Finite-width Effects In Top Quark Production At Hadron Colliders

Production cross sections for <italic>tt&macr;</italic> and <italic> tt&macr;j</italic> events at hadron colliders are calculated, including finite-width effects and off-resonance contributions for the entire decay chain, <italic> t</italic> &rarr; <italic>bW</italic> &rarr; <italic>b</italic>&ell;&nu;, for both top quarks. Original and noteworthy features of the parton-level Monte-Carlo programs developed for this purpose are described and employed techniques discussed. Resulting background rates to Higgs search at the CERN LHC are updated for inclusive <italic>H</italic> &rarr; <italic>WW</italic> studies and for <italic>H</italic> &rarr; &tau;&tau; and <italic>H</italic> &rarr; <italic> WW</italic> decays in weak boson fusion events. A shortcoming that causes an overestimation of total top production rates is identified in a procedure used in previous studies to approximate off-shell cross sections. For suppressed <italic> tt&macr;</italic>(<italic>j</italic>) backgrounds finite- width effects are found to be of same order as typical NLO QCD corrections, i.e. much larger than <math> <f> <sc>O<fen lp='par'><g>G</g>/<mit>m</mit><rp post='par'></fen> </sc></f> </math>. The field-theoretical origin of finite-width effects is elucidated and the <italic>fermion-loop scheme</italic>, a method that is derived from first principles and allows to include finite-width effects for processes with intermediate <italic> W</italic> and <italic>Z</italic> bosons, is reviewed. Its extensibility to processes with intermediate top quarks is explored, which implies the resummation of bosonic one-loop corrections. Thus, the imaginary parts of the <italic> bW</italic>-loop corrections to the tree-level top propagator and <italic> ttg</italic> vertex are calculated. The resulting effective propagator and vertex are found to satisfy the Ward identity corresponding to <italic>SU </italic>(3) gauge invariance. However, an example shows that the use of <italic>bW</italic>-loop-resummed expressions for the top propagator and all tree-level top vertices is generally not sufficient to guarantee good high energy behavior.