The \(W\ell \nu\)-vertex corrections to W-boson mass in the R-parity violating MSSM

Inspired by the astonishing \(7\sigma\) discrepancy between the recent CDF-II measurement and the standard model prediction on the mass of W-boson, we investigate the \(\lambda '\)-corrections to the vertex of \(\mu \rightarrow \nu _\mu e\bar{\nu _e}\) 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 \(2\sigma\) and even \(3\sigma\) levels. However, these corrections together with the oblique contributions can be accordant with the CDF-II result and relevant bounds at the \(3\sigma\) level.