The Two-Higgs Doublet Model beyond tree-level: A gauge-invariant formalism

TL;DR

This paper extends the gauge-invariant bilinear formalism of the two-Higgs-doublet model to include quantum corrections, providing a consistent framework for one-loop calculations that enhance understanding of the model's structure.

Contribution

It introduces a method to incorporate quantum corrections into the gauge-invariant bilinear formalism of the THDM, enabling one-loop computations within a gauge-invariant framework.

Findings

Derived gauge-invariant expressions for one-loop corrections.

Demonstrated the formalism's applicability to the full THDM including gauge and Yukawa sectors.

Provided a concise method for quantum corrections in the bilinear formalism.

Abstract

Employing the gauge-invariant formalism in the two-Higgs-doublet model (THDM) offers profound insights into the model's fundamental structure. A specific set of gauge-invariant bilinear combinations, constructed from the Higgs doublets, establishes a one-to-one correspondence between the components of the doublet fields and real-valued bilinears. This formalism provides a compact and consistent framework to study various aspects of the THDM, including stability, electroweak symmetry breaking, basis transformations, and general symmetries of the Higgs potential. Recently, the bilinear formalism has been extended beyond the Higgs potential to encompass the full THDM, including the gauge and Yukawa sectors, all in gauge-invariant terms. In this work, we advance the formalism further by incorporating quantum corrections. Specifically, we show how bilinears, combined with the $\hbar$-expansion, can be used to compute one-loop corrections. We provide concise, gauge-invariant expressions for these corrections, which are directly applicable to the THDM.