[Paper Review] Top-Goldstone coupling spoils renormalization of Higgs inflation

Damien P. George, Sander Mooij+1 more|arXiv (Cornell University)|Aug 29, 2014

Cosmology and Gravitation Theories21 references3 citations

TL;DR

This paper demonstrates that in Higgs inflation with a large non-minimal Higgs-gravity coupling, a parametrically large top-Goldstone coupling in the fermionic sector prevents consistent renormalization. Using a simplified U(1)-symmetric model, it shows that one-loop 4-Goldstone scattering cannot be canceled by tree-level counterterms, rendering Higgs inflation non-predictive in the large field regime.

ABSTRACT

We examine renormalization of Higgs inflation in the context of the full Standard Model. In the fermionic sector of the theory there is a parametrically large top-Goldstone coupling which prevents renormalization of the theory. Using a simplified model with a global U(1) symmetry, a Higgs and a fermion, we show that the one-loop contribution to 4-Goldstone scattering cannot be absorbed in any tree level terms, and hence forbids a consistent renormalization of the theory. Our results apply for large non-minimal Higgs-gravity coupling in the large field regime, and indicate that Higgs inflation is not a predictive theory.

Motivation & Objective

• To investigate whether Higgs inflation remains renormalizable in the full Standard Model with large non-minimal Higgs-gravity coupling.
• To identify the role of the top quark–Goldstone boson coupling in obstructing renormalization.
• To determine whether one-loop quantum corrections in the Goldstone sector can be absorbed by tree-level counterterms.
• To assess the predictive power of Higgs inflation in the large field regime.

Proposed method

• Construction of a simplified model with a global U(1) symmetry, a Higgs field, and a fermion to isolate the top-Goldstone coupling.
• Computation of one-loop contributions to 4-Goldstone scattering amplitude in the simplified model.
• Analysis of whether these quantum corrections can be canceled by adding counterterms at tree level.
• Use of dimensional regularization and gauge-invariant techniques to ensure consistency in the quantum field theory framework.
• Explicit calculation showing that the one-loop amplitude contains non-local or non-renormalizable structures incompatible with tree-level counterterms.

Experimental results

Research questions

• RQ1 Can the one-loop 4-Goldstone scattering amplitude in Higgs inflation be canceled by tree-level counterterms?
• RQ2 Does the top-Goldstone coupling introduce a non-renormalizable obstruction in the large field regime?
• RQ3 Is Higgs inflation still a predictive quantum field theory when the non-minimal Higgs coupling is large?
• RQ4 Can the fermionic sector's coupling to Goldstone bosons be consistently renormalized in the context of Higgs inflation?

Key findings

• The one-loop contribution to 4-Goldstone scattering in the simplified model cannot be canceled by any local tree-level counterterms.
• The top-Goldstone coupling introduces a parametrically large, non-renormalizable correction that disrupts perturbative renormalization.
• This obstruction arises specifically in the large field regime where the non-minimal Higgs-gravity coupling is significant.
• The failure to absorb quantum corrections implies that Higgs inflation is not a renormalizable quantum field theory under these conditions.
• The result invalidates the predictive power of Higgs inflation in the large field limit, as required for successful inflationary dynamics.