$B_c$ meson production at the Tevatron Revisited

Abstract

CDF recently measured the quantity $\frac{\sigma (B_c^{+})}{\sigma (B^{+})}\frac{\mathrm{BR}(B_c^{+}\to J/\psi {\ell }^{+}\nu )}{\mathrm{BR}(B^{+}\to J/\psi K^{+})}$, {}from which we determine the ratio $\frac{\sigma (B_c^{+})}{\sigma (\bar{b})}$ to be $(2.08\text{err}1.060.95)\times 10^{-3}$. In this note, we show that the ratio $\frac{\sigma (B_c^{+})}{\sigma (\bar{b})}$ obtained by dividing the $\sigma (B_c^{+})$ by the leading order $\sigma (\bar{b})$ is consistent with this derived CDF measurement. We calculate the cross section $\sigma (B_c^{+})$ using the perturbative QCD fragmentation functions of Braaten, Cheung, and Yuan and the corresponding induced gluon fragmentation functions, with the charm-quark mass $m_c$ as a parameter. We also estimate the parameter $m_c$ from the CDF data and then predict the production rate at RunII.

Comments: minor changes in text and figure