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Resummation of Yukawa enhanced and subleading Sudakov logarithms in longitudinal gauge boson and Higgs production

Future colliders will probe the electroweak theory at energies much larger than the gauge boson masses. Large double (DL) and single (SL) logarithmic virtual electroweak Sudakov corrections lead to significant effects for observable cross sections. Recently, leading and subleading universal corrections for external fermions and transverse gauge boson lines were resummed by employing the infrared evolution equation method. The results were confirmed at the DL level by explicit two loop calculations with the physical Standard Model (SM) fields. Also for longitudinal degrees of freedom the approach was utilized for DL-corrections via the Goldstone boson equivalence theorem. In all cases, the electroweak Sudakov logarithms exponentiate. In this paper we extend the same approach to both Yukawa enhanced as well as subleading Sudakov corrections to longitudinal gauge boson and Higgs production. We use virtual contributions to splitting functions of the appropriate Goldstone bosons in the high energy regime and find that all universal subleading terms exponentiate. The approach is verified by employing a non-Abelian version of Gribov's factorization theorem and by explicit comparison with existing one loop calculations. As a side result, we obtain also all top-Yukawa enhanced subleading logarithms for chiral fermion production at high energies to all orders. In all cases, the size of the subleading contributions at the two loop level is non-negligible in the context of precision measurements at future linear colliders.