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Constraining Sea Quark Distributions Through $W^{\pm}$ Cross Section Ratios Measured at STAR

Over the past several years the STAR experiment at RHIC has been contributing to our understanding of the proton structure. Through its instrumentation, STAR is well equipped to measure $W \rightarrow ν+ e$ in $\sqrt{s}$ = 500/510 GeV proton-proton collisions at mid-rapidity (-1.1 $\le η\le $ 1.1) . The $W$ cross section ratio ($W^+/W^-$) is sensitive to unpolarized $u$, $d$, $\bar{u}$, and $\bar{d}$ quark distributions. At these kinematics, STAR is able to measure the quark distributions near Bjorken-$x$ values of 0.1. The RHIC runs in 2011, 2012 and 2013 at $\sqrt{s}$ = 500/510 GeV saw a significant increase in delivered luminosity from previous years. This resulted in a total data sample being collected of about 352 pb$^{-1}$ of integrated luminosity. The increased statistics will lead to a higher precision measurement of the $W^+/W^-$ cross section ratio than was previously measured by STAR's 2009 run, as well as allow for a measurement of its $η$ dependence at mid-rapidity. Presented here is an update of the $W$ cross section ratio analysis from the STAR 2011, 2012 and 2013 runs.