Heavy Fermion Non-Decoupling Effects in Triple Gauge Boson Vertices

TL;DR

This paper investigates how heavy fermions influence triple gauge boson vertices through one-loop effects, revealing non-decoupling phenomena linked to gauge anomalies and providing formulas applicable to the Standard Model and beyond.

Contribution

It derives a general four-dimensional formula for off-shell triple gauge boson vertices involving heavy fermions, accounting for anomaly cancellation and non-decoupling effects.

Findings

Heavy fermion contributions cancel anomalies when gauge invariance is enforced.

Non-decoupling effects persist in certain models, affecting gauge boson interactions.

Results align with experimental data on triple gauge couplings.

Abstract

Within a spontaneously broken gauge group we carefully analyse and calculate triple gauge boson vertices dominated by triangle one-loop Feynman diagrams involving heavy fermions compared to external momenta and gauge boson masses. We perform our calculation strictly in four dimensions and derive a general formula for the off-shell, one-particle irreducible (1PI) effective vertex which satisfies the relevant Ward Identities and the Goldstone boson equivalence theorem. Our goal is to search for non-decoupling heavy fermion effects highlighting their synergy with gauge chiral anomalies. Particularly in the Standard Model, we find that when the arbitrary anomaly parameters are fixed by gauge invariance and/or Bose symmetry, the heavy fermion contribution cancels its anomaly contribution leaving behind anomaly and mass independent contributions from the light fermions. We apply these results in calculating the corresponding CP-invariant one-loop induced corrections to triple gauge boson vertices in the SM, minimal $Z'$models as well as their extensions with a fourth fermion generation, and compare with experimental data.