on the other hand, the $\sigma[\chi_c]/\sigma[J/\psi]$ ratio is process-dependent and strongly suppressed in photoproduction. A search for $\chi_c$ production at HERA that results in a cross section measurement or an upper limit on the cross section would probe directly the color-octet matrix element $\langle {\cal O}^{\chi_J}_8(^3\!S_1)\rangle$ and would test the assumption of a single, universal long-distance factor that is implicit in the color-evaporation model.

The inclusion of color-octet processes is crucial in describing the photoproduction of the spin-singlet states $\eta_c(1S)$, $\eta_c(2S)$, and $h_c(1P)$. With regard to the $P$-wave state $h_c$, the color-octet contribution is required to cancel the infrared divergence that is present in the color-singlet cross section [244]. The production of the $\eta_c$, on the other hand, is dominated by color-octet processes, since the color-singlet cross section vanishes at leading-order, owing to charge-conjugation invariance [245,246], as is the case for $\chi_c$ photoproduction. The cross sections for $\eta_c(1S)$, $\eta_c(2S)$, and $h_c(1P)$ photoproduction are sizable [244,245], but it is not obvious that these particles can be detected experimentally, even with high-statistics data.

The energy spectrum of $J/\psi$'s produced in association with a photon via the process $\gamma p \to J/\psi + \gamma\,X$ is a distinctive probe of color-octet processes [247,250,248,249]. In the color-singlet channel and at leading-order in $\alpha_s$, $J/\psi + \gamma$ can be produced only through resolved-photon interactions. The corresponding energy distribution is therefore peaked at low values of $z$. The intermediate-$z$ and large-$z$ regions of the energy spectrum are expected to be dominated by the color-octet process $\gamma g \to c\bar c_8({}^3\!S_1)\,\gamma$. Observation of a substantial fraction of $J/\psi + \gamma$ events at $z\;\rlap{\lower 3.5 pt \hbox{$\mathchar \sim$}} \raise 1pt \hbox {$>$}\; 0.5$ would provide clear evidence for the presence of color-octet processes in quarkonium photoproduction. Experimentally, this measurement is very difficult due to the large background from photons from $\pi^0$ decays which are produced in the final state.

With the significant increase in statistics at the upgraded HERA collider, it might be possible to study inelastic photoproduction of bottomonium states for the first time. The large value of the $b$ quark mass makes the perturbative QCD predictions more reliable than for charm production, and the application of NRQCD should be on safer ground for the bottomonium system, in which $v^2 \approx 0.1$. However, the production rates for $\Upsilon$ states are suppressed compared with those for $J/\psi$ by more than two orders of magnitude at HERA - a consequence of the smaller $b$ quark electric charge and the phase-space reduction that follows from the larger $b$ quark mass.

Precision measurements of heavy vector mesons remain an important part of the HERA physics program. The systematic errors of the HERA-I measurements of diffractive $J/\psi$ production are mostly limited by the statistics available for systematic studies, and HERA-II data will allow for even more precise results. An important goal for HERA-II will be the investigation of $\Upsilon$ production. The existing measurements of $\Upsilon$ production cross section in diffraction at HERA-I [210,203] indicate that a luminosity of 500 pb$^{-1}$ might yield about 150 events in the detector acceptance. With this statistics a coarse measurement of the energy dependence will be possible.