Top-bottom doublet in the sphaleron background

Moreno, J. M.; Oaknin, D. H.; Quirós, M.

Top-bottom doublet in the sphaleron background

Authors

Moreno, J. M.

Oaknin, D. H.

Quirós, M.

Description

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 $m_b/m_t\rightarrow 0$ limit, with an error ${\cal O}(m_b/m_t)$. We have found that the effects of non-degeneracy provide a $θ$-dependence typically $\sim 10\%$.
12 pages, latex + psfig, 4 uuencoded figures