### Fermion Vacuum Energy Effects on the Higgs Sector
of the Electroweak Theory

**Vishesh Khemani **

*6-106 Center for Theoretical Physics*

M.I.T.

77 Massachusetts Ave.

Cambridge, MA 0213

We calculate the fermion vacuum energy functional of the Gauge-Higgs
configuration space in the Electroweak theory. We compute it
exactly using phaseshifts of the Dirac wave-functions. We render
it finite by using standard renormalization methods in Quantum
Field Theory. We consider the effective energy obtained by adding
the fermion vacuum energy to the classical energy of the background
fields, for a fixed fermion number. For strong values of the
Yukawa coupling, we look for the emergence of a stable, non-topological,
fermionic soliton. This would maintain the cancellation of anomalies
in the low energy theory and allow the heavy fermion to decouple.
We find no such stable configuration. We also study the correction
to the sphaleron energy barrier between topologically inequivalent
vacua and the possible emergence of new barriers. These effects
would modify the rate of fermion number violating processes which
is crucial for baryogenesis in the early universe We find that
the fermion vacuum energy correction to the sphaleron is positive
and large. Moreover, as the Yukawa coupling is increased to make
the fermion heavier than the sphaleron, we find the emergence
of a barrier which maintains the exponential suppression of the
fermion decay, in contrast to the classical picture. This barrier
does not persist as the fermion is made even heavier, and in this
case we demonstrate the existence of an unsuppressed decay path
over the sphaleron.