New determination of the nonperturbative form factor in QCD transverse-momentum resummation for vector boson production

Abstract

In the bmodel for the Collins-Soper-Sterman (CSS) resummation, the resummed form factor is accompanied by the nonperturbative gaussian form factor, which is known to exhibit strong dependence on the the vector boson mass. The nonperturbative form factor of similar nature arises in another approach for the CSS resummation, the minimal pre- scription (MP) based on analytic continuation to treat the impact parameter transform. We perform a global fit of the nonperturbative form factor in the MP resummation at the next-to-leading logarithmic accuracy, with the Z boson production data at the Tevatron and the low energy Drell-Yan data, and find weak dependence on the vector boson mass. with the product of the (anti-)quark distributions for h1,2 and the ellipses standing for the perturbative corrections, the contributions associated with the gluon distributions, etc. This is a benchmark process at the LHC; the comparison with experimental data gives constraints for the PDFs; this is also important for the new physics search. Thus, precise theoretical predictions are desirable. Now the perturbative QCD corrections are known up to NNLO not only for the total cross sections and the rapidity distributions, but also for fully differential cross sections (1). We note that the vector bosons V = � ,Z,W are mostly produced at small transverse mo- mentum QT of typically a few GeV: the vector bosons with the large QT are obtained by the recoil from the hard emission and can be treated by the fixed-order perturbation theory. On the other hand, the large cross section at the small QT is obtained by the recoil from the emis- sion of the soft gluons, whose contributions are accompanied by the logarithmss ln 2 Q 2 /Q 2, �s lnQ 2 /Q 2, which become very large and diverge for small QT and have to be resummed to all orders ins to obtain meaningful results. The contributions due to the multiple gluon emission, where the total sum of the gluon's transverse momenta equals QT, are conveniently treated in the impact parameter b space conjugate to the transverse-momentum space with