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

The STAR experiment at RHIC has provided significant contributions to our understanding of the structure of the proton. The STAR experiment is well equipped to measure $W^\pm\rightarrowe^\pm+\nu$ in $\sqrt{s}=510$ GeV longitudinally polarized $p+p$ collisions. The longitudinal single spin asymmetry in W production, $A_L$, measured as a function of decay positron (electron) pseudo-rapidity $\eta$ for $W^+(W^-)$ is sensitive to the individual helicity polarizations of $u$ and $\bar{d}$ ($d$ and $\bar{u}$) quarks. Due to maximal violation of parity during the production, $W$ bosons couple to left-handed quarks and right-handed anti-quarks and hence offer direct probes of their respective helicity distributions in the nucleon. The published STAR $A_L$ results (2011, 2012 data combined) have been used by several theoretical analyses suggesting a significant impact in constraining the helicity distributions of $\bar{u}$, and $\bar{d}$ quarks. In 2013 STAR collected a dataset at $\sqrt{s}=510$ GeV with a total integrated luminosity of $\sim$300 pb$^{-1}$ with an average beam polarization of $\sim$54\%, a figure of merit three times larger than the dataset used by previous analyses. We will present preliminary results of STAR 2013 W $A_L$ measurement at mid-rapidity ($|\eta|<1$) region.