Heavy-quark production at Fermilab Tevatron Collider energies.

Abstract

We propose a way to test structure functions at low $x$ by measuring the heavy-quark cross section at Fermilab Tevatron Collider energies. We show that the QCD calculation (through order ${\ensuremath{\alpha}}_{s}^{3}$) of the total cross section for the bottom- and top-quark pair cross section is very sensitive to the choice of the structure function at Collider energies. Comparison with the experimental data indicates that some choices of the structure functions seem to be preferred by the data. We illustrate how measurements of the bottom-quark pair cross section at Tevatron Collider energies should be able to make a clear distinction between different choices of the structure functions, therefore providing valuable information about the gluon structure function at low $x$. We find that the bottom-quark cross section at Collider energies is dominated by the $\mathrm{gg}$ initial subprocess, while the top-quark cross section is dominated by the contribution from the $\mathrm{qq}$ subprocess at low energies. At Tevatron energies this contribution becomes 30%, while the rest is due to the $\mathrm{gg}$ initial subprocess. We show that the ratio of the cross section calculated through order ${\ensuremath{\alpha}}_{s}^{3}$ to the one calculated through the order ${\ensuremath{\alpha}}_{s}^{2}$, the so-called $K$ factor, is of order 3 for the bottom-quark cross section and of order 2 for the top-quark cross section at Tevatron energies. We also show that the theoretical uncertainty due to the choice of the structure function has a significant effect on the experimental lower limit of the top-quark mass.