1. Introduction

Single low momentum electrons associated with hadrons have recently been observed in annihilation experiments at DORIS at GeV [1]. The hadron multiplicity in these events is high [1] and the signal is associated with the production of strange particles [2]. These observations invite an interpretation in terms of the production and subsequent semi-leptonic decay of charmed particles (hereafter generically called D). Calculations of two-body channels (, ), which must dominate in this threshold region, show that this hypothesis is tenable provided the D decay spectrum is rather soft [3].

In this paper we are mainly concerned with the form the lepton spectrum will take at higher energies where two-body final states will presumably constitute a small fraction of the total charm cross section. In particular, it is interesting to contrast the lepton spectra expected from charm and from the decay of pair produced heavy leptons . For charmed particles [4] and heavy leptons [5] with masses of order 2 GeV, the lepton spectrum is expected to be softer and the hadron multiplicity higher in the case of charm, the two processes becoming more distinct with increasing energy, as production becomes increasingly inelastic [6]. However, if more flavors exist they may also yield a relatively hard lepton spectrum near their threshold, and it is interesting to see whether such a contribution could easily be detected.

We shall adopt a model in which charmed quark-antiquark pairs are produced () and subsequently fragment to charmed hadrons () which then decay. In sect. 2 we discuss our assumptions for the fragmentation and decay functions and use them to construct a quark-to-lepton fragmentation function in which the D momentum has been integrated out. At energies large compared to , and the transverse momentum in fragmentation, this function depends only on where is the beam energy, and can be written analytically. At subasymptotic energies care is necessary since the fragmentation picture is not Lorentz-invariant. However, we have found an ansatz which we believe interpolates plausibly between exclusive production at threshold and multiparticle production at asymptotic energies.

Our results, presented in sect. 3, show that, regardless of the details of the model, inelastic fragmentation leads to a lepton spectrum which is very strongly peaked at low , and is therefore easily distinguishable from the spectrum from heavy lepton decay. A direct consequence of this is that the angular distribution of the leptons which are the progeny of charmed quarks shows little trace of their parents' distribution relative to the beam axis. However, we find that the lepton fragments of heavier flavors may not be so easy to distinguish.

Having introduced a charmed-quark-to-lepton fragmentation function, it is natural to use it to describe in addition the processes

and to relate them to

Relevant formulae are collected in sect. 4, where we present a brief discussion of how these processes might be treated at finite energies. Our conclusions are summarized in sect. 5.

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