  The sea quark contribution to the nucleon spin is an important piece for a
complete understanding of the nucleon spin structure. The production of $W$
bosons in longitudinally polarized $p + p$ collisions at RHIC provides an
unique probe for the sea quark polarization, through the parity-violating
single-spin asymmetry, $A_L$. At the STAR experiment, $W$ bosons can be
effectively detected through the leptonic decay channel $W \to e \nu $ with the
Electromagnetic Calorimeters and Time Projection Chamber at mid-rapidity. The
previous STAR measurements of $A_L$ for $W$ boson production from datasets
taken in 2011 and 2012 have provided significant constraints on the helicity
distribution functions of $\bar u$ and $\bar d$ quarks. In 2013 the STAR
experiment collected $p+p$ data with an integrated luminosity of about 250
pb$^{-1}$ at $\sqrt s$ = 510 GeV with an average beam polarization of about
$56\%$, which is about three times the total integrated luminosity of previous
years. The final $A_L$ results from the STAR 2013 data sample are presented and
are also combined with previous 2011+2012 results. The comparison with
theoretical expectations suggests a flavor asymmetry with $\Delta \bar{u}(x)$
$>$$\Delta \bar{d}(x)$ for sea quark helicity distributions with $0.05 < x <
0.25$.
