[Paper Review] $Z$ boson mixing and the mass of the $W$ boson

Y. Zeng, Chengfeng Cai+2 more|arXiv (Cornell University)|Apr 19, 2022

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes that tree-level mixing between the Z boson and an extra gauge boson can explain the measured $W$ boson mass excess observed by the CDF collaboration. In the Derivative Portal Dark Matter model, a viable parameter space exists that reproduces the $W$ boson mass, dark matter relic density, and constraints from oblique parameters and indirect detection, with the extra boson near 120 GeV. The U(1) extension model can only contribute ~27 MeV to the $W$ mass due to stringent oblique parameter constraints.

ABSTRACT

We explore the possibility of explaining the $W$ boson mass with an extra gauge boson mixing with the $Z$ boson at tree level. Extra boson mixing with the $Z$ boson will change the expression of the $Z$ boson mass, thus altering the $W$ boson mass. We explore two models in this work. We find that in the Derivative Portal Dark Matter model, there are parameters space which can give the observed $W$ boson mass, as well as the observed Dark Matter relic density. These parameters space can also fulfill the constraints from the electroweak oblique parameters and Dark Matter indirect detection. In the U(1) extension model, the kinetic mixing between extra boson and $B$ boson can also give the observed $W$ boson mass. However, to fulfill electroweak oblique parameters fit the kinetic mixing in the U(1) model can only contribute about $27~\mathrm{MeV}$ extra mass to the Standard Model $W$ boson mass. Both models indicate the extra vector boson with the best fit mass around $120~\mathrm{GeV}$.

Motivation & Objective

• To explain the CDF measurement of the $W$ boson mass ($80.4335 \pm 0.0094$ GeV), which exceeds the SM prediction ($80.357 \pm 0.006$ GeV), indicating possible new physics.
• To investigate whether tree-level mixing between the $Z$ boson and an extra gauge boson can generate the observed $W$ boson mass enhancement.
• To assess the viability of two models—Derivative Portal Dark Matter (DPDM) and U(1) extension—under constraints from electroweak oblique parameters, dark matter relic density, and indirect detection.
• To determine the mass and coupling requirements of the extra vector boson that can simultaneously satisfy the $W$ boson mass measurement and multiple precision electroweak and dark matter constraints.

Proposed method

• Modeling the $Z$ boson mass via a $2\times2$ mass matrix that includes mixing with an extra vector boson, altering the $W$ boson mass through modified gauge couplings.
• Using the Fermilab CDF measurement of $m_W = 80.4335 \pm 0.0094$ GeV as a key input for fitting model parameters.
• Applying constraints from electroweak oblique parameters ($S$, $T$, $U$) to limit viable parameter space in both models.
• Including dark matter relic density and indirect detection constraints in the DPDM model to test cosmological viability.
• Performing a $\chi^2$ analysis to compare model predictions with global electroweak fits, particularly focusing on $S$, $T$, and $U$ parameters.
• Deriving analytical expressions for $T$ and $\chi^2$ in both models to understand the sensitivity of the fit to $s_w$ and mixing parameters.

Experimental results

Research questions

• RQ1 Can tree-level mixing between the $Z$ boson and an extra gauge boson explain the CDF $W$ boson mass measurement without violating other precision electroweak constraints?
• RQ2 What are the viable parameter regions in the Derivative Portal Dark Matter model that simultaneously reproduce the $W$ boson mass, dark matter relic density, and indirect detection limits?
• RQ3 To what extent can the U(1) extension model contribute to the $W$ boson mass enhancement while satisfying oblique parameter constraints?
• RQ4 Why do the $\chi^2$ contours differ significantly between the DPDM and U(1) models despite similar $T$-parameter behavior?
• RQ5 What is the predicted mass of the extra vector boson that best fits the $W$ boson mass anomaly in each model?

Key findings

• In the Derivative Portal Dark Matter model, a viable parameter space exists that reproduces the observed $W$ boson mass, the measured dark matter relic density, and satisfies constraints from oblique parameters and indirect detection.
• The extra vector boson in the DPDM model has a best-fit mass of approximately 120 GeV, consistent with the $W$ boson mass anomaly.
• In the U(1) extension model, the kinetic mixing with the $B$ boson can only contribute about 27 MeV to the $W$ boson mass due to strong constraints from the $S$ parameter.
• The $S$ parameter in the U(1) model deviates significantly from its central value ($0.005$) when the $W$ mass is enhanced, disfavoring large mass contributions.
• The $\chi^2$ in the DPDM model is more sensitive to changes in the $T$ parameter than in the U(1) model, leading to a more constrained and distinct $\chi^2$ contour shape.
• The $T$ parameter in the U(1) model is weakly dependent on the mixing parameter $\epsilon$ when $s_w$ is fixed, but increases in the lower-left region of the contour, indicating a trade-off between $s_w$ and $\epsilon$ to maintain a good fit.