# Difference: AsymmetryFitting (15 vs. 16)

#### Revision 162010-10-19 - AlisonBates

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# B2hh GFact Asymmetry Fitting page

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In the solution for this distribution the resultant pdf needs an error function of a complex number (x+iy), which there is no such routine in root. Hence we wrote a routine to use the infinite series approximation for complex error function from Abramozitz and Stegun (page 299, equation 7.1.29) which yields the folowing results for up to 7 terms of the series summation.
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The new PDF has been plotted showing the real and imaginary parts, along with the old PDF in the following new PDF. The imaginary part is, as expected, zero with only the entry at time t= tmin giving a delta function.
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The new PDF has calculated and its corresponding normalisation. The imaginary part is, as expected, zero with only the entry at time t= tmin giving a delta function.The following plot compares the basic pdf, Christoph's pdf and my new pdf, here.

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A comparision of the normalised old PDF (blue oscillations) and the new UNnormalised PDF (red oscillations) is shown here.
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The area under the curves (summed over the plus and minus tag states) were calculated numerically using a step size of 0.5fs and in a range of tmin to 50ps and the following was found:

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Next the normalisation was implemented and again a comparision of the normalised old PDF (blue oscillations) and the new normalised PDF (red oscillations) is shown here with the real and imaginary PDFs and the old PDF is shown here. The area under the curves (summed over the plus and minus tag states) were calculated numerically using a step size of 0.5fs and in a range of tmin to 50ps and the following was found:

Old PDF area = 0.99983 (0.02% from 1.0)

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Old PDF area = 1.000169 ( < 0.02% from 1.0)
New PDF area = 0.985813 (1.4% from 1.0)
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Now need to understand if this 1.4% is significant (trawled through normalisation calculation and can not find any errors). Next task is to move all this code over to G-Fact so can change to use this new PDF for Bs2KK.
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Need to understand if this 1.4% is significant then the next task is to move all this code over to G-Fact so can change to use this new PDF for Bs2KK.

## Basic Checks with asymmetry fitter

Toy data was generated with a mix of 56.1% Bd → π π, 10.3% Bd → K π and 33.6% combinatoric background with ssb of 0.664 (ssb is S/S+B) generated in a mass region of 5-5.8 GeV. The mistag rates in generation and fitting was ωBs = 0.361and ωBd = 0.355 and ACPBd→Kπ = 0.1. 100 data sets with 100,000 events per data set was used here but Lars ran with 1000 data sets with 100k events per set and found no bias on the pulls and much improved uncertainties. I just show the plots below (100 data sets) for completion.

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