[Paper Review] Explaining the $W$ boson mass anomaly and dark matter with a $U(1)$ dark sector

Kai-Yu Zhang, Wan-Zhe Feng|arXiv (Cornell University)|Apr 17, 2022

Dark Matter and Cosmic Phenomena4 citations

TL;DR

This paper proposes a U(1) dark sector extension of the Standard Model to explain the CDF collaboration's 7σ anomaly in the W boson mass and provide a dark matter candidate. It shows that a U(1)_{A Y + B q} extension with mixed hypercharge and baryon number symmetry can generate a 77 MeV enhancement in the W boson mass, while a pure kinetic mixing model only allows ~10 MeV. The model also provides a viable fermionic dark matter candidate with mass in the few-hundred GeV to TeV range.

ABSTRACT

The $W$ boson mass recently reported by the CDF collaboration shows a deviation from the standard model prediction with an excess at $7σ$ level. We investigate two simple extensions of the standard model with an extra $U(1)$ dark sector. One is the $U(1)_x$ extension, where the $U(1)_x$ gauge field mixes with the standard model through gauge kinetic terms. The other is a general $U(1)_{\mathbf{A} Y+\mathbf{B} q}$ extension of the standard model. Fitting various experimental constraints we find the $U(1)_x$ extension with only kinetic mixing can enhance the $W$ boson mass for at most 10~MeV. While the $U(1)_{\mathbf{A} Y+\mathbf{B} q}$ extension can easily generate 77~MeV enhancement of the $W$ boson mass and also offer a viable dark matter candidate with mass ranging from several hundred GeV to TeV, which may be detected by future dark matter direct detection experiments with improved sensitivities.

Motivation & Objective

• Explain the 7σ deviation in the CDF measurement of the W boson mass from the Standard Model prediction.
• Provide a viable dark matter candidate consistent with cosmological relic density and direct/indirect detection constraints.
• Investigate whether a U(1) dark sector with kinetic mixing or generalized U(1) symmetry can simultaneously resolve the W boson mass anomaly and provide dark matter.
• Assess the viability of the models under electroweak precision tests, particularly Z boson decay width constraints.
• Determine the maximum possible W boson mass enhancement achievable in each model under current experimental constraints.

Proposed method

• Construct a U(1)_x extension of the SM with kinetic mixing between the dark U(1)_x gauge boson and the SM hypercharge U(1)_Y via a gauge kinetic term.
• Use the S, T, U oblique parameters formalism to compute corrections to the W boson mass from new physics contributions in the dark sector.
• Implement a generalized U(1)_{A Y + B q} symmetry where the new U(1) is a linear combination of hypercharge and baryon number, allowing for enhanced mixing effects.
• Calculate the effective couplings of the Z boson to SM fermions in both models using the mixing angle and kinetic mixing parameters.
• Compute the Z boson decay width into fermion pairs and compare with the experimental value to constrain the models.
• Evaluate the dark matter relic density via annihilation into SM fermions via the Z' portal, and compare with direct and indirect detection bounds.

Experimental results

Research questions

• RQ1 Can a U(1) dark sector with kinetic mixing explain the 77 MeV enhancement in the W boson mass observed by CDF?
• RQ2 What is the maximum W boson mass enhancement achievable in a pure kinetic mixing U(1)_x model under current experimental constraints?
• RQ3 Can the U(1)_{A Y + B q} extension generate a 77 MeV W boson mass shift while remaining consistent with electroweak precision observables?
• RQ4 Does the U(1)_{A Y + B q} model provide a viable fermionic dark matter candidate with mass in the 100 GeV–TeV range?
• RQ5 How do direct and indirect dark matter detection constraints shape the viable parameter space of the dark matter candidate in the U(1)_{A Y + B q} model?

Key findings

• The pure kinetic mixing U(1)_x model can enhance the W boson mass by at most 10 MeV, insufficient to explain the 77 MeV CDF anomaly.
• The U(1)_{A Y + B q} model can generate a 77 MeV enhancement in the W boson mass, matching the CDF measurement within 1σ uncertainty.
• The Z boson decay width in both models remains within the experimental error bars (±0.0023 GeV), with deviations of only 0.7–1.0 MeV, indicating compatibility with electroweak precision data.
• The U(1)_{A Y + B q} model provides a fermionic dark matter candidate with mass ranging from several hundred GeV to 1 TeV, consistent with the observed relic density.
• Benchmark points in the U(1)_{A Y + B q} model satisfy current direct and indirect dark matter detection constraints, with prospects for future detection in upcoming experiments.
• The model remains viable under electroweak precision tests, as the modified Z boson decay width remains within the 2.4952 ± 0.0023 GeV experimental range.