A new purpose for the $W$-boson mass measurement: searching for New Physics in lepton+$MET$

We show that the $m_W$ measurement is a direct probe of New Physics (NP) contributing to lepton and missing transverse momentum ($\ell+MET$), independently from indirect tests via the electroweak fit. Such NP modifies the kinematic distributions used to extract $m_W$, necessitating a simultaneous fit to $m_W$ and NP. This effect can in principle bias the $m_W$ measurement, but only to a limited extent for our considered models. Given that, we demonstrate that the agreement at high-precision with SM-predicted shapes results in bounds competitive to, if not exceeding, existing ones for two examples: anomalous $W$ decay involving a $L_{\mu} - L_{\tau}$ gauge boson and $\tilde{\nu}_{l} \tilde{l}$ production in the MSSM.