The Large Higgs Energy Region in Higgs Associated Top Pair Production at the Linear Collider

The process e^+ e^- to t \bar t H is considered in the kinematic end point region where the Higgs energy is close to its maximal energy. In perturbative QCD, using the loop expansion, the amplitudes are plagued by Coulomb singularities that need to be resummed. We show that the QCD dynamics in this end point region is governed by nonrelativistic heavy quarkonium dynamics, and we use a nonrelativistic effective theory to compute the Higgs energy distribution at leading and next-to-leading logarithmic approximation in the nonrelativistic expansion. Updated numbers for the total cross section including the summations in the Higgs energy end point region are presented.