Fermion zero-modes of a new constrained instanton in Yang-Mills-Higgs theory

TL;DR

This paper constructs specific fermion zero-mode solutions in a constrained instanton background within SU(2) Yang-Mills-Higgs theory, highlighting their potential impact on fermionic Green's functions and scattering at high energies.

Contribution

It introduces self-consistent ansaetze for fermion zero-modes in a new constrained instanton, revealing their non-coincidence and potential significance in quantum field theory calculations.

Findings

Fermion zero-modes do not coincide for left- and right-handed components.

Zero-modes likely have maxima at different spatial positions.

Implications for fermion Green's functions and high-energy scattering processes.

Abstract

Self-consistent Ansaetze are presented for the left- and right-handed isodoublet fermion zero-modes of the constrained instanton Istar in the vacuum sector of euclidean SU(2) Yang-Mills-Higgs theory. These left- and right-handed fermion wave functions do not coincide and, most likely, have maxima at different positions. This may be important for the fermion zero-mode contribution to the euclidean 4-point Green's function in chiral Yang-Mills-Higgs theory and the high-energy behaviour of fermion-fermion scattering processes.