One-loop corrections to the Higgs electroweak chiral Lagrangian

TL;DR

This paper calculates one-loop ultraviolet divergences in non-linear Higgs effective theories, revealing their dependence on leading-order Lagrangian terms and emphasizing the importance of chiral logarithms in precision calculations.

Contribution

It provides a detailed computation of one-loop divergences in non-linear Higgs effective theories, highlighting their relation to leading-order terms and the significance of chiral logarithms.

Findings

One-loop divergences are determined by the leading-order Lagrangian.

Divergences are renormalized by O(p^4) operators.

Chiral logarithms significantly affect amplitude calculations.

Abstract

In this talk we study beyond Standard Model scenarios where the Higgs is non-linearly realized. The one-loop ultraviolet divergences of the low-energy effective theory at next-to-leading order, O(p^4), are computed by means of the background-field method and the heat-kernel expansion. The power counting in non-linear theories shows that these divergences are determined by the leading-order effective Lagrangian L_2. We focus our attention on the most important O(p^4) divergences, which are provided by the loops of Higgs and electroweak Goldstones, as these particle are the only ones that couple through derivatives in L_2. The one-loop divergences are renormalized by O(p^4) effective operators, and set their running. This implies the presence of chiral logarithms in the amplitudes along with the O(p^4) low-energy couplings, which are of a similar importance and should not be neglected in next-to-leading order effective theory calculations, e.g. in composite scenarios.