Jets from massive unstable particles: Top-mass determination

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Abstract

We construct jet observables for energetic top quarks that can be used to determine a short-distance top quark mass from reconstruction in ${e}^{+}{e}^{\ensuremath{-}}$ collisions with accuracy better than ${\ensuremath{\Lambda}}_{\mathrm{QCD}}$. Using a sequence of effective field theories we connect the production energy, mass, and top width scales, $Q\ensuremath{\gg}m\ensuremath{\gg}\ensuremath{\Gamma}$, for the top jet cross section, and derive a QCD factorization theorem for the top invariant mass spectrum. Our analysis accounts for ${\ensuremath{\alpha}}_{s}$ corrections from the production and mass scales, corrections due to constraints in defining invariant masses, nonperturbative corrections from the cross talk between the jets, and ${\ensuremath{\alpha}}_{s}$ 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 ${e}^{+}{e}^{\ensuremath{-}}$ collisions applicable at a future linear collider. We show that the invariant mass distribution is not a simple Breit-Wigner function involving the top width. Even at leading order it is shifted and broadened by nonperturbative soft QCD effects. We predict that the invariant mass peak position increases linearly with $Q/m$ due to these nonperturbative 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 ${\ensuremath{\alpha}}_{s}$ corrections to the jet invariant mass spectrum, including a summation of large logarithms between the scales $Q$, $m$, and $\ensuremath{\Gamma}$.

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