  Multijet cross sections at the LHC and Tevatron are sensitive to several
distinct kinematic energy scales. When measuring the dijet invariant mass m_jj
between two signal jets produced in association with other jets or weak bosons,
m_jj will typically be much smaller than the total partonic center-of-mass
energy Q, but larger than the individual jet masses m, such that there can be a
hierarchy of scales m << m_jj << Q. This situation arises in many new-physics
analyses at the LHC, where the invariant mass between jets is used to gain
access to the masses of new-physics particles in a decay chain. At present, the
logarithms arising from such a hierarchy of kinematic scales can only be summed
at the leading-logarithmic level provided by parton-shower programs. We
construct an effective field theory, SCET+, which is an extension of
soft-collinear effective theory that applies to this situation of hierarchical
jets. It allows for a rigorous separation of different scales in a multiscale
soft function and for a systematic resummation of logarithms of both m_jj/Q and
m/Q. As an explicit example, we consider the invariant mass spectrum of the two
closest jets in e+e- -> 3 jets. We also give the generalization to pp -> N jets
plus leptons relevant for the LHC.
