  We construct jet observables for energetic top quarks that can be used to
determine a short distance top quark mass from reconstruction in e+ e-
collisions with accuracy better than Lambda_{QCD}. Using a sequence of
effective field theories we connect the production energy, mass, and top width
scales, Q>> m>> Gamma, for the top jet cross section, and derive a QCD
factorization theorem for the top invariant mass spectrum. Our analysis
accounts for: alpha_s corrections from the production and mass scales,
corrections due to constraints in defining invariant masses, non-perturbative
corrections from the cross-talk between the jets, and alpha_s corrections to
the Breit-Wigner line-shape. This paper mainly focuses on deriving the
factorization theorem for hemisphere invariant mass distributions and other
event shapes in e+e- collisions applicable at a future Linear Collider. We show
that the invariant mass distribution is not a simple Breit-Wigner involving the
top width. Even at leading order it is shifted and broadened by
non-perturbative soft QCD effects. We predict that the invariant mass peak
position increases linearly with Q/m due to these non-perturbative effects.
They are encoded in terms of a universal soft function that also describes soft
effects for massless dijet events. In a future paper we compute alpha_s
corrections to the jet invariant mass spectrum, including a summation of large
logarithms between the scales Q, m and Gamma.
