  We discuss one-loop radiative corrections to the sphaleron-induced baryon
number-violating transition rate near the electroweak phase transition in the
standard model. We emphasize that in the case of a first-order transition a
rearrangement of the loop expansion is required close to the transition
temperature. The corresponding expansion parameter, the effective 3-dimensional
gauge coupling approaches a finite $\lambda$ dependent value at the critical
temperature.
  The $\lambda$
  (Higgs mass) dependence of the 1-loop radiative corrections is discussed in
the framework of the heat kernel method. Radiative corrections are small
compared to the leading sphaleron contribution as long as the Higgs mass is
small compared to the W mass. To 1-loop accuracy, there is no Higgs mass range
compatible with experimental limits where washing-out of a B+L asymmetry could
be avoided for the minimal standard model with one Higgs doublet.
