Systematics Summary

• p_T-shifts: correct back to "particle" jets
• p_T-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 p_T bin, fit "leak-through" distributions with p₀+A_leak×sin(φ)
    • Treat |A_{leak, Col}| + |δA_{leak, Col}| + |A_{leak, Col-like}| + |δA_{leak, 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+A_leak×sin(φ_C)
    • For z and j_T: Treat (|A_{leak, Siv}| + |δA_{leak, Siv}|)×2%/10% + (|A_{leak, Col-like}| + |δA_{leak, Col-like}|)×(|A_{meas, Col-like}| + |δA_{meas, Col-like}|)/25% as systematic
    • For p_T: Treat (|A_{leak, Siv}| + |δA_{leak, Siv}|)×2%/(|A_{meas, Siv}| + |δA_{meas, Siv}|) + (|A_{leak, Col-like}| + |δA_{leak, Col-like}|)×(|A_{meas, Col-like}| + |δA_{meas, 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+A_leak×sin(φ_C-L)
    • Treat (|A_{leak, Siv}| + |δA_{leak, Siv}|)×2%/10% + (|A_{leak, Col}| + |δA_{leak, Col}|)×(|A_{meas, Col}| + |δAmeas, Col|)/25% as systematic
    • For p_T: Treat (|A_{leak, Siv}| + |δA_{leak, Siv}|)×2%/(|A_{meas, Siv}| + |δA_{meas, Siv}|) + (|A_{leak, Col-like}| + |δA_{leak, Col-like}|)×(|A_{meas, Col-like}| + |δA_{meas, Col-like}|)/25% as systematic

Figure 1: Sivers (Combined η Window)

Figure 2: Sivers (η-bins)

Central η	Forward η

Data Tables

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

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

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

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

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

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