Measurement of longitudinal single-spin asymmetries for $W^{\pm}$ boson production in polarized $p+p$ collisions at $\sqrt{s}=510$ GeV at RHIC

$W^\pm$ boson production in longitudinally polarized $p+p$ collisions provides unique and clean access to the individual helicity polarizations of quarks and antiquarks in the colliding protons. Due to maximal violation of parity in the production, $W^\pm$ bosons couple to left-handed quarks and right-handed anti quarks and hence offer direct probes of their respective helicity distributions in the nucleon. These can be observed in measured large parity-violating longitudinal single-spin asymmetries $A_L$, as a function of decay lepton pseudo-rapidity $\eta$, for $W^\pm$ boson production at the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The final results of W $A_L$ measured between $|\eta|<1.1$ at $\sqrt{s}=510$ GeV from the dataset collected in 2011 and 2012 running periods with an integrated luminosity of 86 pb$^{-1}$ and an average beam polarization of $\sim$55\% will be presented. The status for the analysis of W $A_L$ from the larger dataset collected during 2013 (more than 3 times of 2012) at $\sqrt{s}=510$ GeV with an average beam polarization of $\sim$54\% will be reported.