Heavy Fermion Quantum Effects in SU(2)_L Gauge Theory

TL;DR

This paper investigates the impact of a heavy fermion doublet on the electroweak theory, finding no stable fermionic solitons and showing quantum corrections significantly increase sphaleron energy, affecting fermion stability.

Contribution

It provides an exact effective energy functional for heavy fermions in electroweak theory and analyzes their effects on soliton stability and sphaleron energy.

Findings

No evidence for fermionic solitons due to vacuum polarization energy

Quantum corrections increase sphaleron energy substantially

Heavy doublets can be exponentially suppressed in decay when slightly heavier than sphalerons

Abstract

We explore the effects of a heavy fermion doublet in a simplified version of the standard electroweak theory. We integrate out the doublet and compute the exact effective energy functional of spatially varying gauge and Higgs fields. We perform a variational search for a local minimum of the effective energy and do not find evidence for a soliton carrying the quantum numbers of the decoupled fermion doublet. The fermion vacuum polarization energy offsets the gain in binding energy previously argued to be sufficient to stabilize a fermionic soliton. The existence of such a soliton would have been a natural way to maintain anomaly cancellation at the level of the states. We also see that the sphaleron energy is significantly increased due to the quantum corrections of the heavy doublet. We find that when the doublet is slightly heavier than the quantum--corrected sphaleron, its decay is exponentially suppressed owing to a new barrier. This barrier exists only for an intermediate range of fermion masses, and a heavy enough doublet is indeed unstable.