Proton(anti)proton collisions at the LHC or Tevatron typically involve
experimental restrictions on the hadronic final state and generic parton
momentum fractions. In this situation, factorization at the scale of the hard
interaction does not yield standard parton distribution functions (PDFs) for
the initial state. The measurement restricting the hadronic final state
probes the proton prior to the hard collision and the hard collision occurs
between partons inside initialstate jets rather than inside protons. The
proper description of these initialstate jets requires ``beam functions''.
In this talk I discuss a new factorization theorem with beam functions for
the scenario of "isolated DrellYan" pp > X l^+l^, where X is restricted to
contain no central jets. I also discuss the properties of the beam functions
and how they can be related to the standard PDFs at a smaller perturbative
scale.
