Charm and strange meson fragmentation functions

TL;DR

The paper addresses the nonperturbative calculation of fragmentation functions $D_q^h(z)$ for jets producing light and charm pseudoscalar mesons by marrying Dyson–Schwinger–based dressed quark propagators with Bethe–Salpeter amplitudes in a rainbow-ladder framework. Elementary fragmentation functions are computed from a covariant cut diagram and embedded into a system of 25 coupled jet equations to resum the hadronization cascade into $ frac{ ext{p}}{ ext{p}}$, $K$, $D$, and $D_s$ mesons. The results satisfy momentum conservation, display the expected mass/hierarchy effects (e.g., $c o D$ and $c o D_s$ dominance at mid-to-high $z$), and, after DGLAP evolution, show reasonable agreement with kaon fragmentation data from global analyses. This covariant, unified approach provides a bridge between continuum QCD and phenomenology and can be extended to vector mesons, baryons, and polarized fragmentation observables.

Abstract

Quark fragmentation functions describe the hadronization process of a quark where any of the final-state hadrons carries a fraction of its initial momentum. We compute these fragmentation functions for a cascade that includes pions, kaons, and the charmed $D$ and $D_s$ mesons, starting from the elementary quark-to-meson fragmentation process. The latter is obtained from the relevant cut diagram, and employs Poincaré covariant Bethe-Salpeter wave functions and quark propagators. We derive a set of twenty-five coupled jet equations that describe the cascade of emitted mesons in the fragmentation process. Their solutions yield full fragmentation functions that offer a consistent picture of the quark fragmentations across the light and heavy sectors.

Figures (14)

• Figure 1: Cut diagram of the fragmentation function $d^{m}_{q}(z)$ in Eq. \ref{['EQ:fragLF']}. Orange circles with outgoing/incoming double-solid lines denote the meson in the fragmentation process, solid lines are quark propagators and the solid dots represent the $\gamma_{+}$ between the two quarks with momentum $k$.
• Figure 2: Quark fragmentation cascade process.
• Figure 3: Distribution of momentum fractions carried by a meson $m$ produced by an initial up quark. Note that the moments for fragmentation into $D^+$ and $D^0$ are consistent with zero and therefore ignored in the chart.
• Figure 4: Momentum fraction distributions carried by a meson $m$ produced by an initial strange quark. The moment of $D_s^{D^+}$ is much smaller than that of $s\to D^+, D^-, D^0, \bar{D}^0$ fragmentations.
• Figure 5: Momentum fraction distributions carried by a meson $m$ produced by an initial charm quark. The moments of the $c\to D^-$ and $c\to D_s^-$ fragmentations are negligibly small.