Large impact parameters in the Collins-Soper-Sterman resummation formalism

When there are two large disparate scales involved, perturbative QCD cross sections may receive large corrections. These corrections spoil the convergence of the perturbative expansion. A well-known example is the Drell-Yan process cross section differential with respect to the transverse momentum of the lepton pair. When qT << Q, with Q being the invariant mass of the lepton pair and qT its transverse momentum, the cross section at n-th order of perturbation theory has large contributions anslnm Q2/q2 T/q2 T , with m = 0, 1...2n - 1. These contributions have to be summed through all orders to obtain a reliable theoretical prediction for the cross section. The resummation is performed in the impact parameter space (b-space) and is known as the Collins, Soper, and Sterman resummation, or CSS formalism. In the CSS formalism, the cross section is given by the inverse Fourier transform of the resummed b-space expression. While at small values of b, b ≲ 1 GeV-1, this expression is determined mostly by perturbative contributions, at larger values of b nonperturbative effects become important. These effects cannot be fully calculated. Over the years different approaches have been employed to address the problem of large b in the CSS formalism. In this dissertation, these approaches are reviewed and compared. Particular attention is given to an approach based on the analytic continuation of the b-space expression to the complex plane ("complex-b" approach). A modification of the complex-b approach is proposed. The original b * approach of Collins, Soper, and Sterman is revisited. An unproved description of the low energy Drell-Yan and Z boson production qT-differential cross sections is presented. The obtained results have direct implications for precision measurements of the W boson mass at the Run-2 Tevatron and LHC.