Complex Singlet Extension of the Standard Model

Abstract: We analyze a simple extension of the Standard Model (SM) obtained by adding a complex singlet to the scalar sector (cxSM). We show that the cxSM can contain one or two viable cold dark matter candidates and analyze the conditions on the parameters of the scalar potential that yield the observed relic density. When the cxSM potential contains a global U(1) symmetry that is both softly and spontaneously broken, it contains both a viable dark matter candidate and the ingredients necessary for a strong first order electroweak phase transition as needed for electroweak baryogenesis. We also study the implications of the model for discovery of a Higgs boson at the Large Hadron Collider.

• The paper introduces a complex singlet field that extends the SM, enabling viable dark matter candidates and a strong electroweak phase transition.
• It formulates a detailed scalar potential incorporating symmetry operations and breaking, leading to distinct vacuum structures and mass spectra.
• The analysis constrains parameter space with numerical insights that align with dark matter relic density and suggest new Higgs signatures at the LHC.

Detailed Analysis of the Complex Singlet Extension of the Standard Model

The paper "Complex Singlet Extension of the Standard Model" presents an intricate and comprehensive examination of an extension to the Standard Model (SM) involving the inclusion of a complex singlet scalar field. This approach addresses profound cosmological issues such as cold dark matter (CDM) and the cosmic baryon asymmetry, while offering new avenues for electroweak symmetry breaking (EWSB) studies.

Motivation and Context

The Standard Model, though profoundly successful in explaining several electroweak interactions, remains incomplete, particularly in describing CDM and baryon asymmetry. The SM fails to provide adequate CP-violation or support a strong first order electroweak phase transition (EWPT), both crucial for baryon asymmetry. Extending the scalar sector by adding a complex singlet addresses these gaps. The primary theoretical framework involves a new potential in the scalar sector affected by the complex singlet. This extension, termed as cxSM, elucidates the possibility of introducing a viable dark matter candidate alongside the potential for a strong first order EWPT, which is instrumental for electroweak baryogenesis.

Model Structure and Theoretical Findings

The research proposes that the addition of a complex scalar singlet introduces multiple layers of novel phenomena and practical implications:

1. Vacuum Structure and Scalar Potential: The scalar potential with added singlet is meticulously formulated, incorporating terms accounting for both symmetry operations and symmetry breaking. The inclusion of real and imaginary components of the singlet leads to variant classification of potential vacuum structures, each correlating to unique physical predictions.
2. Particle Spectra and Symmetry Breaking: A concise classification arising from the symmetry conditions on the potential is provided, detailing potential mass spectra for the scalar constituents. Two prime cases are discussed: one maintaining a $U(1)$ symmetric singlet (no singlet vev) and another where the singlet vev breaks symmetry, creating real scalar bosons and a stable pseudoscalar.
3. Implications for Higgs and LHC Discoveries: The extension holds significant implications for experiments at the Large Hadron Collider (LHC) by influencing Higgs boson discovery and its decay channels, especially those associated with potential invisible modes. These implications are encapsulated in the adjustments to the expected Higgs signatures, providing both challenges and opportunities for LHC experiments.

Numerical and Phenomenological Insights

The analysis yields noteworthy results:

• Cold Dark Matter Candidates: The cxSM can incorporate either one or two viable CDM candidates. Detailed constraints and parameter tuning ensure that the relic density conforms to experimental observations, e.g., WMAP data, while remaining within detection limits established by experiments such as XENON and CDMS.
• EWPT and Baryogenesis: Importantly, it is shown that the cxSM can support a strong first order EWPT under certain parameter scenarios, which is a crucial precursor for baryogenesis. These scenarios are quantified, showing the interplay between negative quartic interactions and thermal scalar dynamics.

Implications for Future Research and Applications

The paper firmly establishes the cxSM as a robust theoretical model ripe for further exploration. It expands the landscape of scalar extensions by thorough analytical and numerical investigations, opening doors for new collider signatures and constraints, while offering potential paths for higher order theoretical models involving supersymmetric extensions or additional hidden sectors.

The cxSM provides a versatile framework that intersects various unexplored dimensions of particle physics and cosmology, presenting a fertile ground for upcoming theoretical explorations and experimental validations. Future advancements in collider experiments and dark matter searches will either substantiate or challenge the predictions of the cxSM, potentially steering new directions in physic research beyond the SM.