Bc meson production at the Tevatron revisited

CDF recently measured the quantity σ(Bc+)σ(B+)BR(Bc+→J/ψℓ+ν)BR(B+→J/ψK+), from which we determine the ratio σ(Bc+)σ(b̄) to be (2.08+1.06−0.95)×10−3. In this note, we show that the ratio σ(Bc+)σ(b̄) obtained by dividing the σ(Bc+) by the leading order σ(b̄) is consistent with this derived CDF measurement. We calculate the cross section σ(Bc+) using the perturbative QCD fragmentation functions of Braaten, Cheung, and Yuan and the corresponding induced gluon fragmentation functions, with the charm-quark mass mc as a parameter. We also estimate the parameter mc from the CDF data and then predict the production rate at RunII.