$B_c$ meson production at the Tevatron Revisited

CDF recently measured the quantity $\frac{σ(B_c^+)}{σ(B^+)} \frac{{\rm BR}(B_c^+ \to J/ψ\ell^+ ν)}{{\rm BR}(B^+ \to J/ψK^+)}$, {}from which we determine the ratio $\frac{σ(B_c^+)}{σ(\bar b)}$ to be $(2.08\err{1.06}{0.95})\times 10^{-3}$. In this note, we show that the ratio $\frac{σ(B_c^+)}{σ(\bar b)}$ obtained by dividing the $σ(B_c^+)$ by the leading order $σ(\bar b)$ is consistent with this derived CDF measurement. We calculate the cross section $σ(B_c^+)$ 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.

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