Measurement of the longitudinal spin asymmetries for weak boson production in proton-proton collisions at $\sqrt{s}$ = 5100 GeV

Figure 1: Distribution of the product of Q, the TPC reconstructed charge-sign, and ET /pT in the BEMC (a) and EEMC (b) regions. The positron (red) and electron (blue) candidate events have been fitted with double-Gaussian distributions. The excluded regions are marked by hatched shades.

(a) BEMC
Q*ET/pT data
-3.92 0.0±0.0
-3.76 1.0±1.0
-3.60 1.0±1.0
-3.44 2.0±1.4
-3.28 1.0±1.0
-3.12 4.0±2.0
-2.96 7.0±2.6
-2.80 6.0±2.4
-2.64 11.0±3.3
-2.48 15.0±3.9
-2.32 15.0±3.9
-2.16 19.0±4.4
-2.00 22.0±4.7
-1.84 36.0±6.0
-1.68 58.0±7.6
-1.52 86.0±9.3
-1.36 210.0±14.5
-1.20 333.0±18.2
-1.04 463.0±21.5
-0.88 356.0±18.9
-0.72 253.0±15.9
-0.56 185.0±13.6
-0.40 120.0±11.0
-0.24 68.0±8.2
-0.08 55.0±7.4
0.08 47.0±6.9
0.24 82.0±9.1
0.40 166.0±12.9
0.56 391.0±19.8
0.72 844.0±29.1
0.88 1318.0±36.3
1.04 1506.0±38.8
1.20 1270.0±35.6
1.36 870.0±29.5
1.52 558.0±23.6
1.68 414.0±20.3
1.84 245.0±15.7
2.00 159.0±12.6
2.16 132.0±11.5
2.32 70.0±8.4
2.48 74.0±8.6
2.64 37.0±6.1
2.80 41.0±6.4
2.96 25.0±5.0
3.12 19.0±4.4
3.28 18.0±4.2
3.44 5.0±2.2
3.60 5.0±2.2
3.76 3.0±1.7
3.92 1.0±1.0

(b) EEMC
Q*ET/pT data
-3.90 1.0±1.0
-3.70 2.0±1.4
-3.50 4.0±2.0
-3.30 7.0±2.6
-3.10 1.0±1.0
-2.90 6.0±2.4
-2.70 3.0±1.7
-2.50 7.0±2.6
-2.30 7.0±2.6
-2.10 12.0±3.5
-1.90 6.0±2.4
-1.70 11.0±3.3
-1.50 19.0±4.4
-1.30 23.0±4.8
-1.10 29.0±5.4
-0.90 19.0±4.4
-0.70 26.0±5.1
-0.50 19.0±4.4
-0.30 15.0±3.9
-0.10 13.0±3.6
0.10 14.0±3.7
0.30 15.0±3.9
0.50 14.0±3.7
0.70 23.0±4.8
0.90 31.0±5.6
1.10 24.0±4.9
1.30 18.0±4.2
1.50 14.0±3.7
1.70 12.0±3.5
1.90 7.0±2.6
2.10 9.0±3.0
2.30 4.0±2.0
2.50 3.0±1.7
2.70 6.0±2.4
2.90 4.0±2.0
3.10 0.0±0.0
3.30 1.0±1.0
3.50 1.0±1.0
3.70 1.0±1.0
3.90 2.0±1.4

Figure 2: $E_T^e$ distributions of electron (top) and positron (bottom) candidate events (black), background contributions, and sum of backgrounds and $W \rightarrow e\nu$ MC signal (red-dashed) in the BEMC region.

Panel of Electron (-1.1, -0.5)
E_T Z -> ee W->tau->e 2nd eemc data-driven QCD W->env MC data
11 0.0 0.0 0.0 0.0 0.0 0.0±0.0
13 0.0 0.0 0.0 0.0 0.0 0.0±0.0
15 3.5 4.5 195.3 118.9 3.4 344.0±18.5
17 1.9 3.8 108.3 71.1 6.0 175.0±13.2
19 3.0 3.0 53.5 37.6 10.3 108.0±10.4
21 1.3 2.7 26.3 19.4 13.2 74.0±8.6
23 0.9 4.2 22.7 12.3 16.9 59.0±7.7
25 0.8 3.5 14.4 6.9 19.1 51.0±7.1
27 1.0 2.6 5.9 3.8 22.8 42.0±6.5
29 0.4 2.1 9.0 2.6 31.7 34.0±5.8
31 1.1 1.2 2.3 1.7 36.8 52.0±7.2
33 0.7 0.9 -0.9 1.5 43.8 42.0±6.5
35 0.7 0.5 5.2 0.8 50.9 66.0±8.1
37 0.5 0.2 1.7 0.6 61.2 58.0±7.6
39 0.3 0.0 2.5 0.3 54.5 70.0±8.4
41 0.6 0.0 -1.1 0.3 30.7 45.0±6.7
43 0.9 0.1 0.2 0.4 11.5 27.0±5.2
45 0.8 0.0 1.9 0.3 3.9 14.0±3.7
47 0.4 0.0 0.4 0.1 1.6 11.0±3.3
49 0.5 0.0 0.7 0.2 0.3 3.0±1.7
51 0.1 0.0 -0.2 0.1 0.5 0.0±0.0
53 0.1 0.0 -0.1 0.1 0.0 1.0±1.0
55 0.0 0.0 -0.1 0.0 0.2 0.0±0.0
57 0.0 0.0 0.0 0.1 0.1 1.0±1.0
59 0.0 0.0 0.0 0.0 0.0 0.0±0.0

Panel of Electron eta (-0.5, 0.0)
E_T Z -> ee W->tau->e 2nd eemc data-driven QCD W->env MC data
11 0.0 0.0 0.0 0.0 0.0 0.0±0.0
13 0.0 0.0 0.0 0.0 0.0 0.0±0.0
15 1.8 3.0 67.8 93.1 2.3 176.0±13.3
17 1.9 4.2 41.0 58.8 2.0 100.0±10.0
19 1.1 5.2 29.9 32.4 3.8 61.0±7.8
21 1.9 3.7 14.4 19.1 5.5 39.0±6.2
23 2.7 3.3 7.5 12.6 7.6 27.0±5.2
25 2.2 3.5 5.0 7.6 13.1 20.0±4.5
27 2.1 3.0 4.5 4.6 18.6 34.0±5.8
29 2.3 3.0 4.0 3.1 23.4 19.0±4.4
31 2.1 1.5 3.1 1.6 33.3 28.0±5.3
33 1.6 1.3 4.9 2.0 43.0 42.0±6.5
35 1.7 0.7 2.0 0.7 60.8 66.0±8.1
37 1.5 0.8 6.7 1.3 76.0 90.0±9.5
39 2.0 0.1 0.4 0.3 77.0 73.0±8.5
41 1.0 0.0 2.9 0.3 47.1 49.0±7.0
43 0.6 0.0 1.4 0.2 19.4 40.0±6.3
45 0.3 0.0 3.5 0.2 6.9 16.0±4.0
47 0.1 0.1 2.2 0.2 2.7 5.0±2.2
49 0.0 0.0 -0.2 0.2 0.6 2.0±1.4
51 0.0 0.0 0.8 0.0 0.7 1.0±1.0
53 0.0 0.0 1.8 0.2 0.8 0.0±0.0
55 0.0 0.0 -0.1 0.2 0.2 0.0±0.0
57 0.0 0.0 0.0 0.2 0.3 0.0±0.0
59 0.0 0.0 -0.2 0.1 0.1 0.0±0.0

Panel of Electron (0.0, 0.5)
E_T Z -> ee W->tau->e 2nd eemc data-driven QCD W->env MC data
11 0.0 0.0 0.0 0.0 0.0 0.0±0.0
13 0.0 0.0 0.0 0.0 0.0 0.0±0.0
15 1.8 3.3 51.5 100.2 1.8 166.0±12.9
17 1.9 4.7 37.7 63.5 2.6 103.0±10.1
19 0.7 4.3 31.4 37.7 4.0 61.0±7.8
21 1.1 4.6 14.4 22.1 6.5 36.0±6.0
23 2.6 3.7 13.3 13.1 8.3 31.0±5.6
25 1.6 3.9 5.2 7.7 12.3 29.0±5.4
27 1.8 3.2 4.3 5.2 18.5 29.0±5.4
29 2.2 2.6 7.5 3.4 24.0 35.0±5.9
31 1.3 2.1 7.4 1.8 33.6 40.0±6.3
33 0.1 1.4 7.0 2.0 44.5 42.0±6.5
35 0.3 1.1 0.1 1.0 63.4 61.0±7.8
37 1.4 0.7 2.9 0.8 83.9 77.0±8.8
39 0.5 0.3 1.9 0.9 83.5 71.0±8.4
41 0.9 0.1 0.8 0.2 45.7 65.0±8.1
43 0.5 0.1 0.5 0.2 20.2 29.0±5.4
45 0.4 0.0 0.1 0.2 7.7 19.0±4.4
47 0.3 0.0 -0.8 0.3 1.8 5.0±2.2
49 0.0 0.0 0.6 0.3 1.3 5.0±2.2
51 0.0 0.0 -0.1 0.2 0.3 0.0±0.0
53 0.0 0.0 0.0 0.1 0.3 0.0±0.0
55 0.0 0.0 0.0 0.0 0.2 1.0±1.0
57 0.0 0.0 -0.1 0.3 0.2 0.0±0.0
59 0.0 0.0 0.0 0.0 0.1 2.0±1.4

Panel of Electron eta (0.5, 1.1)
E_T Z -> ee W->tau->e 2nd eemc data-driven QCD W->env MC data
11 0.0 0.0 0.0 0.0 0.0 0.0±0.0
13 0.0 0.0 0.0 0.0 0.0 0.0±0.0
15 2.2 3.0 145.0 101.1 3.3 275.0±16.6
17 1.9 4.6 78.2 61.6 5.9 132.0±11.5
19 2.0 4.0 51.7 35.2 9.1 75.0±8.7
21 1.3 4.5 25.4 17.6 12.3 79.0±8.9
23 2.5 3.8 13.8 12.2 18.4 42.0±6.5
25 1.0 3.5 6.8 7.7 20.8 46.0±6.8
27 0.9 2.4 3.9 3.8 25.8 54.0±7.3
29 1.5 2.0 1.9 3.1 34.1 51.0±7.1
31 1.3 1.7 3.4 1.8 41.6 52.0±7.2
33 0.6 1.0 3.9 1.7 51.6 74.0±8.6
35 1.0 0.4 1.9 0.9 59.5 80.0±8.9
37 0.5 0.3 1.0 0.3 61.5 84.0±9.2
39 0.8 0.4 0.7 0.4 59.5 72.0±8.5
41 0.3 0.0 1.4 0.1 33.2 47.0±6.9
43 0.3 0.1 0.0 0.3 12.1 28.0±5.3
45 0.2 0.0 0.2 0.3 4.7 14.0±3.7
47 0.1 0.0 -0.2 0.3 3.1 7.0±2.6
49 0.0 0.0 1.0 0.3 0.8 2.0±1.4
51 0.0 0.0 2.5 0.1 0.4 1.0±1.0
53 0.0 0.0 0.0 0.2 0.3 1.0±1.0
55 0.0 0.0 0.0 0.0 0.2 0.0±0.0
57 0.0 0.0 -0.1 0.0 0.0 0.0±0.0
59 0.0 0.0 0.0 0.0 0.1 0.0±0.0

Panel of Positron eta (-1.1, -0.5)
E_T Z -> ee W->tau->e 2nd eemc data-driven QCD W->env MC data
11 0.0 0.0 0.0 0.0 0.0 0.0±0.0
13 0.0 0.0 0.0 0.0 0.0 0.0±0.0
15 1.7 13.6 255.9 153.3 36.2 458.0±21.4
17 1.8 11.5 144.9 92.0 49.8 314.0±17.7
19 2.0 13.1 93.2 48.6 61.8 208.0±14.4
21 1.6 13.5 42.5 25.1 70.3 180.0±13.4
23 1.5 11.3 23.6 15.9 77.3 146.0±12.1
25 1.5 10.9 21.9 8.9 89.1 117.0±10.8
27 1.0 7.7 14.4 5.0 95.4 129.0±11.4
29 0.7 5.7 10.5 3.3 100.4 133.0±11.5
31 1.4 4.0 8.3 2.2 112.1 132.0±11.5
33 1.3 2.5 3.1 2.0 130.4 154.0±12.4
35 1.1 1.5 2.5 1.1 152.8 181.0±13.5
37 0.3 1.1 3.5 0.9 179.3 215.0±14.7
39 0.8 0.5 1.5 0.4 172.9 168.0±13.0
41 0.8 0.2 4.6 0.4 96.7 108.0±10.4
43 1.1 0.0 4.2 0.5 37.7 60.0±7.7
45 0.2 0.0 1.7 0.4 13.6 34.0±5.8
47 0.4 0.0 -1.1 0.1 4.8 19.0±4.4
49 0.3 0.1 2.2 0.2 2.8 7.0±2.6
51 0.3 0.0 0.7 0.1 1.7 8.0±2.8
53 0.0 0.0 0.8 0.1 0.3 2.0±1.4
55 0.0 0.0 -0.1 0.0 0.5 1.0±1.0
57 0.1 0.0 0.0 0.1 0.5 0.0±0.0
59 0.0 0.0 0.0 0.0 0.2 1.0±1.0

Panel of Positron eta (-0.5, 0.0)
E_T Z -> ee W->tau->e 2nd eemc data-driven QCD W->env MC data
11 0.0 0.0 0.0 0.0 0.0 0.0±0.0
13 0.0 0.0 0.0 0.0 0.0 0.0±0.0
15 2.5 19.0 64.7 90.1 18.5 195.0±14.0
17 2.1 22.6 45.4 58.3 31.5 161.0±12.7
19 1.6 20.9 37.9 31.7 49.6 148.0±12.2
21 1.4 20.6 21.3 18.1 74.0 150.0±12.2
23 1.6 18.5 16.1 11.7 100.4 149.0±12.2
25 1.0 16.3 10.1 7.5 130.0 197.0±14.0
27 1.3 13.1 8.0 4.6 162.9 175.0±13.2
29 1.5 8.3 3.5 2.9 191.6 210.0±14.5
31 1.3 6.5 6.2 1.4 227.1 248.0±15.7
33 1.9 5.1 3.6 1.9 261.2 276.0±16.6
35 1.5 2.6 1.0 0.7 298.3 271.0±16.5
37 1.2 1.3 -0.9 1.2 324.7 284.0±16.9
39 0.8 0.5 3.1 0.2 278.0 263.0±16.2
41 1.2 0.5 2.4 0.3 165.8 182.0±13.5
43 0.8 0.1 -2.2 0.3 63.2 98.0±9.9
45 0.8 0.3 -0.1 0.2 25.6 51.0±7.1
47 0.6 0.3 2.3 0.1 9.7 15.0±3.9
49 0.2 0.0 0.7 0.2 4.8 8.0±2.8
51 0.0 0.0 -0.6 0.0 2.4 5.0±2.2
53 0.2 0.0 -0.1 0.2 1.2 5.0±2.2
55 0.0 0.0 -0.3 0.1 0.3 0.0±0.0
57 0.0 0.0 0.7 0.2 0.4 0.0±0.0
59 0.0 0.0 -0.1 0.1 0.3 0.0±0.0

Panel of Positron eta (0.0, 0.5)
E_T Z -> ee W->tau->e 2nd eemc data-driven QCD W->env MC data
11 0.0 0.0 0.0 0.0 0.0 0.0±0.0
13 0.0 0.0 0.0 0.0 0.0 0.0±0.0
15 1.1 21.5 78.7 96.5 22.0 206.0±14.4
17 0.8 19.8 58.4 61.4 35.1 191.0±13.8
19 1.4 20.3 16.0 36.4 55.3 146.0±12.1
21 2.0 22.0 15.3 21.4 78.1 151.0±12.3
23 1.5 18.9 21.0 12.7 108.6 197.0±14.0
25 2.2 16.2 10.5 7.3 142.1 174.0±13.2
27 2.2 11.8 8.7 4.9 172.1 216.0±14.7
29 1.8 9.3 6.8 3.3 207.3 231.0±15.2
31 1.9 8.6 5.0 1.6 242.4 237.0±15.4
33 0.9 4.8 5.1 1.8 284.5 308.0±17.5
35 0.4 3.2 -0.5 0.8 319.8 310.0±17.6
37 2.2 2.1 2.4 0.7 334.9 340.0±18.4
39 0.3 0.6 -4.8 0.8 298.7 278.0±16.7
41 0.6 0.2 4.1 0.2 164.2 193.0±13.9
43 0.4 0.1 -1.5 0.2 66.9 104.0±10.2
45 0.6 0.1 0.2 0.2 27.9 44.0±6.6
47 0.2 0.0 1.4 0.2 12.2 23.0±4.8
49 0.2 0.2 0.2 0.3 5.1 14.0±3.7
51 0.1 0.2 -0.4 0.2 3.2 7.0±2.6
53 0.0 0.0 -0.4 0.1 1.1 3.0±1.7
55 0.1 0.0 -0.3 0.0 0.8 2.0±1.4
57 0.1 0.0 -0.1 0.2 0.3 0.0±0.0
59 0.0 0.0 1.1 0.0 0.3 1.0±1.0

Panel of Positron eta (0.5, 1.1)
E_T Z -> ee W->tau->e 2nd eemc data-driven QCD W->env MC data
11 0.0 0.0 0.0 0.0 0.0 0.0±0.0
13 0.0 0.0 0.0 0.0 0.0 0.0±0.0
15 2.7 14.4 156.8 174.1 37.6 409.0±20.2
17 1.9 13.8 104.8 106.2 51.6 258.0±16.1
19 2.3 14.4 74.7 60.6 63.9 182.0±13.5
21 1.9 13.8 35.2 30.4 80.8 147.0±12.1
23 2.6 11.4 25.2 21.1 86.1 157.0±12.5
25 1.0 9.7 26.3 13.3 90.6 153.0±12.4
27 1.1 9.5 8.3 6.5 106.2 132.0±11.5
29 1.3 6.7 6.0 5.4 112.0 147.0±12.1
31 0.6 5.2 6.7 3.1 129.1 143.0±12.0
33 1.6 2.4 1.4 3.0 142.7 154.0±12.4
35 0.4 1.8 1.8 1.6 173.3 191.0±13.8
37 0.6 1.2 3.3 0.5 205.5 191.0±13.8
39 0.5 0.4 -4.1 0.7 184.9 192.0±13.9
41 0.9 0.0 2.1 0.2 109.2 135.0±11.6
43 1.0 0.1 0.2 0.5 47.7 72.0±8.5
45 0.4 0.1 1.3 0.5 15.9 26.0±5.1
47 0.2 0.0 -0.7 0.5 6.1 20.0±4.5
49 0.1 0.1 -0.9 0.5 3.2 11.0±3.3
51 0.0 0.0 -0.3 0.2 1.5 3.0±1.7
53 0.0 0.0 1.2 0.3 0.4 4.0±2.0
55 0.1 0.0 -0.1 0.1 0.6 1.0±1.0
57 0.0 0.0 0.0 0.0 0.0 1.0±1.0
59 0.0 0.0 0.0 0.0 0.1 2.0±1.4

Figure 3: Signed $p_{T}$-balance distributions for electron (left) and positron (right) candidate events (black crosses), background contributions, and sum of backgrounds and $W \rightarrow e\nu$ MC signal (red-dashed) in the EEMC region.

Panel of Electron |eta| (1.0, 2.0)
Signed pT-balance Z -> ee W->tau->e data-driven QCD W->env MC data
-38 0.1 0.0 0.1 0.0 0.0±0.0
-34 0.0 0.0 0.0 0.0 1.0±1.0
-30 0.3 0.0 0.3 0.0 0.0±0.0
-26 0.5 0.0 0.5 0.0 0.0±0.0
-22 0.4 0.0 0.4 0.0 0.0±0.0
-18 0.4 0.0 0.4 0.0 0.0±0.0
-14 0.4 0.0 0.4 0.0 2.0±1.4
-10 0.9 0.0 0.9 0.0 1.0±1.0
-6 2.4 0.0 4.4 0.0 3.0±1.7
-2 2.9 0.0 4.9 0.0 3.0±1.7
2 2.7 0.1 8.8 0.1 6.0±2.4
6 1.9 0.1 4.0 0.0 10.0±3.2
10 0.8 0.1 7.8 0.2 15.0±3.9
14 0.4 0.0 2.3 0.2 5.0±2.2
18 0.3 0.2 2.4 0.4 8.0±2.8
22 0.4 0.1 0.5 3.1 7.0±2.6
26 1.7 0.7 5.3 15.8 27.0±5.2
30 0.9 0.8 3.6 26.7 40.0±6.3
34 0.4 0.3 2.6 22.5 26.0±5.1
38 0.0 0.3 1.3 22.0 24.0±4.9
42 0.2 0.0 0.2 12.4 11.0±3.3
46 0.0 0.0 0.0 1.7 3.0±1.7
50 0.0 0.0 0.0 0.5 1.0±1.0
54 0.0 0.0 0.0 0.2 0.0±0.0
58 0.0 0.0 0.0 0.0 0.0±0.0

Panel of Positron |eta| (1.0, 2.0)
Signed pT-balance Z -> ee W->tau->e data-driven QCD W->env MC data
-38 0.0 0.0 0.0 0.0 0.0±0.0
-34 0.1 0.0 0.1 0.0 0.0±0.0
-30 0.1 0.0 0.1 0.0 1.0±1.0
-26 0.1 0.0 0.1 0.0 1.0±1.0
-22 0.0 0.0 0.0 0.0 0.0±0.0
-18 0.3 0.0 0.3 0.0 1.0±1.0
-14 0.3 0.0 2.2 0.0 1.0±1.0
-10 0.5 0.0 1.5 0.0 1.0±1.0
-6 1.8 0.0 4.7 0.0 3.0±1.7
-2 2.8 0.0 5.8 0.0 6.0±2.4
2 2.1 0.0 9.1 0.0 7.0±2.6
6 1.4 0.0 6.4 0.0 10.0±3.2
10 0.3 0.0 7.2 0.2 10.0±3.2
14 0.4 0.1 4.5 0.5 7.0±2.6
18 0.4 0.2 4.6 1.2 6.0±2.4
22 0.1 0.3 1.4 3.6 12.0±3.5
26 0.6 1.4 4.0 19.4 23.0±4.8
30 0.4 1.1 2.5 24.7 26.0±5.1
34 0.2 0.8 3.0 24.4 26.0±5.1
38 0.1 0.3 0.4 30.0 28.0±5.3
42 0.0 0.0 0.0 22.5 14.0±3.7
46 0.2 0.0 0.2 3.8 5.0±2.2
50 0.0 0.0 0.0 0.8 0.0±0.0
54 0.0 0.0 0.0 0.1 0.0±0.0
58 0.0 0.0 0.0 0.0 0.0±0.0

Figure 4: Longitudinal single-spin asymmetries, $A_L$, for $W^\pm$ production as a function of the positron or electron pseudorapidity, $\eta_e$, separately for the STAR 2011+2012 (black squares) and 2013 (red diamonds) data samples for 25 $< E_T^e <$ 50\,GeV. The 2011+2012 results have been offset to slightly smaller $\eta$ values for clarity. Shown also are the final asymmetries for high-energy decay leptons from $W$ and $Z/\gamma^*$ production from the PHENIX experiment with their statistical and systematic uncertainties~\cite{Adare:2015gsd,Adare:2018csm}.

STAR 2011+2012
Q η A_L AL_down AL_up
P -1.18 0.009 0.242 0.239
P -0.72 -0.239 0.057 0.058
P -0.25 -0.343 0.045 0.046
P 0.25 -0.429 0.045 0.045
P 0.72 -0.472 0.056 0.056
P 1.18 -0.649 0.214 0.223
N -1.22 0.195 0.240 0.236
N -0.76 0.247 0.099 0.100
N -0.26 0.280 0.104 0.103
N 0.26 0.202 0.105 0.103
N 0.76 0.391 0.099 0.098
N 1.22 0.182 0.251 0.243

STAR 2013
Q η A_L stat syst
P -1.24 -0.493 0.181 0.015
P -0.71 -0.253 0.035 0.013
P -0.24 -0.323 0.026 0.008
P 0.25 -0.401 0.026 0.007
P 0.72 -0.553 0.034 0.015
P 1.24 -0.365 0.183 0.019
N -1.27 0.269 0.185 0.003
N -0.74 0.265 0.060 0.004
N -0.27 0.279 0.066 0.002
N 0.26 0.252 0.066 0.003
N 0.74 0.385 0.059 0.006
N 1.27 0.218 0.185 0.003

PHENIX 2011+2012
Q η A_L stat syst_up syst_dn
P 0.00 -0.27 0.10 0.01 0.01
N 0.00 0.28 0.16 0.02 0.02

PHENIX 2013
Q η A_L stat syst_up syst_dn
P -0.17 -0.35 0.07 0.10 0.10
P 0.67 -0.38 0.07 0.10 0.10
N -0.67 0.17 0.12 0.02 0.01
N 0.67 0.10 0.13 0.03 0.01

PHENIX Muon 2011-2013
Q η A_L stat syst_up syst_dn
P -1.67 0.10 0.14 0.24 0.20
P 1.67 -0.28 0.14 0.23 0.29
N -1.73 0.29 0.16 0.38 0.44
N 1.73 0.10 0.16 0.38 0.35

Figure 5: Longitudinal single-spin asymmetry, $A_L$, for $W^\pm$ production as a function of the lepton pseudorapidity, $\eta_e$, for the combined 2011+2012 and 2013 (red circles) STAR data samples for 25 < $E_T^e$ < 50GeV in comparison to theory predictions (See text for details).

Q η A_L stat syst
P -1.22 -0.312 0.145 0.012
P -0.71 -0.251 0.030 0.011
P -0.24 -0.331 0.023 0.007
P 0.25 -0.412 0.023 0.005
P 0.72 -0.534 0.029 0.013
P 1.22 -0.482 0.140 0.014
N -1.25 0.241 0.146 0.002
N -0.75 0.260 0.051 0.004
N -0.27 0.281 0.056 0.001
N 0.26 0.239 0.056 0.002
N 0.75 0.385 0.051 0.004
N 1.25 0.205 0.148 0.002

Figure 6: The difference of the light sea-quark polarizations as a function of $x$ at a scale $Q^2$ = 10\,(GeV/c)$^2$. The green band shows the NNPDFpol1.1 results~\cite{Nocera:2014gqa} and the blue band shows the corresponding distribution after the 2013 $W$ data are included by reweighting.

x NNPDFpol1.1 mean NNPDFpol1.1 low NNPDFpol1.1 up NNPDFpol1.1rw mean NNPDFpol1.1rw low NNPDFpol1.1rw up
0.01000 0.01884 0.00491 0.03277 0.02361 0.01327 0.03395
0.01122 0.01958 0.00487 0.03429 0.02456 0.01365 0.03546
0.01259 0.02039 0.00483 0.03594 0.02557 0.01407 0.03708
0.01413 0.02126 0.00481 0.03771 0.02666 0.01453 0.03879
0.01585 0.02219 0.00478 0.03961 0.02782 0.01505 0.04058
0.01778 0.02319 0.00474 0.04165 0.02905 0.01563 0.04246
0.01995 0.02424 0.00470 0.04378 0.03035 0.01630 0.04439
0.02239 0.02533 0.00468 0.04598 0.03171 0.01708 0.04635
0.02512 0.02645 0.00467 0.04824 0.03314 0.01795 0.04833
0.02818 0.02760 0.00471 0.05049 0.03462 0.01895 0.05028
0.03162 0.02876 0.00484 0.05268 0.03614 0.02011 0.05217
0.03548 0.02992 0.00506 0.05478 0.03770 0.02142 0.05398
0.03981 0.03107 0.00538 0.05676 0.03927 0.02288 0.05566
0.04467 0.03218 0.00584 0.05852 0.04083 0.02453 0.05713
0.05012 0.03187 0.00661 0.05713 0.04234 0.02635 0.05834
0.05623 0.03288 0.00729 0.05848 0.04381 0.02828 0.05934
0.06310 0.03381 0.00804 0.05959 0.04518 0.03032 0.06003
0.07079 0.03593 0.00883 0.06303 0.04641 0.03239 0.06043
0.07943 0.03651 0.00973 0.06330 0.04745 0.03445 0.06045
0.08912 0.03678 0.01058 0.06298 0.04821 0.03630 0.06012
0.10000 0.03664 0.01134 0.06193 0.04860 0.03780 0.05940
0.11220 0.03538 0.01200 0.05876 0.04854 0.03887 0.05820
0.12589 0.03479 0.01228 0.05731 0.04797 0.03910 0.05683
0.14125 0.03274 0.01270 0.05278 0.04666 0.03834 0.05499
0.15849 0.02981 0.01275 0.04687 0.04452 0.03642 0.05262
0.17783 0.02623 0.01066 0.04180 0.04146 0.03324 0.04968
0.19953 0.02237 0.00561 0.03913 0.03743 0.02895 0.04590
0.22387 0.01935 0.00309 0.03562 0.03250 0.02385 0.04114
0.25119 0.01688 0.00341 0.03034 0.02686 0.01825 0.03546
0.28184 0.01412 0.00323 0.02501 0.02082 0.01251 0.02914
0.31623 0.01118 0.00266 0.01970 0.01485 0.00716 0.02253
0.35481 0.00818 0.00174 0.01462 0.00945 0.00282 0.01608
0.39811 0.00534 0.00068 0.01001 0.00509 -0.00008 0.01026
0.44668 0.00294 -0.00024 0.00613 0.00209 -0.00141 0.00559
0.50119 0.00123 -0.00072 0.00319 0.00051 -0.00146 0.00248
0.56234 0.00033 -0.00065 0.00132 0.00015 -0.00083 0.00112
0.63096 0.00010 -0.00071 0.00092 0.00050 -0.00048 0.00147
0.70795 0.00017 -0.00105 0.00139 0.00087 -0.00052 0.00227
0.79433 0.00018 -0.00099 0.00135 0.00073 -0.00056 0.00203
0.89125 0.00007 -0.00043 0.00057 0.00022 -0.00029 0.00073