  New physics searches at the LHC or Tevatron typically look for a specific
number of hard jets, leptons and photons. To obtain an exclusive N-jet sample,
one can measure the event shape "N-jettiness" \tau_N and veto additional
undesired jets by requiring \tau_N <<1. However, this leads to large logarithms
of \tau_N in the cross section, that need to be summed for reliable theory
predictions. For N=0 in hadronic collisions, \tau_N reduces to the "beam
thrust" eventshape \tau_B. We derive a factorization theorem for pp -> XL,
where a central jet veto \tau_B<<1 is imposed on the hadronic final state X and
L is non-hadronic. This factorization theorem enables us to sum large
logarithms of \tau_B in the cross section. The initial state is described by
"beam functions", which depend on the momentum fraction x and the (transverse)
virtuality t of the colliding partons. The dependence on t can be calculated in
perturbation theory by matching beam functions onto the parton distribution
functions (PDFs) at the intermediate scale \mu_B^2 ~ t, and we have calculated
all one-loop matching coefficients. Unlike the PDFs, the evolution of the beam
function is in t and does not affect x or the parton type. We show results for
the beam thrust cross section for Drell-Yan and Higgs production through gluon
fusion at next-to-next-to-leading-logarithmic order. For N>0, we obtain a
factorization formula with inclusive jet and beam functions that allows us to
sum the large logarithms of \tau_N.
