  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.
