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, qT​, and beam thrust, T, as examples of exclusive
observables. The theoretical description depends on the hierarchy between the
hard, mass, and the qT​ (or T) scales, ranging from the decoupling
limit qT​≪m to the massless limit m≪qT​. The phenomenologically
relevant intermediate regime m∼qT​ 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
qT​ and T in all relevant hierarchies. For the qT​ 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 qT​, which is important for the precision measurement of the
W-boson mass at the LHC.Comment: 42 pages + appendices, 21 figures; v2: journal versio