GOOFy -- a systematic approach

TL;DR

This paper introduces GOOFy transformations, a new class of symmetry transformations for bosonic and fermionic fields, which lead to invariant models with RGE-stable parameter relations, including a potential extension of the 2HDM.

Contribution

The paper systematically defines GOOFy transformations, explores their invariance conditions, and demonstrates their implications for RGE-stable relations in various field theories, including the 2HDM.

Findings

GOOFy transformations leave the Lagrangian invariant for certain models.

Invariance under GOOFy leads to RGE-stable parameter relations.

The Standard Model cannot be GOOFy-invariant, but 2HDM can.

Abstract

We investigate in detail a new class (GOOFy) of transformations for bosonic and fermionic fields that leave the Lagrangian density unchanged. The transformations act upon complex scalar fields \Phi and \Phi^\dagger employing generalized charge conjugation (C) transformation in a non-consistent manner, i.e. allowing for \Phi\dagger \to (\Phi\dagger)^\prime \neq (\Phi^\prime)^\dagger. Requiring invariance of the kinetic terms under such transformations specifies the form of (\Phi\dagger)^\prime. An analogous strategy is also adopted for fermionic fields. This offers a systematic way to construct new GOOFy-invariant field-theoretical models. It turns out that theories which are invariant with respect these GOOFy transformations satisfy relations among parameters that are found to be RGE-stable up to two and three loop orders, thus constituting fixed-points under running of the RGE. This has been verified for various theories containing different numbers of bosonic and fermionic fields. In particular it has been shown that the Standard Model (SM) can not be a viable electroweak theory if demanding invariance under GOOFy transformations. However, the two-Higgs-Doublet Model (2HDM) may be invariant under GOOFy transformations (Yukawa couplings included), providing an interesting phenomenological example of physics beyond the SM. The most striking aspect of this study is the RGE stability of new relations between model parameters in a wide class of field theories. We also present a set of new relations between 2HDM potential parameters that constitute a fixed point under the running of the RGE up to at least three loop order.