Onia Processes

The unphysical colour-octet states follow the id scheme of 99 n_q n_s n_r n_L n_J where n_q is the quark flavour of the state and n_s is the colour-octet state type. Here 0 is 3S1, 1 is 1S0, and 2 is 3PJ. All remaining numbers follow the standard PDG numbering scheme. If a physical state is requested without a corresponding colour-octet state, a colour-octet state is automatically added to the ParticleData when a colour-octet process is selected. The colour-octet state is created with a mass given by the mass of the physical state plus the singlet-octet mass splitting parameter Onia:massSplit, which is by default set at 200 MeV, and decays exclusively to a gluon and the physical state. If the user wishes to manually set the mass splitting for each colour-octet state individually then Onia:forceMassSplit can be set to off. By default the widths of the octet states are set to vanish. This is not realistic, given their presumably rather rapid decay, but a nonvanishing width is not likely to have any measurable consequences that go beyond what comes from viewing the singlet-octet mass splitting as an effective parameter.

The original Fortran code for these processes has been contributed by Stefan Wolf [unpublished]. For the C++ version only the unpolarized expressions are retained, since the theoretical predictions of the colour-octet model anyway do not agree with the experimental observations. Furthermore, the polarization effects are modest, so isotropic decay is not a bad starting point. Such an event sample can afterwards be reweighted at will by the user, to test various assumptions. The expressions for the colour-singlet production of the 3S1 and 3PJ states can be found in Bai83 and Gas87. Colour-octet expressions can be found in Cho96 for the 1S0, 3S1, and 3PJ states, and the matrix elements for the 3DJ states are taken from Yua98.

The implementation of charmonium and bottomonium production, including the colour-octet production mechanism, requires information on long-distance NRQCD matrix elements for the various wavefunctions involved. Default values for these are encoded in the O parameters and are taken from Nas00; see also Bar07. The 3DJ long-distance matrix elements are extracted from Yua98.

Note that states that differ only by the radial excitation number n_r share the same short-distance matrix elements. The program has therefore been written such that further radial excitations can be easily added by editing this file, without requiring a recompilation of the code. All related arrays must be expanded in exactly the same way, however, i.e. the code of the colour singlet state, the long-distance matrix elements and the individual process on/off switches.

Double production of charmonium and bottomonium 3S1 states is also available, but with only the colour-singlet processes included. The short-distance matrix elements for these processes can be found in Hum83 and Qia02. Arrays seperate to those used for single charmonium and bottomonium production set the long-distance NRQCD matrix elements. For consistency these values should be the same as those provided for single charmonium and bottomonium production, but are seperated to allow further control by the user if needed.

The description of final-state radiation is in this case based on some further model assumptions.

Most of the processes below are divergent in the limit pT → 0, and therefore a pTmin scale should be set. Comparisons with data indicate that this divergence can be tamed the same way as for the normal QCD 2 → 2 cross sections Bar07,Kra08, which makes sense, since they are all dominated by the same kind of t-channel gluon exchange. It is therefore possible to use the SuppressSmallPT user hook to impose a reweighting that cancels the low-pT divergence.

An eikonalized description of these processes, excluding double onia production, is included in the multiparton-interactions framework. Here the low-pT damping is automatic, and additionally the framework is more consistent (e.g. with respect to energy-momentum constraints and the impact-parameter description) for events where the onium production is not the hardest subprocess, as would often be the case in the low-pT limit. Force the mass splitting between the colour-singlet states and their corresponding colour-octet state to be Onia:massSplit. Mass splitting in GeV between the physical colour-singlet states and their corresponding colour-octet state. Common switch for the group of onia production. Common switch for the group of 3S1 onia production, e.g. J/psi and Upsilon. Common switch for the group of 3PJ onia production, e.g. chi_c and chi_b. Common switch for the group of 3DJ onia production, e.g. psi(3770). Common switch for the group of charmonium production, e.g. J/psi and chi_c. Common switch for the group of bottomonium production, e.g. Upsilon and chi_b.

Charmonium 3S1 States

Charmonium 3PJ States

Charmonium 3DJ States

Double Charmonium 3S1 States

Bottomonium 3S1 States

Bottomonium 3PJ States

Bottomonium 3DJ States

Double Bottomonium 3S1 States