Nonrelativistic QCD analysis of bottomonium production at the Fermilab Tevatron

Recent data from the CDF Collaboration on the production of spin-triplet bottomonium states at the Fermilab Tevatron $p\overline{p}$ collider are analyzed within the NRQCD factorization formalism. The color-singlet matrix elements are determined from electromagnetic decays and from potential models. The color-octet matrix elements are determined by fitting the CDF data on the cross sections for ${\rm Y}\mathrm{}\left(1S\right),$ ${\rm Y}\mathrm{}\left(2S\right),$ and ${\rm Y}\mathrm{}\left(3S\right)\mathrm{}$ at large $p_T$ and the fractions of ${\rm Y}\mathrm{}\left(1S\right)\mathrm{}$ coming from ${\chi }_b\mathrm{}\left(1P\right)\mathrm{}$ and ${\chi }_b\mathrm{}\left(2P\right).$ We use the resulting matrix elements to predict the cross sections at the Tevatron for the spin-singlet states ${\eta }_b\mathrm{}\left(\mathrm{nS}\right)\mathrm{}$ and $h_b\mathrm{}\left(\mathrm{nP}\right).$ We argue that ${\eta }_b\mathrm{}\left(1S\right)\mathrm{}$ may be observable in run II through the decay ${\eta }_b\to J/\psi +J/\psi .$