Tree-level Unitarity in SU(2)${}_L\times$U(1)${}_Y\times$U(1)${}_{Y^{\prime }}$ Models

Abstract

In models with a U(1) gauge extension beyond the Standard Model, one can derive sum rules for the couplings of the theory that are a consequence of tree-level unitarity. In this paper, we provide a comprehensive list of coupling sum rules for a general SU(2)${}_L\times$U(1)${}_Y\times$U(1)${}_{Y^{\prime }}$ gauge theory coupled to an arbitrary set of fermion and scalar multiplets. These results are of particular interest for models of dark matter that employ an extended gauge sector mediated by a new (dark) $Z^{\prime }$ gauge boson. For the case of a minimal extension of the Standard Model with a U(1)${}_{Y^{\prime }}$ gauge boson, we clarify the definitions of the weak mixing angle and the electroweak $\rho$ parameter. We demonstrate the utility of a generalized $\rho$ parameter (denoted by ${\rho }^{\prime }$) whose definition naturally follows from the unitarity sum rules developed in this paper.

arXiv comment29 pages, 2 figures, 2 tables. Version 3 coincides with the published version. Version 4 adds some clarifying remarks to footnotes 3 and 4 and reorganizes the material of Section 6.3

References in corpus (25)

• The Physics of Heavy Z' Gauge Bosons
• Illuminating Dark Photons with High-Energy Colliders
• Implications of Generalized Z-Z' Mixing
• Serendipity in dark photon searches
• Tree-level unitarity constraints in the most general 2HDM
• Direct Detection Constraints on Dark Photon Dark Matter
• "Dark" Z implications for Parity Violation, Rare Meson Decays, and Higgs Physics
• Di-photon excess illuminates Dark Matter
• The Dark Z' Portal: Direct, Indirect and Collider Searches
• Constraints on Dark Photon from Neutrino-Electron Scattering Experiments
• Neutrino-Electron Scattering: General Constraints on Z' and Dark Photon Models
• Higgs Decays as a Window into the Dark Sector
• A Resolution of the Flavor Problem of Two Higgs Doublet Models with an Extra U(1)_H Symmetry for Higgs Flavor
• The Dark $L_{\mu }-L_{\tau }$ Rises via Kinetic Mixing
• Multi-Higgs doublet models: physical parametrization, sum rules and unitarity bounds
• One-Loop Corrections to the Perturbative Unitarity Bounds in the $CP$-Conserving Two-Higgs Doublet Model with a Softly Broken ${\mathbb{Z}}_2$ Symmetry
• Higgs phenomenology in Type-I 2HDM with U(1)_H Higgs gauge symmetry
• Dark photon kinetic mixing effects for the CDF W-mass measurement
• Theoretical Constraints on Additional Higgs Bosons in Light of the 126 GeV Higgs
• Dark Higgs Dark Matter
• (In)Visible signatures of the minimal dark abelian gauge sector
• Multi-Higgs doublet models: the Higgs-fermion couplings and their sum rules
• Charged Higgs Discovery in the W plus "Dark" Vector Boson Decay Mode
• Impact of extra particles on indirect Z' limits
• The Z Penguin in Generic Extensions of the Standard Model

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