The Plan

Step 1: Unmatched Corrections

• Correct full detector-jet spectrum for underlying event contributions
• Correct pion-in-jet spectrum for underlying event contributions
• Correct full detector-jet spectrum to remove detector jets that do not match to a particle jet
• Correct pion-in-jet spectrum to remove events that do not match to a pion-in-jet at the particle-jet level

Step 2: Unfolding

• Unfold full jet p_T spectrum, regardless of pions
  • Use RooUnfold Bayesian for 1-D unfolding
• Unfold pion-in-jet spectrum, e.g. in terms of jet p_T, pion z, pion j_T
  • Use RooUnfold Bayesian for 2-D or 3-D unfolding, TBD

Step 3: Efficiency Correction

• Correct full jet reconstruction efficiency using embedded Monte Carlo
• Correct full pion-in-jet reconstruction efficiency using embedded Monte Carlo

First Look at Unfolding

For this first look, I do the following analysis:

• Loop over events
  • Select events with M.C. |z_vtx| < 30 cm (not sure about this one)
    • Loop over particle jets
      • Select jets with |η| < 0.5
      • Histogram the particle-jet p_T spectrum, i.e. spectrum of "all" particle jets
      • Loop over detector jets
        • Select jets from events with the "best" vertex, positive-rank vertex, and |reco. z_vtx| < 30 cm
        • Select jets with no tracks with p_T > 30 GeV/c, R_T < 0.94, ∑p_T,ch > 0.5 GeV/c, |η_det-0.1| < 0.8, and |η| < 0.5
        • Select events with |M.C. z_vtx-reco. z_vtx| < 2 cm
        • Select jets with p_T > 5 GeV/c
        • Calculate angular separation, ΔR = (Δη²+Δφ²)^1/2
      • Select events with ΔR_min < 0.5 and call the associated detector jet its "match"
      • Histogram the "matched" particle-jet p_T spectrum
      • Histogram the "matched" particle-jet p_T vs. associated detector-jet p_T spectrum
      • Loop over particles within the particle jet
        
        • Select pions
        • Histogram the particle-jet p_T vs. true pion z vs. true pion j_T spectrum
        • Loop over detector jets
          • Select jets from events with the "best" vertex, positive-rank vertex, and |reco. z_vtx| < 30 cm
          • Select jets with no tracks with p_T > 30 GeV/c, R_T < 0.94, ∑p_T,ch > 0.5 GeV/c, |η_det-0.1| < 0.8, and |η| < 0.5
          • Select events with |M.C. z_vtx-reco. z_vtx| < 2 cm
          • Select jets with p_T > 5 GeV/c
          • Select events with ΔR = (Δη²+Δφ²)^1/2 < 0.5
          • Loop over tracks within the detector jet
            • Select tracks with z > 0.1
            • Select tracks with N_hits,dE/dx > 5
            • Select tracks within the "pion" n_σ(π) range, as defined by the 2011 Collins paper
            • Calculate angular separation, ΔR = (Δη²+Δφ²)^1/2
          • Select events with particle ΔR_min < 0.5 and call the associated track its "match"
          • Histogram the "matched" particle-jet p_T vs. true pion z vs. true pion j_T spectrum
          • Histogram the associated detector-jet p_T vs. reco pion z vs. reco pion j_T spectrum for the matched "truth" bins
  • Loop over detector jets
    • Select jets from events with the "best" vertex, positive-rank vertex, and |reco. z_vtx| < 30 cm
    • Select jets with no tracks with p_T > 30 GeV/c, R_T < 0.94, ∑p_T,ch > 0.5 GeV/c, |η_det-0.1| < 0.8, and |η| < 0.5
    • Select events with |M.C. z_vtx-reco. z_vtx| < 2 cm
    • Select jets with p_T > 5 GeV/c
    • Histogram the detector-jet p_T spectrum, i.e. spectrum of "all" detector jets passing the cuts
    • Loop over all particle jets
      • Select particle-jets with |η| < 0.5
      • Calculate angular separation, ΔR = (Δη²+Δφ²)^1/2
    • Select events with ΔR_min < 0.5 and call the associated particle jet its "match"
    • Histogram the "matched" detector-jet p_T spectrum
    • Histogram the "matched" detector-jet p_T vs. associated particle-jet p_T spectrum
    • Loop over tracks within the detector jet
      • Select tracks with z > 0.1
      • Select tracks with N_hits,dE/dx > 5
      • Select tracks within the "pion" n_σ(π) range, as defined by the 2011 Collins paper
      • Histogram the detector-jet p_T vs. track z vs. track j_T spectrum
      • Loop over particle jets
        • Select events with ΔR = (Δη²+Δφ²)^1/2 < 0.5
        • Loop over particles within the particle jet
          • Calculate angular separation, ΔR = (Δη²+Δφ²)^1/2
        • Select events with particle ΔR_min < 0.5 and call the associated particle its "match"
        • Histogram the "matched" detector-jet p_T vs. track z vs. track j_T spectrum
        • Histogram the associated particle-jet p_T vs. particle z vs. particle j_T spectrum for the matched "reco" bins

Figure 1: Jet Efficiency Corrections

Figure 1 shows (left) the ratio of "matched" particle jets to "all" particle jets vs. particle-jet p_T and (right) the ratio of "matched" detector jets to "all" detector jets vs. detector-jet p_T. Jets were subject to the selection criteria described above.

Figure 2: Migration Matrix

Figure 2 shows the migration matrix based upon matched detector jets, as described above.

Figure 3: Unfolded Jet Spectra

Figure 3 shows the jet p_T spectra for particle jets with |η| < 0.5 (green), uncorrected VPDMB data (blue) with selection criteria as described above, and unfolded VPDMB data (red). The unfolding was done with the Bayesian algorithm in RooUnfold with four iterations, passing it the migration matrix from Fig. 2 and entering "0" for both the "measured" and "truth" fields in RooUnfoldResponse. This is because I wanted to handle the inefficiency and "fakes" corrections by hand. All spectra and uncertainties were scaled by 1/bin width. The particle-jet spectrum is normalized to the data yield within the range 6-55 GeV/c. Note: this means that for this first pass, I essentially have no buffer bins for the unfolding. Before unfolding, data were scaled by the matched-detector-jet fractions from Fig. 1 (right) to correct the yield for unmatched detector jets. After unfolding, the data were scaled by the inverse of the matched-particle-jet fractions from Fig. 1 (left) to correct the yield for unmatched particle jets.