Factorization and Resummation for Massive Quark Effects in Exclusive Drell-Yan

Exclusive differential spectra in color-singlet processes at hadron colliders are benchmark observables that have been studied to high precision in theory and experiment. We present an effective-theory framework utilizing soft-collinear effective theory to incorporate massive (bottom) quark effects into resummed differential distributions, accounting for both heavy-quark initiated primary contributions to the hard scattering process as well as secondary effects from gluons splitting into heavy-quark pairs. To be specific, we focus on the Drell-Yan process and consider the vector-boson transverse momentum, \(q_T\), and beam thrust, \(\mathcal T\), as examples of exclusive observables. The theoretical description depends on the hierarchy between the hard, mass, and the \(q_T\) (or \(\mathcal T\)) scales, ranging from the decoupling limit \(q_T \ll m\) to the massless limit \(m \ll q_T\). The phenomenologically relevant intermediate regime \(m \sim q_T\) requires in particular quark-mass dependent beam and soft functions. We calculate all ingredients for the description of primary and secondary mass effects required at NNLL\('\) resummation order (combining NNLL evolution with NNLO boundary conditions) for \(q_T\) and \(\mathcal T\) in all relevant hierarchies. For the \(q_T\) distribution the rapidity divergences are different from the massless case and we discuss features of the resulting rapidity evolution. Our results will allow for a detailed investigation of quark-mass effects in the ratio of \(W\) and \(Z\) boson spectra at small \(q_T\), which is important for the precision measurement of the \(W\)-boson mass at the LHC.