Triply Differential Jet Cross Sections for Hadron Collisions at Orderαs3in QCD

We discuss cross sections for $\mathrm{h}\mathrm{a}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{n}\phantom{\rule{0ex}{0ex}}+\phantom{\rule{0ex}{0ex}}\mathrm{h}\mathrm{a}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{n}\ensuremath{\rightarrow}\phantom{\rule{0ex}{0ex}}2\phantom{\rule{0ex}{0ex}}\mathrm{j}\mathrm{e}\mathrm{t}\mathrm{s}\phantom{\rule{0ex}{0ex}}+\phantom{\rule{0ex}{0ex}}\mathrm{a}\mathrm{n}\mathrm{y}\mathrm{t}\mathrm{h}\mathrm{i}\mathrm{n}\mathrm{g}$ in which three jet variables are measured. Such cross sections are useful especially for determining parton distributions. We define a new cross section $d\ensuremath{\sigma}/{\mathrm{dX}}_{A}{\mathrm{dX}}_{B}d{\ensuremath{\eta}}_{*}$ for which the perturbation theory is nicely behaved even in the kinematic regime where the parton distributions are probed at large momentum fractions. The cross section $d\ensuremath{\sigma}/{\mathrm{dE}}_{T1}d{\ensuremath{\eta}}_{1}d{\ensuremath{\eta}}_{2}$, which has been used in the past, is not so well behaved in this region. We calculate these cross sections at order ${\ensuremath{\alpha}}_{s}^{3}$ in QCD.