Abstract
We derive the fragmentation function (FF), which describes the probability for a charm quark to emit a $D$ meson with a certain momentum fraction, in the Nambu-Jona-Lasinio (NJL) model. The corresponding elementary FF is calculated with the quark-meson coupling determined in the NJL model involving charm quarks. The FF in the infinite momentum frame is constructed through the jet process governed by the elementary FF, and then evolved to the charm scale, at which it is defined. To prepare the FF suitable for an analysis of $D$ meson production at CLEO, we further match the above FF to that in the finite momentum frame at one loop in QCD. It is shown that the charm quark FF including the finite momentum effects leads to theoretical results in agreement with the CLEO data.
Highlights
Parton fragmentation functions (FFs) contain important information on strong dynamics of hadron production in high energy scattering processes
We review the evaluation of the elementary FF dmq ðzÞ in the Nambu– Jona-Lasinio (NJL) model, which describes the probability of a single emission of the pseudoscalar meson m by the parent quark q with the light-cone momentum fraction z
In this paper we have derived the charm quark FFs for D mesons in the NJL model, which describe the probability for a D meson to take a fraction z of a parent charm momentum
Summary
Parton fragmentation functions (FFs) contain important information on strong dynamics of hadron production in high energy scattering processes. Suzuki proposed a simple model [33,34] similar to leading-order perturbative QCD (pQCD) formalism [35], in which the fragmenting process is factorized into the convolution of a parton-level splitting kernel with a nonperturbative heavy hadron distribution amplitude This approach was extended to the next-toleading order (NLO) in [36], whose results agree with the data from CLEO [37] and Belle [38,39], and with two phenomenological models [40,41] at the charm mass scale.
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