[Paper Review] Hiding Scalar Higgs Portal Dark Matter

Wei Chao|arXiv (Cornell University)|Jan 25, 2016

Dark Matter and Cosmic Phenomena3 citations

TL;DR

This paper proposes a Higgs portal dark matter model with a complex scalar singlet where the CP-odd component (a) is the dark matter candidate, stabilized by a hidden $Z_2$ symmetry. The CP-even component (s) mixes with the SM Higgs via a trilinear coupling but acquires no vacuum expectation value, suppressing tree-level direct detection. The model achieves the correct relic density via quartic couplings alone, yielding direct detection cross sections $2\sim5$ orders below the LUX limit, making it viable despite no direct detection signal.

ABSTRACT

We investigate a Higgs portal dark matter model by extending the Standard model (SM) with a complex singlet, $S=(s+ia )/\sqrt{2}$, where $a $ is a dark matter candidate and $S$ gets no vacuum expectation value but $s$ mixies with the SM Higgs via a trilinear interaction. We point out an interesting scenario, where only quartic coupling contributes to the dark matter relic abundance and there is no tree level contribution to the direct detection. Numerical analysis shows that the direction detection cross section, which arises at the one-loop level, is about $2\sim 5$ orders below the current LUX bound. Constraints from Higgs measurements as well as collider signatures of the model at the LHC are studied.

Motivation & Objective

• To resolve the tension between correct dark matter relic density and stringent direct detection constraints in Higgs portal models.
• To propose a mechanism where tree-level direct detection is forbidden due to vacuum misalignment and symmetry protection.
• To demonstrate that the relic density can be generated purely via quartic couplings, avoiding tree-level scattering.
• To explore collider signatures at the LHC, particularly in the mono-Higgs channel, for indirect detection.

Proposed method

• Extend the Standard Model with a complex scalar singlet $S = (s + ia)/\sqrt{2}$, where $a$ is the dark matter candidate stabilized by a $U(1)$ symmetry.
• Introduce a trilinear coupling $\alpha S H^\dagger H$ that mixes the CP-even component $s$ with the SM Higgs, without giving $S$ a vacuum expectation value.
• Use a potential with a partially broken $Z_2$ symmetry, preserving $Z_2$ for the CP-odd scalar $a$ but explicitly breaking it for $s$, leading to mass splitting.
• Perform a universal Higgs fit to ATLAS and CMS data to constrain the mixing angle $\theta$, requiring $|\theta| < 0.526$.
• Compute the dark matter relic density using only the quartic coupling $\lambda_s$, and evaluate direct detection cross sections at one-loop level.
• Simulate LHC collider signatures, particularly $pp \to 2a + h$, to assess detectability in the mono-Higgs channel.

Experimental results

Research questions

• RQ1 Can a Higgs portal dark matter model achieve the correct relic density without tree-level direct detection?
• RQ2 What is the impact of a trilinear mixing term between the SM Higgs and a CP-even scalar singlet on direct detection constraints?
• RQ3 How small can the direct detection cross section be in such a model, and does it evade current LUX limits?
• RQ4 What are the viable collider signatures for this model at the LHC, particularly in the mono-Higgs channel?
• RQ5 Can the model be constrained by Higgs precision measurements and invisible Higgs decays?

Key findings

• The direct detection cross section is suppressed to $2\sim5$ orders of magnitude below the current LUX limit, making the model effectively invisible to direct detection experiments.
• The relic density is successfully generated via the quartic coupling $\lambda_s$ alone, with no tree-level contribution to scattering off nuclei.
• The model satisfies constraints from Higgs measurements, with the mixing angle constrained to $|\theta| < 0.526$ from a global fit to ATLAS and CMS data.
• The production cross section for $pp \to 2a + h$ at $\sqrt{s} = 13~{\rm TeV}$ LHC is approximately $10~{\rm fb}$ for a dark matter mass of $100~{\rm GeV}$.
• The model avoids tree-level direct detection due to the absence of a vacuum expectation value for the complex singlet and the protection of the CP-odd component by a hidden $Z_2$ symmetry.
• The model remains viable despite no direct detection signal, with potential discovery possible at the LHC in the mono-Higgs channel.