$E_T^e$ distributions of electron candidate events, background contributions, and sum of backgrounds and $W \rightarrow e\nu$ MC signal in the BEMC region for $-0.5 < \eta_e < 0$.

$E_T^e$ distributions of electron candidate events, background contributions, and sum of backgrounds and $W \rightarrow e\nu$ MC signal in the BEMC region for $0 < \eta_e < 0.5$.

$E_T^e$ distributions of electron candidate events, background contributions, and sum of backgrounds and $W \rightarrow e\nu$ MC signal in the BEMC region for $0.5 < \eta_e < 1.1$.

$E_T^e$ distributions of positron candidate events, background contributions, and sum of backgrounds and $W \rightarrow e\nu$ MC signal in the BEMC region for $-1.1 < \eta_e < -0.5$.

$E_T^e$ distributions of positron candidate events, background contributions, and sum of backgrounds and $W \rightarrow e\nu$ MC signal in the BEMC region for $-0.5 < \eta_e < 0$.

$E_T^e$ distributions of positron candidate events, background contributions, and sum of backgrounds and $W \rightarrow e\nu$ MC signal in the BEMC region for $0 < \eta_e < 0.5$.

$E_T^e$ distributions of positron candidate events, background contributions, and sum of backgrounds and $W \rightarrow e\nu$ MC signal in the BEMC region for $0.5 < \eta_e < 1.1$.

Signed $p_{T}$-balance distributions for electron candidate events, background contributions, and sum of backgrounds and $W \rightarrow e\nu$ MC signal in the EEMC region.

Signed $p_{T}$-balance distributions for positron candidate events, background contributions, and sum of backgrounds and $W \rightarrow e\nu$ MC signal in the EEMC region.

Longitudinal single-spin asymmetries, $A_L$, for $W^+$ production as a function of the positron pseudorapidity, $\eta_e$ for the STAR 2011+2012 data samples for 25 $< E_T^e <$ 50 GeV.

Longitudinal single-spin asymmetries, $A_L$, for $W^-$ production as a function of the electron pseudorapidity, $\eta_e$ for the STAR 2011+2012 data samples for 25 $< E_T^e <$ 50 GeV.

Longitudinal single-spin asymmetries, $A_L$, for $W^+$ production as a function of the positron pseudorapidity, $\eta_e$ for the STAR 2013 data samples for 25 $< E_T^e <$ 50 GeV.

Longitudinal single-spin asymmetries, $A_L$, for $W^-$ production as a function of the electron pseudorapidity, $\eta_e$ for the STAR 2013 data samples for 25 $< E_T^e <$ 50 GeV.

Longitudinal single-spin asymmetries, $A_L$, for $W^+$ production as a function of the lepton pseudorapidity, $\eta_e$ for the combined 2011+2012 and 2013 STAR data samples for 25 $< E_T^e <$ 50 GeV.

Longitudinal single-spin asymmetries, $A_L$, for $W^-$ production as a function of the lepton pseudorapidity, $\eta_e$ for the combined 2011+2012 and 2013 STAR data samples for 25 $< E_T^e <$ 50 GeV.

The difference of the light sea-quark polarizations $x(\Delta \bar{u} - \Delta \bar{d})$ as a function of $x$ at a scale $Q^2$ = 10 (GeV/c)$^2$. The table shows original NNPDFpol1.1 results, and NNPDFpol1.1rw presents the corresponding distribution after the 2013 $W$ data are included by reweighting.