Fragmentation functions for gluon into $B_c$ or $B_c^*$ meson

TL;DR

This paper calculates the gluon fragmentation functions into $B_c$ and $B_c^*$ mesons, providing key functions and fits that complement previous NLO work on heavy quark fragmentation.

Contribution

It introduces the first calculation of gluon fragmentation functions into $B_c$ and $B_c^*$ mesons, including their renormalization and fitting functions.

Findings

Fragmentation functions $D_{g o B_c}$ and $D_{g o B_c^*}$ are obtained.

Functions are presented as figures and fitting formulas.

Results complement previous NLO fragmentation studies.

Abstract

In the paper, we calculate the fragmentation functions for $g \to B_c$ and $g \to B_c^*$. The ultraviolet divergences in the calculation are removed through the renormalization of the operator definition of the fragmentation functions under the modified minimal subtraction scheme. We then obtain the fragmentation functions $D_{g \to B_c}(z,\mu_F)$ and $D_{g \to B_c^*}(z,\mu_F)$, which are presented as figures and fitting functions. The obtained fragmentation functions are complementary to the previous work on the next-to-leading order fragmentation functions for $\bar{b}\to B_c(B_c^*)$ and $c\to B_c(B_c^*)$.