Systematics Summary

• pT-shifts: correct back to "particle" jets
• pT-shift uncertainties:
• Sivers: statistical + systematic uncertainties from gains, energy scale, etc. (i.e. Carl's spreadsheet)
• Collins+Collins-like: statistical only to this point
• Matching probabilities:
• Sivers: product of the vertex-matching and parton-jet-matching probabilities is treated as a dilution
• Collins+Collins-like: product of the vertex-matching and particle-jet-matching probabilities is treated as a dilution
• The difference between the measured asymmetry (i.e. what is plotted) and the asymmetry corrected for dilution (not plotted) is treated as a systematic uncertainty
• Angular resolutions: Sivers, Collins, and Collins-like angular resolutions are treated as a dilution and treated analogously to those due to matching probabilities
• Leak-through:
• Sivers:
• Assume Collins and Collins-like contribute as 0.25×z
• For each pT bin, fit "leak-through" distributions with p0+Aleak×sin(φ)
• Treat |Aleak, Col| + |δAleak, Col| + |Aleak, Col-like| + |δAleak, Col-like| as systematic uncertainty
• Collins:
• Weight Sivers and Collins-like contributions as constants (10% and 25%, respectively)
• For each bin, fit "leak-through" distributions with p0+Aleak×sin(φC)
• For z and jT: Treat (|Aleak, Siv| + |δAleak, Siv|)×2%/10% + (|Aleak, Col-like| + |δAleak, Col-like|)×(|Ameas, Col-like| + |δAmeas, Col-like|)/25% as systematic
• For pT: Treat (|Aleak, Siv| + |δAleak, Siv|)×2%/(|Ameas, Siv| + |δAmeas, Siv|) + (|Aleak, Col-like| + |δAleak, Col-like|)×(|Ameas, Col-like| + |δAmeas, Col-like|)/25% as systematic
• Collins-like:
• Weight Sivers and Collins contributions as constants (10% and 25%, respectively)
• For each bin, fit "leak-through" distributions with p0+Aleak×sin(φC-L)
• Treat (|Aleak, Siv| + |δAleak, Siv|)×2%/10% + (|Aleak, Col| + |δAleak, Col|)×(|Ameas, Col| + |δAmeas, Col|)/25% as systematic
• For pT: Treat (|Aleak, Siv| + |δAleak, Siv|)×2%/(|Ameas, Siv| + |δAmeas, Siv|) + (|Aleak, Col-like| + |δAleak, Col-like|)×(|Ameas, Col-like| + |δAmeas, Col-like|)/25% as systematic

Figure 2: Sivers (η-bins)

 Central η Forward η

Data Tables

Table 1: Sivers Combined Eta Window (xF > 0)

pT [GeV/c] AN AN Stat. Err. Syst. Err. Matching Syst. Err. Resolution 5.930±0.190 7.010±0.260 8.170±0.290 10.100±0.370 11.790±0.500 0.004831 0.007527 -0.007381 0.005938 -0.001656 0.003824 0.006171 0.010085 0.018425 0.055632 0.002771642 0.003099013 0.00204353 0.000804287 0.000324385 9.85918E-05 0.000153612 0.000150633 0.000121184 3.37959E-05 5.000E-04 6.000E-04 1.500E-03 1.500E-03 3.500E-03 0.002818106 0.003160297 0.00253943 0.001706331 0.003515163 0.736952317 0.512120741 0.251802711 0.092609526 0.063185982

Table 2: Sivers Combined Eta Window (xF < 0)

pT [GeV/c] AN AN Stat. Err. Syst. Err. Matching Syst. Err. Resolution 5.930±0.190 7.010±0.260 8.170±0.290 10.100±0.370 11.790±0.500 -0.000097 0.011568 0.010382 0.019964 0.0007 0.003821 0.006157 0.010094 0.018568 0.058539 5.56509E-05 0.004762772 0.002874398 0.002704075 0.000137119 1.97959E-06 0.000236082 0.000211878 0.000407429 1.42857E-05 5.000E-04 6.000E-04 1.500E-03 1.500E-03 3.500E-03 0.000503091 0.004806218 0.003249162 0.003118977 0.003502714 0.131664847 0.78061029 0.321890468 0.167975927 0.059835564

Table 3: Sivers Central Eta Window (xF > 0)

pT [GeV/c] AN AN Stat. Err. Syst. Err. Matching Syst. Err. Resolution 5.930±0.190 7.010±0.260 8.170±0.290 10.100±0.370 11.790±0.500 0.004558 0.009319 -0.004172 -0.005975 0.041775 0.004854 0.007825 0.012644 0.022468 0.059865 0.002593891 0.00312778 0.00116817 0.001076324 0.002379891 9.30204E-05 0.000190184 8.51429E-05 0.000121939 0.000852551 7.700E-04 8.000E-04 1.670E-03 1.940E-03 3.100E-03 0.002707365 0.003234066 0.002039797 0.002221923 0.004000091 0.557759528 0.413299121 0.161325283 0.098892794 0.066818521

Table 4: Sivers Central Eta Window (xF < 0)

pT [GeV/c] AN AN Stat. Err. Syst. Err. Matching Syst. Err. Resolution 5.930±0.190 7.010±0.260 8.170±0.290 10.100±0.370 11.790±0.500 0.002048 0.007391 0.006356 0.005506 0.008755 0.004856 0.007813 0.012682 0.022764 0.065948 0.001165487 0.002480677 0.001779696 0.00099184 0.000498766 4.17959E-05 0.000150837 0.000129714 0.000112367 0.000178673 7.700E-04 8.000E-04 1.670E-03 1.940E-03 3.100E-03 0.0013975 0.002610844 0.002443981 0.002181736 0.003144947 0.287788318 0.33416669 0.192712581 0.095841507 0.047688285

Table 5: Sivers Forward η Window (xF > 0)

pT [GeV/c] AN AN Stat. Err. Syst. Err. Matching Syst. Err. Resolution 5.930±0.190 7.010±0.260 8.170±0.290 10.100±0.370 11.790±0.500 0.005276 0.004579 -0.01299 0.0304 -0.276645 0.006206 0.010035 0.016719 0.032196 0.150634 0.003071396 0.002491389 0.003539176 0.001974255 0.113969082 0.000107673 9.3449E-05 0.000265102 0.000620408 0.005645816 4.700E-04 1.000E-03 1.590E-03 2.050E-03 5.300E-03 0.003109014 0.002686215 0.003888977 0.002912918 0.114231855 0.500969093 0.267684609 0.232608251 0.090474527 0.75834045

Table 6: Sivers Forward η Window (xF < 0)

pT [GeV/c] AN AN Stat. Err. Syst. Err. Match Syst. Err. Resolution 5.930±0.190 7.010±0.260 8.170±0.290 10.100±0.370 11.790±0.500 -0.003585 0.018409 0.01734 0.048703 -0.029225 0.006193 0.01 0.016673 0.032095 0.127114 0.002086989 0.010016156 0.00472435 0.0031629 0.012039785 7.31633E-05 0.000375694 0.000353878 0.000993939 0.000596429 4.700E-04 1.000E-03 1.590E-03 2.050E-03 5.300E-03 0.002140509 0.01007296 0.004997281 0.003897993 0.013168225 0.345633573 1.007296013 0.299722947 0.121451725 0.103593824
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