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

Vishesh Khemani

6-106 Center for Theoretical Physics
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.