Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1205.3781

Vacuum Stability Conditions From Copositivity Criteria

Kristjan Kannike
View original source ↗Read source document ↗Export metadata ↓

Abstract

A scalar potential of the form $λ_{ab} ϕ_a^2 ϕ_b^2$ is bounded from below if its matrix of quartic couplings $λ_{ab}$ is copositive -- positive on non-negative vectors. Scalar potentials of this form occur naturally for scalar dark matter stabilised by a $\mathbb{Z}_2$ symmetry. Copositivity criteria allow to derive analytic necessary and sufficient vacuum stability conditions for the matrix $λ_{ab}$. We review the basic properties of copositive matrices and analytic criteria for copositivity. To illustrate these, we re-derive the vacuum stability conditions for the inert doublet model in a simple way, and derive the vacuum stability conditions for the $\mathbb{Z}_2$ complex singlet dark matter, and for the model with both a complex singlet and an inert doublet invariant under a global U(1) symmetry.

Explore related subjects

hep-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Kristjan Kannike. 2013-11-25. Vacuum Stability Conditions From Copositivity Criteria. https://doi.org/10.1140/epjc%2Fs10052-012-2093-z

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

First constraints on QCD axion dark matter using James Webb Space Telescope observations

We present the first constraints on QCD axion dark matter using measurements from the James Webb Space Telescope. By utilizing publicly available MIRI and NIRSpec blank-sky observations, originally collected for sky subtraction purposes, we derive strong limits on the axion-photon coupling constant $g_{a γγ}$ in the mass range 0.1-4 eV. This analysis underscores the potential of blank-sky observations as a powerful tool for constraining dark matter models and demonstrates how astrophysical missions can be repurposed for particle physics research.

hep-ph↗
arXiv2026

Interplay between Electroweak Symmetry Breaking and Higgs Portal Dark Matter

Models of Dark Matter must contend with the fact that the presence of electroweak symmetry breaking along the thermal evolution of the Universe modifies the masses, interactions and, thus, the thermally averaged cross sections. We study in detail the impact of taking (not taking) the presence of the electroweak symmetry breaking into account in the calculations of the Dark Matter relic density in Higgs portal models, providing a model-independent measure of such differences. By focusing on a particular model, we show that ignoring this effect can lead to the inclusion (exclusion) of wrong (viable) regions of parameter space.

hep-ph↗
arXiv2026

Sensitivity Analysis of Singlet Vector-Like B Quarks via Photon-Induced and Z-Initiated Processes at FCC-$μp$

This study presents a systematic sensitivity analysis of singlet-type vector-like $B$ quark production at an FCC--$μp$ collider with a centre-of-mass energy of $\sqrt{s}=24.5~\mathrm{TeV}$ through photon- and $Z$-initiated production mechanisms. The analysis focuses on the $B\to Zb$ decay channel, considering the leptonic decay of the $Z$ boson and the hadronic decay of the accompanying $W$ boson, leading to the final state $\ell^+\ell^-bjj$. Detector-resolution effects are incorporated through a simplified Gaussian smearing procedure, and the discovery and exclusion sensitivities are evaluated using an Asimov-based statistical framework. For the photon-induced channel, the most favourable sensitivity is obtained for $R_L=0.05$ and $\mathcal{L}=1000~\mathrm{fb^{-1}}$. Over the mass range $M_B=2$--$3~\mathrm{TeV}$, the expected $5σ$ discovery reach is approximately $g^\ast\simeq0.263$--$0.328$, while the $95\%$ C.L. exclusion sensitivity extends to $g^\ast\simeq0.162$--$0.197$. On the other hand, the $Z$-initiated channel provides a substantially stronger sensitivity and extends the investigated mass range up to $M_B=4.5~\mathrm{TeV}$. For $R_L=0.05$ and $\mathcal{L}=500~\mathrm{fb^{-1}}$, the $5σ$ discovery reach is approximately $g^\ast\simeq0.038$--$0.056$, while the corresponding $95\%$ C.L. exclusion sensitivity reaches $g^\ast\simeq0.021$--$0.032$. These results demonstrate that photon- and $Z$-initiated single production at an FCC--$μp$ collider provide complementary probes of heavy vector-like $B$ quarks. Moreover, the $Z$-initiated channel offers particularly strong sensitivity to small effective couplings in the multi-TeV mass region beyond the present direct LHC reach.

hep-ph↗