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New physics searches at the LHC or Tevatron typically look for a specificnumber 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 additionalundesired jets by requiring \tau_N <<1. However, this leads to large logarithmsof \tau_N in the cross section, that need to be summed for reliable theorypredictions. For N=0 in hadronic collisions, \tau_N reduces to the "beamthrust" 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 andL is non-hadronic. This factorization theorem enables us to sum largelogarithms 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 inperturbation theory by matching beam functions onto the parton distributionfunctions (PDFs) at the intermediate scale \mu_B^2 ~ t, and we have calculatedall one-loop matching coefficients. Unlike the PDFs, the evolution of the beamfunction is in t and does not affect x or the parton type. We show results forthe beam thrust cross section for Drell-Yan and Higgs production through gluonfusion at next-to-next-to-leading-logarithmic order. For N>0, we obtain afactorization formula with inclusive jet and beam functions that allows us tosum the large logarithms of \tau_N.

Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis)