Probing Sea Quark Polarization in the Proton With A$_L$ in the $W \rightarrow \mu$ Decay Channel

The Relativistic Heavy Ion Collider (RHIC) is the only polarized hadron collider in the world - it offers us a unique opportunity to study nucleon spin structure. In this talk, I will present a study how we constrain the contribution of sea-quark polarization to the proton spin in the context of PHENIX's W-Physics program. This year, the W-Physics program at PHENIX has accumulated $240 pb^{-1}$ of longitudinally polarized p+p data at $\sqrt{s}$ = 510 GeV. I will describe the analysis of this data set, focusing on PHENIX's forward muon detectors at $ 1.2 < |\eta| < 2.2 $ , and discuss how we exploit the kinematics of the $W \rightarrow \mu$ decay in order to learn about sea-quark polarization with $A_L$.