Supersymmetric scalar production in the electroweak Sudakov regime of lepton colliders

We consider the production of supersymmetric (SUSY) scalar pairs at lepton colliders, for c.m. energies much larger than the mass of the heaviest SUSY (real or virtual) particle involved in the process. In that energy regime, we derive the leading and subleading terms of the electroweak Sudakov logarithms in the MSSM, first working at one loop with physical states and then resumming to all orders with asymptotic expansions. We show that the first order of the resummed expression reproduces the physical one loop approximation, and compute systematically the possible effects on various observables both at one loop and to all orders. We discuss the regimes and the observables where the one loop approximation can or cannot be trusted, working in an energy range between 1 TeV and 4 TeV under a “light” SUSY mass assumption. As a by-product of our analysis, we propose a determination of the MSSM parameter $\tan \beta$ showing how a relative accuracy $\simeq 25\%$ can be easily achieved in the region $\tan \beta \gtrsim 14,$ under reasonable experimental assumptions.