Top Quark Pair Production at Higher Energies at the First

For a proper theoretical description of the top quark pair production cross section at the First Muon Collider in the kinematic regime away from the threshold the complete mass and energy dependence has to be taken into account. Two-loop calculations for the photon mediated total cross section are reviewed. For experiments at the Z pole quark mass effects in the total hadronic cross section σ(e + e − → hadrons) can often be neglected in the first approximation and treated perturbatively in an expansion in the ratio M 2 quark /s, where √ s is the c.m. energy. The situation is quite different for top quark pair production at the First Muon Collider, where c.m. energies up to 500 GeV are planned. Here, the t ¯ t threshold energy 1 (√ s) thr = 2M t ≈ 350 GeV and the c.m. energies are comparable in size and an expansion in M 2 t /s is not adequate. In the immediate vicinity of the threshold point conventional multi-loop perturbation theory breaks down and a resummation of Coulomb terms ∼ (C F α s π/β) n , n = 0, 1, 2,. .. (β = (1 − 4M 2 t /s) 1/2 being the c.m. velocity of the top quarks), has to be carried out to all orders in the strong coupling (see [1, 2]). This complication is avoided if only energies sufficiently above the threshold point are considered. As a rule of thumb one can take the relation C F α s π/β < 2 as a requirement to avoid the complication of the threshold regime [3]. For t ¯ t production this means that conventional multi-loop methods can be used for c.m. energies which are at least 10 GeV above the threshold point. 1 Throughout this talk Mt is understood as the top quark pole mass. The constants CA = 3, CF = 4/3 and T = 1/2 denote SU(3) group theoretical factors and α is the electromagnetic coupling.