  We study the low transverse momentum (p_T) distribution of the Z-boson at
hadron colliders for p_T ~ Lambda_{QCD} using a factorization and resummation
formula derived in the Soft Collinear Effective Theory (SCET). In the region
p_T ~ Lambda_{QCD}, new non-perturbative effects arise that cannot be entirely
captured by the standard parton distribution functions, and require an
additional new non-perturbative transverse momentum function (TMF). The TMF is
field-theoretically defined in SCET, fully gauge invariant, and captures the
non-perturbative dynamics that affects the p_T-distribution in the region p_T ~
Lambda_{QCD}. The TMF also reduces to the expected perturbative result in the
region p_T >> Lambda_{QCD}. We develop phenomenological models for these TMFs
in the non-perturbative region and present example fits to the available data.
