Using the RATIO method to calculate the BG energy in a jetcone

• For many (1000) Central Hijing events, take a random cone centre on the GRID such that the cone does not overlap the edge of the GRID, and sum the energy within varying R (Actual Summed E)

• For the same R, Calculate the energy in the cone 2 ways event-by-event:
  • 1. Cone Method: Using the GRID energy with the usual PtCut = 2GeV, calculate the energy in the cone by summing the energy OUTSIDE the cone and then scaling for the cone size
  • 2. Ratio Method: Use the GRID energy with NO CUTS and calculate the energy in the cone by summing energy OUTSIDE it, then MULTIPLY by the Ratio E_cuts/E_{No cuts} (=0.4685 plot2), and scale for the cone size (Andreas's suggestion)

• Compare the calculations to the Actual Summed E to make a choice between methods

Finding the RATIO

Finding the RATIO for the case of a Perfect TPC

Finding the RATIO for the case of a Perfect TPC and TRACKS ONLY

Finding the RATIO for the case of 90% TPC, NEW HADRON CORRECTION

Results for BG E calculated 2 ways - Actual Summed BG E in cone (1000 EVENTS)

Points are the mean and error bars indicate the RMS of the distributions shown below.

R ECalc - EActual ECalcRATIO - EActual 0.1 -0.5 +- 3 -0.5 +- 3 0.2 -1 +- 7 -1 +- 6 0.3 -1 +- 10 -1 +- 10 0.35 -3 +- 12 -3 +- 11 0.4 -6 +- 14 -6 +- 13 0.5 -8 +- 19 -7 +- 17 0.6 -13 +- 25 -11 +- 21 0.7 -9 +- 32 -7 +- 24 0.8 -3 +- 42 -2 +- 28 0.9 -3 +- 55 -3 +- 33 1.0 -14 +- 77 -9 +- 40

Results for BG E calculated 2 ways - Actual Summed BG E in cone (1000 EVENTS) (Revised Random Method of cone centering)

R ECalc - EActual ECalcRatio - EActual 0.1 -0.3 +- 3 -0.3 +- 3 0.2 -1 +- 6 -1 +- 6 0.3 -4 +- 10 -3 +- 10 0.35 -4 +-12 -4 +- 11 0.4 -5 +- 14 -5 +- 13 0.5 -7 +- 19 -6 +- 17 0.6 -9 +- 24 -8 +- 20 0.7 -9 +- 31 -7 +- 24 0.8 -10 +- 37 -7 +- 27 0.9 -6 +- 46 -5 +- 31 1.0 -8 +- 59 -5 +- 35

JetE in cone Calculated 2 ways:

• 1. Take 2 sets of data - one with PtCut and one without. Use data WITHOUT cuts to calculate BG in cone, multiply by ratio (E_cuts/E_{No cuts}), and then subtract from data set WITH cuts (E in cone)
• 2. Take 1 set of data - NO CUTS and calculate BG from E outside cone and subtract from E in cone

Resulting Resolution Plots

R Ratio method resolution (&Delta) 0.1 0.68371 0.2 0.471642 0.3 0.423018 0.35 0.428693 0.4 0.439072 0.5 0.451647 0.6 0.488276 0.7 0.543133 0.8 0.569408 0.9 0.592072 1.0 0.612731

R Ratio method resolution (&Delta) 0.1 0.633233 0.2 0.396245 0.3 0.302286 0.35 0.29516 0.4 0.295466 0.5 0.300916 0.6 0.317932 0.7 0.333055 0.8 0.383377 0.9 0.416489 1.0 0.438317

Resolution Plots with Perfect TPC (100% efficiency and no momentum smearing)

R 50GeV case 100GeV case 0.1 0.690296 0.639071 0.2 0.46123 0.390963 0.3 0.405389 0.29266 0.35 0.41718 0.285318 0.4 0.40847 0.285496 0.5 0.442251 0.295535 0.6 0.484921 0.309135 0.7 0.521831 0.344467 0.8 0.538957 0.363386 0.9 0.573666 0.394673 1.0 0.606978 0.431124

TRACKS ONLY for comparison!