D Had Analysis - Process - fa vs. log L

Introduction

fa — the fraction of events that are smeared according to the second Gaussian. We'd like to see this parameter's effect on the fitting procedure by looking at its corresponding log likelihood value.

Procedure

Mode 0 (Kpi)

• For mode 0 (Kpi), to plot the fa vs. log likelihood for data, we get¹:

The central value of fa from Signal MC table is: 0.182, we can read the -Log(L) value from the plot as: -981717.57. By reducing the maximum value of Log(L) by 0.5, i.e. -981717.07, we have the corresponding fa to be 0.13 and 0.38 respectively.

Then we fit the data with 0.13 and 0.38, comparing the yields with the regular one.

• fa 0.13

; INVALID LISP CODE

• fa 0.38

; INVALID LISP CODE

Mode 1 (Kpipi0)

• For mode 1 (Kpipi0), we get²:

The central value of fa from Signal MC is: 0.196,By reducing the maximum value of Log(L) by 0.5, we have the corresponding fa to be 0.19 and 0.24 respectively.

Then we fit the data with 0.19 and 0.24, comparing the yields with the regular one.

• fa 0.19

; INVALID LISP CODE

• fa 0.24

; INVALID LISP CODE

Conclusion

The difference are below 0.15% level, negligible.

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1. Details about this plot can be found here.

2. Details about this plot can be found here.