Authors Referees APS Members |
January 2008, to be published in Physical Review D1
Jets from massive unstable particles: Top-mass determination
\vspace*{0.3cm} 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 $\Lambda_{\rm QCD}$. Using a sequence of effective field theories we connect the production energy, mass, and top width scales, $Q\gg m\gg\Gamma$, 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 $\Gamma$. © 2008 The American Physical Society.
|
