Understanding Bottom Production ∗

We describe calculations of bb production to next-to-next-to-leading order (NNLO) and next-to-next-to-leading logarithm (NNLL) near threshold in pp interactions. Our calculations are in good agreement with the bb total cross section measured by HERA-B. Factorization assumes it is possible to separate QCD cross sections into universal, non-perturbative parton densities and a perturbatively calculable hard scattering function, the partonic cross section. However, some remnants of long-distance dynamics in the hard scattering function can dominate corrections at higher orders near production threshold. These Sudakov corrections have the form of distributions singular at partonic threshold. Threshold resummation techniques organize the singular distributions to all orders, extending the reach of QCD into near threshold production. The singular functions organized by resummmation are the plus distributions, [ln l x/x] + , where x denotes the 'distance' from partonic threshold. The first attempts to resum the heavy quark cross section were at leading logarithm (LL) and exploited the fact that to LL, the Sudakov corrections to the heavy quark cross section were identical to those obtained for Drell-Yan production [1–3]. This early resummation calculation, like some of the later results that followed, used an empirical cutoff to keep the strong coupling constant from blowing up. Resummation beyond LL cannot make use of this universality because the color structure of each partonic process must be treated separately [4]. The NLL QQ terms were first resummed in Ref. [5] for a simplified case and later fully solved for the qq channel [6]. The exponents in the gg channel were calculationally unwieldly, requiring large cutoffs even for tt production where the resummation should work best. However, one advantage of the resummed cross section is that when it is expanded in powers of α s , it provides estimates of unknown finite-order corrections without resorting to a cutoff or other prescriptions. We have calculated