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Fermion Fluctuation Determinant and Sphaleron Bound

We investigate analytically the fermionic fluctuation determinant at finite temperatures in the minimal standard model, including all operators up to dimension 6 and all contributions to the effective potential to all orders in the high $T$ expansion, to 1 loop. We apply the results to find corrections to the Sphaleron erasure rate in the broken phase. We conclude that the analytic treatment of fermions is very reliable and that there is a great deal of baryon erasure after the phase transition for any physical Higgs mass.