Structure of dimension-six derivative interactions in pseudo Nambu-Goldstone N Higgs doublet models

TL;DR

This paper analyzes the structure of dimension-six derivative interactions in multi-Higgs doublet models where Higgs fields are pseudo Nambu-Goldstone bosons, revealing relations among operators and implications for high-energy scattering amplitudes.

Contribution

It derives the general form of dimension-six derivative interactions in N Higgs doublet models and identifies relations reducing the number of independent operators.

Findings

Relations among dimension-six operators reduce their independent count.

Explicit scattering amplitudes for gauge and Higgs bosons are derived at high energy.

Comparison between two-Higgs and one-Higgs doublet models highlights differences.

Abstract

We derive the general structure of dimension-six derivative interactions in the N Higgs doublet models, where Higgs fields arise as pseudo Nambu-Goldstone modes of a strongly interacting sector. We show that there are several relations among the dimension-six operators, and therefore the number of independent operators decreases compared with models on which only SU(2)_L x U(1)_Y invariance is imposed. As an explicit example, we derive scattering amplitudes of longitudinal gauge bosons and Higgs bosons at high energy on models involving two Higgs doublets, and compare them with the amplitudes in the case of one Higgs doublet.