Fragmentation functions for a quark into a spin-singlet quarkonium: Different flavor case

TL;DR

This paper calculates the fragmentation functions for a quark of one flavor to produce a spin-singlet quarkonium of a different flavor, providing numerical results and applying them to specific Z boson decay processes.

Contribution

It introduces a calculation of flavor-changing quark-to-quarkonium fragmentation functions with ultraviolet divergence removal and applies these to Z decay processes.

Findings

Fragmentation functions are expressed as two-dimensional integrals.

Numerical results for light and bottom quark fragmentation into η_c are provided.

Application to Z decays demonstrates the utility of the calculated functions.

Abstract

In the paper, we calculate the fragmentation functions for a quark to fragment into a spin-singlet quarkonium, where the flavor of the initial quark is different from that of the constituent quark in the quarkonium. The ultraviolet divergences in the phase space integral are removed through the operator renormalization under the modified minimal subtraction scheme. The fragmentation function $D_{q \to \eta_Q}(z,\mu_F)$ is expressed as a two-dimensional integral. Numerical results for the fragmentation functions of a light quark or a bottom quark to fragment into the $\eta_c$ are presented. As an application of those fragmentation functions, we study the processes $Z \to \eta_c+q\bar{q}g(q=u,d,s)$ and $Z \to \eta_c+b\bar{b}g$ under the fragmentation and the direct nonrelativistic QCD approaches.