We define and study the properties of generalized beam functions (BFs) and
fragmenting jet functions (FJFs), which are fully-unintegrated parton
distribution functions (PDFs) and fragmentation functions (FFs) for
perturbative k_T. We calculate at one loop the coefficients for matching them
onto standard PDFs and FFs, correcting previous results for the BFs in the
literature. Technical subtleties when measuring transverse momentum in
dimensional regularization are clarified, and this enables us to renormalize in
momentum space. Generalized BFs describe the distribution in the full
four-momentum k_mu of a colliding parton taken out of an initial-state hadron,
and therefore characterize the collinear initial-state radiation. We illustrate
their importance through a factorization theorem for pp -> l^+ l^- + 0 jets,
where the transverse momentum of the lepton pair is measured. Generalized FJFs
are relevant for the analysis of semi-inclusive processes where the full
momentum of a hadron, fragmenting from a jet with constrained invariant mass,
is measured. Their significance is shown for the example of e^+ e^- -> dijet+h,
where the perpendicular momentum of the fragmenting hadron with respect to the
thrust axis is measured.Comment: Journal versio
