4. Dilepton Production in Neutrino and Muon Interactions

These processes have been discussed by several authors [9,11,12,20,21] in quark fragmentation models of the type employed here. The soft spectrum postdicted by the model agrees qualitatively with the data. More speculatively, the same approach might be applied to the spectrum of leptons from charmed particles produced in hadron collisions. At asymptotic energies the D meson and the product lepton emerge (in the laboratory frame) along the direction of the momentum transfer , the cross section being given in terms of our function eqs. (9) and (10)) by (3)

in standard notation. is measured directly in annihilation, and so measurements of the electron spectrum at fixed and in high-energy neutrino and muon experiments will provide a direct test of the underlying picture. Since in the electromagnetic case the distribution is fixed and the cross section concentrated at small , it is predicted essentially uniquely in terms of data according to our model.

In this picture the D meson carries a fraction of the momentum of the ejected quark. At subasymptotic energies this is a frame dependent quantity but, as in the case, the ambiguity should be resolved by demanding that the limit corresponds to the exclusive process with the lowest threshold, in conformity with the behavior of , and so that in all cases and the normalization (eq. (3)) of one charmed particle per charmed quark is maintained (4). I.e. we must choose a frame (most conveniently with and parallel) in which for given and in the exclusive process and . Furthermore for hadronic final states of relatively low invariant mass it is necessary to choose some modified scaling variable (e.g. as done in refs. [20,22]) which causes the cross section to vanish smoothly at threshold. In view of this extra ambiguity we give only asymptotic formulae here, extrapolation to low energy being altogether more complicated and more dangerous than in the case.

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