  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.
