Fitting

Fitting R(t), the MC ratio


We model the interference with events generated with our Monte Carlo generator, STARlight. Two sets are generated, one with interference and one without. A ratio is arrived at by dividing the t spectra of the sets. The ratio is then fit with a function [R(t)] which figures into the overall fit applied to the data: Ae-kt(1+c[R(t)-1]). Various fitting functions, (five parameter fit, six parameter fit, fifth order polynomial, and sixth order polynomial fit) have been tried in order to optimize the fit and assess systematic error.

Table 1:
Fitting Summary Summary of the &chi2/dof for fits as presented below and extracted c parameters (where c =1 corresponds to expected degree of interference and c=0 corresponds to no interference). When the &chi2/dof is significantly greater than 1, the statistical error associated with the c parameter is multiplied by a correction factor defined as the SQRT of the &chi2/dof as per a method prescribed in the particle data book. In addition the difference between the statistical error and the 'corrected' error is taken in the last column.
Dataset/FitRapidity&chi²/dof c statistical error × correctionExcess Error
Minbias/par5 0 < y < 0.544.2/470.9539±0.076 n/a -0.002
0.5 < y < 1.080.18/47 0.9275±0.1100.1440.034
Minbias/par6 0 < y < 0.546.11/470.9485±0.076 n/a -0.001
0.5 < y < 1.080.04/47 0.9224±0.1090.1420.033
Minbias/pol5 0 < y < 0.545.88/470.9507±0.076n/a-0.001
0.5 < y < 1.081.67/47 0.9266±0.1100.1450.074
Minbias/pol6 0 < y < 0.546.28/470.9479±0.076n/a-0.001
0.5 < y < 1.079.16/47 0.9287±0.1100.1430.033
Topology/par5 0.1 < y < 0.587.73/470.8223±0.1200.1640.044
0.5 < y < 1.085.09/47 1.048±0.2090.2810.072
Topology/par6 0.1 < y < 0.580.58/470.8381±0.1140.1530.039
0.5 < y < 1.085.21/47 0.9966±0.1990.2610.062
Topology/pol5 0.1 < y < 0.590.63/470.8212±0.1240.1720.048
0.5 < y < 1.084.53/47 1.081±0.2130.2860.073
Topology/pol6 0.1 < y < 0.583.05/470.8371±0.1190.1580.039
0.5 < y < 1.087.9/47 0.9637±0.20390.2790.075

A. Minbias Fits

Figure 1 & 2:

Five Parameter fit. Fitting scheme for the minbias set, 0.0 < y < 0.5. Plot with statistics here. (left panel)

Five Parameter fit. Fitting scheme for the minbias set, 0.5 < y < 1.0. Plot with statistics here. (right panel)


Figure 3 & 4:

Six Parameter fit. Fitting scheme for the minbias set, 0.0 < y < 0.5. Plot with statistics here. (left panel)

Six Parameter fit. Fitting scheme for the minbias set, 0.5 < y < 1.0. Plot with statistics here. (right panel)


Figure 5 & 6:

Fifth order polynomial fit. Fitting scheme for the minbias set, 0.0 < y < 0.5. Plot with statistics here. (left panel)

Fifth order polynomial fit. Fitting scheme for the minbias set, 0.5 < y < 1.0. Plot with statistics here. (right panel)


Figure 7 & 8:

Sixth order polynomial fit. Fitting scheme for the minbias set, 0.0 < y < 0.5. Plot with statistics here. (left panel)

Sixth order polynomial fit. Fitting scheme for the minbias set, 0.5 < y < 1.0. Plot with statistics here. (right panel)


B. Topology Fits

Figure 9 & 10:

Five Parameter fit. Fitting scheme for the topology set, 0.05 < y < 0.5. Plot with statistics here. (left panel)

Five Parameter fit. Fitting scheme for the topology set, 0.5 < y < 1.0. Plot with statistics here. (right panel)


Figure 11 & 12:

Six Parameter fit. Fitting scheme for the topology set, 0.05 < y < 0.5. Plot with statistics here. (left panel)

Six Parameter fit. Fitting scheme for the topology set, 0.5 < y < 1.0. Plot with statistics here. (right panel)


Figure 13 & 14:

Fifth order polynomial fit. Fitting scheme for the topology set, 0.05 < y < 0.5. Plot with statistics here. (left panel)

Fifth order polynomial fit. Fitting scheme for the topology set, 0.5 < y < 1.0. Plot with statistics here. (right panel)


Figure 14 & 15:

Sixth order polynomial fit. Fitting scheme for the topology set, 0.05 < y < 0.5. Plot with statistics here. (left panel)

Sixth order polynomial fit. Fitting scheme for the topology set, 0.5 < y < 1.0. Plot with statistics here. (right panel)