Basis-independent methods for the two-Higgs-doublet model III: The CP-conserving limit, custodial symmetry, and the oblique parameters S, T, U

Abstract: In the Standard Model, custodial symmetry is violated by the hypercharge U(1) gauge interactions and the Yukawa couplings, while being preserved by the Higgs scalar potential. In the two-Higgs doublet model (2HDM), the generic scalar potential introduces new sources of custodial symmetry breaking. We obtain a basis-independent expression for the constraints that impose custodial symmetry on the 2HDM scalar potential. These constraints impose CP-conservation on the scalar potential and vacuum, and in addition add one extra constraint on the scalar potential parameters. We clarify the mass degeneracies of the 2HDM that arise as a consequence of the custodial symmetry. We also provide a computation of the "oblique" parameters (S, T, and U) for the most general CP-violating 2HDM in the basis-independent formalism. We demonstrate that the 2HDM contributions to T and U vanish in the custodial symmetry limit, as expected. Using the experimental bounds on S and T from precision electroweak data, we examine the resulting constraints on the general 2HDM parameter space.

• The paper introduces a basis-independent framework to systematically identify CP-conserving scenarios in the two-Higgs-doublet model.
• It demonstrates that enforcing custodial symmetry leads to mass degeneracies among Higgs bosons, aligning the model with electroweak precision tests.
• The study computes oblique parameters S, T, and U to set stringent constraints on the scalar potential and symmetry-breaking effects.

Analysis of the Two-Higgs-Doublet Model: Custodial Symmetry and CP Conservation

The paper by Howard E. Haber and Deva O'Neil provides a comprehensive examination of the Two-Higgs-Doublet Model (2HDM), focusing on its symmetry properties and contributions to precision electroweak observables. This analysis leverages a basis-independent formalism, which facilitates the study of CP conservation and custodial symmetry within the 2HDM without the ambiguities introduced by choosing specific field bases.

CP Conservation

CP violation is inherent in the most general form of the 2HDM due to complex parameters in the Higgs potential and Yukawa interactions. The paper delineates conditions for CP conservation, which require either real potential parameters or symmetries that restrict their complex nature. The authors introduce a basis-independent approach that characterizes CP-violating effects through invariant quantities like the complex couplings in the Higgs potential. This formalism allows for systematic identification of CP-conserving scenarios across possible parametrizations. The classification covers both cases where $Z_6 \neq 0$ and $Z_6 = 0$, offering a nuanced picture of when and how CP-violating terms can be absent.

Custodial Symmetry

Custodial symmetry is crucial in preserving the 𝜌-parameter close to unity, a key feature of the Standard Model at tree level. This symmetry is softly broken by hypercharge interactions and fermion Yukawa couplings. In the 2HDM, additional custodial-breaking terms may arise, impacting precision electroweak measurements such as the 𝑆, 𝑇, and 𝑈 parameters. The paper provides a basis-independent characterization of custodial symmetry conditions, integrating them with CP-conservation criteria to identify the parameter regions where both symmetries coexist. The analysis shows that enforcing custodial symmetry leads to mass degeneracies among the Higgs bosons, a notable impact that affects the parameter space accessible for phenomenological studies.

Implications and Future Directions

The interplay between CP conservation and custodial symmetry is pivotal in defining the 2HDM's parameter landscape and making the model consistent with experimental data. The $T$ parameter, related to deviations from custodial symmetry, is particularly significant for constraining models beyond the Standard Model. The authors compute the contributions of the 2HDM to $S$, $T$, and $U$ parameters using a basis-independent calculation of gauge boson polarization functions, thereby placing bounds on scalar potential parameters that adhere to both unitarity and electroweak precision data.

Practical and Theoretical Considerations

By integrating CP conservation and custodial symmetry into the framework, this analysis provides both theoretical clarity and practical guidance in 2HDM research. The paper advances the understanding of parameter correlations and symmetry breaking in the Higgs sector, paving the way for experimental tests at high-energy colliders. The methodology adopted could be extended to other multi-Higgs frameworks and models requiring robust symmetry considerations.

In conclusion, the paper's approach exemplifies the efficacy of basis-independent methods in studying complex symmetries within extended Higgs sectors, setting a standard for future analyses in theoretical and phenomenological research.