[Paper Review] New $W$-Boson mass in the light of doubly warped braneworld model

Basabendu Barman, Ashmita Das+1 more|arXiv (Cornell University)|May 3, 2022

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes that the recently measured $W$-boson mass excess by the CDF collaboration—76 MeV above the Standard Model prediction—can be explained within a 6-dimensional doubly warped braneworld model. By placing all Standard Model fields in the bulk and leveraging two warping scales, the lowest-lying Kaluza-Klein mode of the bulk $W$ boson naturally acquires the observed mass of $80,433.5 \pm 9.4$ MeV on the visible brane, while preserving the gauge hierarchy solution without introducing intermediate energy scales.

ABSTRACT

The recent observation by CDF collaboration has disclosed a modification in the mass of the $W$ boson. In this regard we show that this modification in the mass of the $W$ boson can be well explained in the background of a 6-dimensional warped geometry model, where the double warping is associated with the two extra spatial dimensions. We consider that all the Standard Model fields are residing in the bulk, where the bulk Higgs field gives rise to the spontaneous symmetry breaking in the 6-dimensional spacetime. Allowing a little hierarchy between the two moduli we exactly obtain the observed mass for the $W$ boson, which is identified as the lowest lying Kaluza-Klein mass mode of the bulk $W$ boson on the $(3+1)$ dimensional visible brane. The essential feature of the 5-dimensional Randall-Sundrum scenario such as the resolution of the gauge hierarchy problem without introducing any intermediate scale between the Planck and the TeV scale, remains intact.

Motivation & Objective

• To explain the $76$ MeV excess in the $W$-boson mass measured by the CDF collaboration, which deviates by $7\sigma$ from the Standard Model prediction.
• To explore whether a 6-dimensional warped geometry model with two extra spatial dimensions can naturally generate the observed $W$-boson mass without introducing an intermediate scale between the Planck and TeV scales.
• To maintain the resolution of the hierarchy problem via the warp factor on the visible brane, while ensuring compatibility with precision electroweak constraints and Tevatron bounds.
• To demonstrate that the model's parameter space, particularly the ratio of moduli, can be tuned to reproduce the exact CDF measurement without fine-tuning.

Proposed method

• Employing a 6-dimensional doubly warped geometry model with flat $(3+1)$-dimensional branes, extending the Randall-Sundrum scenario to two extra dimensions.
• Placing all Standard Model fields, including the Higgs field, in the bulk to allow spontaneous symmetry breaking in 6D spacetime.
• Using Kaluza-Klein reduction to compute the mass spectrum of the $W$ boson, identifying the lowest-lying KK mode as the physical $W$ boson on the visible brane.
• Adjusting the two moduli parameters—$k \sim 0.25$ and a hierarchy $R_y / r_z \sim \mathcal{O}(10)$—to reproduce the observed $W$-boson mass.
• Applying the Goldberger-Wise stabilization mechanism in 6D to stabilize both moduli without unnatural fine-tuning, following Bhaumik and SenGupta (2022).
• Verifying that the resulting gauge couplings, KK masses, and precision electroweak constraints are satisfied under the same parameter set.

Experimental results

Research questions

• RQ1 Can a 6-dimensional doubly warped braneworld model with bulk SM fields reproduce the CDF II $W$-boson mass measurement of $80,433.5 \pm 9.4$ MeV?
• RQ2 Does this model preserve the resolution of the hierarchy problem via a warp factor of $\sim 10^{-16}$ on the visible brane, without introducing an intermediate scale?
• RQ3 Can the model satisfy precision electroweak constraints and Tevatron bounds on KK states while generating a $W$-boson mass $\sim 76$ MeV heavier than the SM prediction?
• RQ4 Is the observed $W$-boson mass achievable through a controlled hierarchy between the two moduli in the 6D geometry, without fine-tuning?

Key findings

• The lowest-lying Kaluza-Klein mode of the bulk $W$ boson in the 6D doubly warped model reproduces the CDF II measured mass of $80,433.5 \pm 9.4$ MeV exactly, within experimental uncertainty.
• The model achieves this result with a warp factor on the visible brane of $\sim 10^{-16}$, preserving the solution to the hierarchy problem without introducing any intermediate energy scale.
• A hierarchy of $R_y / r_z \sim \mathcal{O}(10)$ between the two moduli, along with $k \sim 0.25$, is sufficient to generate the observed $W$-boson mass.
• The model respects precision electroweak constraints and Tevatron bounds on KK states, as previously shown in Das et al. (2011), under the same parameter set.
• The Goldberger-Wise stabilization mechanism in 6D ensures moduli stability without fine-tuning, supporting the viability of the chosen parameter values.
• The framework generalizes to higher dimensions, suggesting that multi-warped extra dimensions could provide a natural mechanism for explaining the $W$-boson mass anomaly.