The charm hadrons have a mass in an intermediate range, where the effects of the naïve weak decay matrix element is partly but not fully reflected in the kinematics of final-state particles. Therefore different decay strategies are combined. We start with hadronic decays, and subsequently consider semileptonic ones.
For the four `main' charm hadrons, , , and , a number of branching ratios are already known. The known branching ratios have been combined with reasonable guesses, to construct more or less complete tables of all channels. For hadronic decays of and , where rather much is known, all channels have an explicitly listed particle content. However, only for the two-body decays and some three-body decays is resonance production properly taken into account. It means that the experimentally measured branching ratio for a decay channel, say, is represented by contributions from a direct channel as well as from indirect ones, such as and . For a channel like , on the other hand, not all possible combinations of resonances (many of which would have to be off mass shell to have kinematics work out) are included. This is more or less in agreement with the philosophy adopted in the PDG tables [PDG92]. For and knowledge is rather incomplete, and only two-body decay channels are listed. Final states with three or more hadron are only listed in terms of a flavour content.
The way the program works, it is important to include all the allowed decay channels up to a given multiplicity. Channels with multiplicity higher than this may then be generated according to a simple flavour combination scheme. For instance, in a decay, the normal quark content is , where one is the spectator quark and the others come from the weak decay of the quark. The spectator quark may also be annihilated, like in . The flavour content to make up one or two hadrons is therefore present from the onset. If one decides to generate more hadrons, this means new flavour-antiflavour pairs have to be generated and combined with the existing flavours. This is done using the same flavour approach as in fragmentation, section .
In more detail, the following scheme is used.
When a multiplicity is to be picked, this is done according to a
Gaussian distribution, centered at
and with a
width , with the final number rounded off to the nearest
integer. The value for the number of quarks
is 2 or 4,
as described above, and
Semileptonic branching ratios are explicitly given in the program for all the four particles discussed here, i.e. it is never necessary to generate the flavour content using the fragmentation description. This does not mean that all branching ratios are known; a fair amount of guesswork is involved for the channels with higher multiplicities, based on a knowledge of the inclusive semileptonic branching ratio and the exclusive branching ratios for low multiplicities.
In semileptonic decays it is not appropriate to distribute the
lepton and neutrino momenta according to phase space. Instead the
matrix element is used, in the limit that decay product masses may
be neglected and that quark momenta can be replaced by hadron
momenta. Specifically, in the decay
where is a charm hadron and and ordinary hadron, the matrix
There are a few charm hadrons, such as and , which decay weakly but are so rare that little is known about them. For these a simplified generic charm decay treatment is used. For hadronic decays only the quark content is given, and then a multiplicity and a flavour composition is picked at random, as already described. Semileptonic decays are assumed to produce only one hadron, so that matrix element can be simply applied.