Top-bottom Doublet in the Sphaleron Background *

We consider the top-bottom doublet in the background of the sphaleron for the realistic case of large non-degeneracy of fermion masses, in particular m b = 5 GeV and m t = 175 GeV. We propose an axially symmetric (r, θ)-dependent ansatz for fermion fields and investigate the effects of the non-degeneracy on them. The exact solution is described, with an error less than 0.01%, by a set of ten radial functions. We also propose an approximate solution, in the m b /m t → 0 limit, with an error O(m b /m t). We have found that the effects of non-degeneracy provide a θ-dependence typically ∼ 10%.