[Paper Review] The $W\ellν$-vertex corrections to W-boson mass in the R-parity violating MSSM

Min-Di Zheng, Feng-Zhi Chen+1 more|arXiv (Cornell University)|Apr 13, 2022

Particle physics theoretical and experimental studies8 citations

TL;DR

This paper investigates $W$-boson mass corrections in the R-parity violating minimal supersymmetric standard model (RPV-MSSM), focusing on $\lambda^\prime$-induced $W\ell\nu$ vertex corrections. It finds that while these vertex corrections alone cannot fully explain the CDF-II $7\sigma$ discrepancy, they can help reconcile the $m_W$ measurement with the $3\sigma$ level when combined with oblique corrections, offering a viable NP explanation within current experimental bounds.

ABSTRACT

Inspired by the astonishing $7σ$ discrepancy between the recent CDF-II measurement and the standard model prediction on the mass of $W$-boson, we investigate the $λ'$-corrections to the vertex of $μ oν_μe\bar{ν_e}$ decay in the context of the $R$-parity violating minimal supersymmetric standard model. These corrections can raise the $W$-boson mass independently. Combined with recent $Z$-pole and kaon decay measurements, $m_W \lesssim 80.37$ GeV can be reached. We find that these vertex corrections cannot explain the CDF result entirely at the $2σ$ and even $3σ$ levels. However, these corrections together with the oblique contributions can be accordant with the CDF-II result and relevant bounds at the $3σ$ level.

Motivation & Objective

• To investigate whether $\lambda^\prime$-induced $W\ell\nu$ vertex corrections in the RPV-MSSM can explain the $7\sigma$ discrepancy between the CDF-II $W$-boson mass measurement and the SM prediction.
• To assess the viability of these vertex corrections as a source of $W$-boson mass enhancement independent of oblique corrections.
• To determine whether the combined effects of $\lambda^\prime$ vertex corrections and oblique corrections in RPV-MSSM can accommodate the CDF-II result within experimental bounds.
• To constrain the parameter space of $\lambda^\prime$ couplings using $Z$-pole and kaon decay measurements.

Proposed method

• The study computes one-loop $W\ell\nu$ vertex corrections induced by the $\lambda^\prime\hat{L}\hat{Q}\hat{D}$ superpotential term in the RPV-MSSM.
• It uses the relation $m_W^2/m_Z^2 = \frac{1}{2} + \sqrt{\frac{1}{4} - \frac{\pi\alpha}{\sqrt{2}G_\mu m_Z^2}(1 + \Delta r)}$ to relate $m_W$ to the $\Delta r$ correction, decomposed into SM and NP contributions.
• The NP contribution $\Delta r$ is split into self-energy ($h^s$), vertex ($h^v$), and box ($h^b$) corrections, with $h^v$ dominated by $\lambda^\prime$-mediated diagrams.
• Numerical results are obtained using FeynHiggs-2.18.1 to compute $h^s$ for benchmark MSSM parameters, while $h^v$ is analytically derived as $h^\prime_{aa} \propto x_t f_W(x_t) |\tilde{\lambda}^\prime_{a33}|^2$.
• The combined effect of $h^s$ and $h^v$ is evaluated in the context of $Z$-pole and kaon decay constraints, with parameter scans over $M_{\tilde{Q}_3}, M_{\tilde{U}_3}, M_{\tilde{D}_3}, A_t, A_b$.
• The model's predictions are compared to the CDF-II $m_W = 80.4335 \pm 0.0094$ GeV and SM prediction $m_W^{\rm SM} = 80.357 \pm 0.006$ GeV at $2\sigma$ and $3\sigma$ levels.

Experimental results

Research questions

• RQ1 Can $\lambda^\prime$-induced $W\ell\nu$ vertex corrections in the RPV-MSSM raise the $W$-boson mass sufficiently to explain the CDF-II anomaly?
• RQ2 To what extent do these vertex corrections alone reconcile with the $m_W$ discrepancy at the $2\sigma$ and $3\sigma$ levels?
• RQ3 Can the combination of $\lambda^\prime$ vertex corrections and oblique corrections in RPV-MSSM explain the CDF-II $m_W$ measurement while satisfying $Z$-pole and kaon decay constraints?
• RQ4 What is the allowed parameter space for $\tilde{\lambda}^\prime_{a33}$ coupling that enables $m_W$ enhancement within experimental bounds?

Key findings

• Pure $\lambda^\prime$-induced $W\ell\nu$ vertex corrections alone cannot explain the CDF-II $W$-boson mass measurement at the $2\sigma$ level, and even fail at the $3\sigma$ level.
• The vertex corrections contribute an enhancement of $\sim 0.0742 \times x_t f_W(x_t) |\tilde{\lambda}^\prime_{a33}|^2$ GeV to $m_W$, with $x_t = m_t^2 / m_{\tilde{t}}^2$.
• When combined with oblique corrections ($h^s \approx -8 \times 10^{-4}$), the model can raise $m_W$ to approximately 80.38 GeV within the $3\sigma$ allowed region of $Z$-pole and kaon decay constraints.
• The $3\sigma$-compatible region for explaining the CDF-II result exists only in a narrow overlap near the upper edge of the $m_W^{\rm CDF}$ measurement range.
• The benchmark point with $M_{\tilde{Q}_3} = 2.1$ TeV, $M_{\tilde{U}_3} = 10$ TeV, and $A_t = A_b = 1.5$ TeV yields a $m_W^{\rm NP} \approx 80.370 + 0.0742 x_t f_W(x_t) |\tilde{\lambda}^\prime_{a33}|^2$ GeV, consistent with $m_W^{\rm CDF}$ at $3\sigma$ when combined with oblique effects.
• The study confirms that $\lambda^\prime$ vertex corrections are insufficient alone but can play a complementary role in explaining the $m_W$ anomaly when combined with other NP contributions in the RPV-MSSM framework.