$B_c$ Meson Productions Via Induced Gluon Fragmentation

Abstract

Gluons cannot directly fragment into $B_c$ mesons until at order ${\alpha }_s^3$. However, the Altarelli-Parisi evolution of the $\bar{b}$-quark fragmentation functions $D_{\bar{b}\to B_c}(z)$ and $D_{\bar{b}\to B_c^{\ast }}(z)$ from the heavy quark mass scales up to the collider energy scale $Q$ can induce the gluon fragmentation functions $D_{g\to B_c}(z)$ and $D_{g\to B_c^{\ast }}(z)$, respectively, through the gluon splitting $g\to \bar{b}$ at the order ${\alpha }_s^3\log (Q/m_{b,c})$. We will determine these induced gluon fragmentation functions. The $B_c$ meson productions due to the induced gluon fragmentation will be evaluated and compared to the productions by the direct $\bar{b}$-quark fragmentation. The contribution from the induced gluon fragmentation is found to be a significant portion of the total $B_c$ and $B_c^{\ast }$ meson productions, and therefore cannot be ignored.

Comments: LaTeX(RevTeX 2.0), 13 pages and 4 figures (not included, send upon request to cheung@nuhep1.phys.nwu.edu), NUHEP-TH-93-30 and UCD-93-35