# Difference: AsymmetryFitting (1 vs. 19)

#### Revision 192010-11-26 - AlisonBates

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# B2hh GFact Asymmetry Fitting page

#### Revision 182010-11-26 - AlisonBates

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# B2hh GFact Asymmetry Fitting page

#### Revision 172010-11-22 - MichaelWright

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# B2hh GFact Asymmetry Fitting page

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

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 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

Line: 23 to 23
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.
Changed:
<
<
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.
>
>
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.

Changed:
<
<
A comparision of the normalised old PDF (blue oscillations) and the new UNnormalised PDF (red oscillations) 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:

Changed:
<
<
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)

>
>
Old PDF area = 1.000169 ( < 0.02% from 1.0)
New PDF area = 0.985813 (1.4% from 1.0)
Changed:
<
<
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.
>
>
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.

Line: 120 to 118

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#### Revision 152010-10-12 - AlisonBates

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 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

#### Revision 142010-10-06 - AlisonBates

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 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

Line: 25 to 25
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.
Changed:
<
<
A comparision of the normalised old PDF (blue oscillations) and the new UNnormalised PDF (red oscillations) is shown here. I am now attempting to code up the normalisation and will upload the comparison plots once successful.
>
>
A comparision of the normalised old PDF (blue oscillations) and the new UNnormalised PDF (red oscillations) is shown here.

>
>
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)

New PDF area = 0.985813 (1.4% from 1.0)

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.

## 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.

Line: 111 to 118

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>
>
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#### Revision 132010-10-05 - AlisonBates

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 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

Line: 11 to 11

1. Move to MC data/ real data (Bd) for first looks.

## PDF modeling for Bs

Changed:
<
<
The basic pdf of
>
>
The basic pdf that was implemented in the asymmetry fitter had the following form

Changed:
<
<
>
>

Changed:
<
<
with standard values has been plotted with q=+1 (red) and q=-1 (blue) and gives the following distribution. The integrated area from tmin to 10.0 is 0.994402. >
>
This PDF has been plotted with standard values for the Bs→KK decay for the tags of q=+1 (red) and q=-1 (blue) and shown here Old PDF distribution. The integrated area from tmin (nominally set to 1.0) to 10.0 is 0.994402.
I am studiying the pdf obtained from the following distribution
Changed:
<
<
>
>

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.

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.

Changed:
<
<
The resultant pdf needs an error function of a complex number (x+iy) which there is no such routine in Root so using the infinite series approximation for complex error function from Abramozitz and Stegun we have written a routine which yields the folowing results for up to 7 terms of the series summation.
>
>
A comparision of the normalised old PDF (blue oscillations) and the new UNnormalised PDF (red oscillations) is shown here. I am now attempting to code up the normalisation and will upload the comparison plots once successful.

## Basic Checks with asymmetry fitter

Line: 107 to 109

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>
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#### Revision 122010-10-05 - AlisonBates

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 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

Line: 15 to 15
Changed:
<
<
with standard values has been plotted with q=+1 (red) and q=-1 (blue) and gives the following distribution. The integrated area from tmin to 10.0 is 0.994402.
>
>
with standard values has been plotted with q=+1 (red) and q=-1 (blue) and gives the following distribution. The integrated area from tmin to 10.0 is 0.994402. Line: 23 to 23
Changed:
<
<
The resultant pdf needs an error function of a complex number (x+iy) which there is no such routine in Root so using the infinite series approximation for complex error function from Abramozitz and Stegun we have written a routine which yileds the folowing results for up to 6 terms of the series summation. >
>
The resultant pdf needs an error function of a complex number (x+iy) which there is no such routine in Root so using the infinite series approximation for complex error function from Abramozitz and Stegun we have written a routine which yields the folowing results for up to 7 terms of the series summation.

## Basic Checks with asymmetry fitter

Line: 108 to 106

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>
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#### Revision 112010-10-05 - AlisonBates

Line: 1 to 1

 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

Line: 23 to 23
Changed:
<
<
and obtained the following for q=+1 (red) and q=-1(blue)....
>
>
The resultant pdf needs an error function of a complex number (x+iy) which there is no such routine in Root so using the infinite series approximation for complex error function from Abramozitz and Stegun we have written a routine which yileds the folowing results for up to 6 terms of the series summation. ## Basic Checks with asymmetry fitter

Line: 105 to 107

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>
>
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#### Revision 102010-10-04 - AlisonBates

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 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

Line: 21 to 21
I am studiying the pdf obtained from the following distribution
Changed:
<
<
>
>

Changed:
<
<
and obtained the following for q=+1 (red) and q=-1(blue).
>
>
and obtained the following for q=+1 (red) and q=-1(blue)....

Deleted:
<
< ## 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.

#### Revision 92010-09-14 - AlisonBates

Line: 1 to 1

 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

The aims for the asymmetry fitter are the following

Changed:
<
<
• Perform basic checks of current fitting package with toy data for Bd and Bs asymmetries (see below).
• Implement an automatic method such that when the mass region is changed, the normalisation for the pdfs is changed.
• Add proper time pdf to the fitting package (started looking at this below).
• Add Bs→KK pdf to fit package
• Alter the parameters that are being varied by the minimiser to d, θ and γ
• Move to MC data/ real data (Bd) for first looks.
>
>
1. Perform basic checks of current fitting package with toy data for Bd and Bs asymmetries. In process of checking by Alison and will copy below once completed..
2. Implement an automatic method such that when the mass region is changed, the normalisation for the pdfs is changed. DONE by Paul.
3. Add proper time pdf to the fitting package. Stand alone model of pdfs done - see below.
4. Alter the parameters that are being varied by the minimiser to d, θ and γ.
6. Move to MC data/ real data (Bd) for first looks.

## PDF modeling for Bs

The basic pdf of

with standard values has been plotted with q=+1 (red) and q=-1 (blue) and gives the following distribution. The integrated area from tmin to 10.0 is 0.994402. I am studiying the pdf obtained from the following distribution

and obtained the following for q=+1 (red) and q=-1(blue). ## 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.

Line: 88 to 104

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>
>
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#### Revision 82010-08-23 - AlisonBates

Line: 1 to 1

 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

Line: 14 to 14
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.
Changed:
<
<
Adir Bd - input was 0.38 and fitted was 0. ± 0. ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0. ± 0. ( AmixBd)
>
>
Adir Bd - input was 0.38 and fitted was 0.3814 ± 0.0043 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.6089 ± 0.0026 ( AmixBd)
Next I generated a data sample with the following composition (calculating for our mass range...) and simultaneously fitted for the Bd2pipi asymmetries and the Bs2KK asymmetries (for now there is still no proper time description in the fitting pdf but there is Gaussian smear on the data generation). Note the mistag rates will change for simultaneous fitting to ωBs = 0.347and ωBd = 0.370.
Line: 84 to 86

>
>
 META FILEATTACHMENT attachment="B2pipiB2KpiCBAdirnew.gif" attr="" comment="" date="1282552940" name="B2pipiB2KpiCBAdirnew.gif" path="B2pipiB2KpiCBAdirnew.gif" size="15497" stream="B2pipiB2KpiCBAdirnew.gif" tmpFilename="/usr/tmp/CGItemp26948" user="AlisonBates" version="1" attachment="B2pipiB2KpiCBAmixnew.gif" attr="" comment="" date="1282552948" name="B2pipiB2KpiCBAmixnew.gif" path="B2pipiB2KpiCBAmixnew.gif" size="15308" stream="B2pipiB2KpiCBAmixnew.gif" tmpFilename="/usr/tmp/CGItemp26845" user="AlisonBates" version="1"

#### Revision 72010-08-20 - AlisonBates

Line: 1 to 1

 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

Line: 9 to 9

• Add Bs→KK pdf to fit package
• Alter the parameters that are being varied by the minimiser to d, θ and γ
Changed:
<
<
• Move to MC data/ real data (Bd) for first looks. So far it looks like around 0.3fb-1 data is enough for asymmetry fitter
>
>
• Move to MC data/ real data (Bd) for first looks.

## Basic Checks with asymmetry fitter

Changed:
<
<
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.
>
>
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.
Adir Bd - input was 0.38 and fitted was 0. ± 0. ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0. ± 0. ( AmixBd)
Changed:
<
<
Everything below is out of date and will be removed as soon as the above is updated with the newest and unbiased results. Jobs running now.
>
>
Next I generated a data sample with the following composition (calculating for our mass range...) and simultaneously fitted for the Bd2pipi asymmetries and the Bs2KK asymmetries (for now there is still no proper time description in the fitting pdf but there is Gaussian smear on the data generation). Note the mistag rates will change for simultaneous fitting to ωBs = 0.347and ωBd = 0.370.

>
>

Everything below is out of date and will be removed as soon as the above is updated with the newest and unbiased results. Jobs running now.

### 1. Bd → π π

50 datasets were generated with 6099 events per data set using 0.68 b2pipi (sf1=1 and ssb = 0.68) and 0.32 combinatoric background (MassDistribution) mass distribution. The asymmetry fitter was used to fit for Bd asymmetries only with sf1'=0.68 and obtained the following:
Adir Bd - input was 0.38 and fitted was 0.3953 ± 0.0476 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.6503 ± 0.0311 ( AmixBd)
Then re-ran same job with 150 data sets with 2000 events per data set and fitted for the following:
Adir Bd - input was 0.38 and fitted was 0.4338 ± 0.0196 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.6619 ± 0.0197 ( AmixBd)
The asymmetry plot is shown here .

#### Revision 62010-08-20 - AlisonBates

Line: 1 to 1

 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

The aims for the asymmetry fitter are the following

• Perform basic checks of current fitting package with toy data for Bd and Bs asymmetries (see below).
>
>
• Implement an automatic method such that when the mass region is changed, the normalisation for the pdfs is changed.

• Add proper time pdf to the fitting package (started looking at this below).
• Add Bs→KK pdf to fit package
Deleted:
<
<

• Alter the parameters that are being varied by the minimiser to d, θ and γ
Changed:
<
<
• Move to MC data/ real data (Bd) for first looks. So far 0.3fb-1 data is enough for asymmetry fitter

Most of the following is on my web page http://ppewww.physics.gla.ac.uk/~alison/B2hh.html where all the attached files are there and work. I have now stopped using my web page and will now just post all my results here.

>
>
• Move to MC data/ real data (Bd) for first looks. So far it looks like around 0.3fb-1 data is enough for asymmetry fitter

## 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.

Adir Bd - input was 0.38 and fitted was 0. ± 0. ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0. ± 0. ( AmixBd)

Everything below is out of date and will be removed as soon as the above is updated with the newest and unbiased results. Jobs running now.

### 1. Bd → π π

50 datasets were generated with 6099 events per data set using 0.68 b2pipi (sf1=1 and ssb = 0.68) and 0.32 combinatoric background (MassDistribution) mass distribution. The asymmetry fitter was used to fit for Bd asymmetries only with sf1'=0.68 and obtained the following:
Adir Bd - input was 0.38 and fitted was 0.3953 ± 0.0476 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.6503 ± 0.0311 ( AmixBd)
Then re-ran same job with 150 data sets with 2000 events per data set and fitted for the following:
Adir Bd - input was 0.38 and fitted was 0.4338 ± 0.0196 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.6619 ± 0.0197 ( AmixBd)
The asymmetry plot is shown here .

#### Revision 52010-08-17 - AlisonBates

Line: 1 to 1

 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

Line: 16 to 16
50 datasets were generated with 6099 events per data set using 0.68 b2pipi (sf1=1 and ssb = 0.68) and 0.32 combinatoric background (MassDistribution) mass distribution. The asymmetry fitter was used to fit for Bd asymmetries only with sf1'=0.68 and obtained the following:
Adir Bd - input was 0.38 and fitted was 0.3953 ± 0.0476 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.6503 ± 0.0311 ( AmixBd)
Then re-ran same job with 150 data sets with 2000 events per data set and fitted for the following:
Adir Bd - input was 0.38 and fitted was 0.4338 ± 0.0196 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.6619 ± 0.0197 ( AmixBd)
The asymmetry plot is shown here .
Changed:
<
<
******100 data sets with 10k events per data set using 0.68 b2pipi (sf1=1 and ssb = 0.68) and 0.32 combinatoric background and mass window of 5229 - 5329 MeV, I fit the following asymmetries:
>
>
******240 data sets with 6k (running just now will update when gets to 300) events per data set using 0.68 b2pipi (sf1=1 and ssb = 0.68) and 0.32 combinatoric background and mass window of 5229 - 5329 MeV, I fit the following asymmetries:

Changed:
<
<
Adir Bd - input was 0.38 and fitted was 0.4078 ± 0.0077 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.599 ± 0.006 ( AmixBd)
>
>
Adir Bd - input was 0.38 and fitted was 0.4175 ± 0.0080 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.675 ± 0.006 ( AmixBd)

### 2. Bs → K K

Line: 74 to 74

 META FILEATTACHMENT attachment="AsymPLotBigJob2BddecaysCB.gif" attr="" comment="" date="1281343417" name="AsymPLotBigJob2BddecaysCB.gif" path="AsymPLotBigJob2BddecaysCB.gif" size="10241" stream="AsymPLotBigJob2BddecaysCB.gif" tmpFilename="/usr/tmp/CGItemp24278" user="AlisonBates" version="1" attachment="AmixBs2KKCBwithsmearing.gif" attr="" comment="" date="1281353531" name="AmixBs2KKCBwithsmearing.gif" path="AmixBs2KKCBwithsmearing.gif" size="14465" stream="AmixBs2KKCBwithsmearing.gif" tmpFilename="/usr/tmp/CGItemp24427" user="AlisonBates" version="1" attachment="AdirBs2KKCBwithsmearing.gif" attr="" comment="" date="1281353541" name="AdirBs2KKCBwithsmearing.gif" path="AdirBs2KKCBwithsmearing.gif" size="14349" stream="AdirBs2KKCBwithsmearing.gif" tmpFilename="/usr/tmp/CGItemp24470" user="AlisonBates" version="1"
Changed:
<
<
 META FILEATTACHMENT attachment="justbdandcbnarrowmassAdir.gif" attr="" comment="" date="1281970753" name="justbdandcbnarrowmassAdir.gif" path="justbdandcbnarrowmassAdir.gif" size="15130" stream="justbdandcbnarrowmassAdir.gif" tmpFilename="/usr/tmp/CGItemp24531" user="AlisonBates" version="1" attachment="justbdandcbnarrowmassAmix.gif" attr="" comment="" date="1281970761" name="justbdandcbnarrowmassAmix.gif" path="justbdandcbnarrowmassAmix.gif" size="15434" stream="justbdandcbnarrowmassAmix.gif" tmpFilename="/usr/tmp/CGItemp24527" user="AlisonBates" version="1"
>
>
 META FILEATTACHMENT attachment="justbdandcbnarrowmassAdir.gif" attr="" comment="" date="1282042955" name="justbdandcbnarrowmassAdir.gif" path="justbdandcbnarrowmassAdir.gif" size="16256" stream="justbdandcbnarrowmassAdir.gif" tmpFilename="/usr/tmp/CGItemp24363" user="AlisonBates" version="3" attachment="justbdandcbnarrowmassAmix.gif" attr="" comment="" date="1282042963" name="justbdandcbnarrowmassAmix.gif" path="justbdandcbnarrowmassAmix.gif" size="15927" stream="justbdandcbnarrowmassAmix.gif" tmpFilename="/usr/tmp/CGItemp24188" user="AlisonBates" version="3"

#### Revision 42010-08-16 - AlisonBates

Line: 1 to 1

 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

Line: 15 to 15

### 1. Bd → π π

50 datasets were generated with 6099 events per data set using 0.68 b2pipi (sf1=1 and ssb = 0.68) and 0.32 combinatoric background (MassDistribution) mass distribution. The asymmetry fitter was used to fit for Bd asymmetries only with sf1'=0.68 and obtained the following:
Adir Bd - input was 0.38 and fitted was 0.3953 ± 0.0476 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.6503 ± 0.0311 ( AmixBd)
Then re-ran same job with 150 data sets with 2000 events per data set and fitted for the following:
Adir Bd - input was 0.38 and fitted was 0.4338 ± 0.0196 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.6619 ± 0.0197 ( AmixBd)
The asymmetry plot is shown here .

>
>
******100 data sets with 10k events per data set using 0.68 b2pipi (sf1=1 and ssb = 0.68) and 0.32 combinatoric background and mass window of 5229 - 5329 MeV, I fit the following asymmetries:

Adir Bd - input was 0.38 and fitted was 0.4078 ± 0.0077 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.599 ± 0.006 ( AmixBd)

### 2. Bs → K K

50 datasets were generated with 6099 events per data set using 0.68 bs2KK (sf3=1 and ssb = 0.68) and 0.32 combinatoric background ( mass distribution ). The asymmetry fitter was used to fit for Bs asymmetries only with sf3'=0.68 and obtained the following Adir for Bd and Amix for Bs which in numbers are:
Adir Bs - input was 0.1 and fitted was 0.0811 ± 0.0275
Amix Bs - input was 0.25 and fitted was 0.1799 ± 0.0346

Line: 69 to 74

 META FILEATTACHMENT attachment="AsymPLotBigJob2BddecaysCB.gif" attr="" comment="" date="1281343417" name="AsymPLotBigJob2BddecaysCB.gif" path="AsymPLotBigJob2BddecaysCB.gif" size="10241" stream="AsymPLotBigJob2BddecaysCB.gif" tmpFilename="/usr/tmp/CGItemp24278" user="AlisonBates" version="1" attachment="AmixBs2KKCBwithsmearing.gif" attr="" comment="" date="1281353531" name="AmixBs2KKCBwithsmearing.gif" path="AmixBs2KKCBwithsmearing.gif" size="14465" stream="AmixBs2KKCBwithsmearing.gif" tmpFilename="/usr/tmp/CGItemp24427" user="AlisonBates" version="1" attachment="AdirBs2KKCBwithsmearing.gif" attr="" comment="" date="1281353541" name="AdirBs2KKCBwithsmearing.gif" path="AdirBs2KKCBwithsmearing.gif" size="14349" stream="AdirBs2KKCBwithsmearing.gif" tmpFilename="/usr/tmp/CGItemp24470" user="AlisonBates" version="1"
>
>
 META FILEATTACHMENT attachment="justbdandcbnarrowmassAdir.gif" attr="" comment="" date="1281970753" name="justbdandcbnarrowmassAdir.gif" path="justbdandcbnarrowmassAdir.gif" size="15130" stream="justbdandcbnarrowmassAdir.gif" tmpFilename="/usr/tmp/CGItemp24531" user="AlisonBates" version="1" attachment="justbdandcbnarrowmassAmix.gif" attr="" comment="" date="1281970761" name="justbdandcbnarrowmassAmix.gif" path="justbdandcbnarrowmassAmix.gif" size="15434" stream="justbdandcbnarrowmassAmix.gif" tmpFilename="/usr/tmp/CGItemp24527" user="AlisonBates" version="1"

#### Revision 32010-08-09 - AlisonBates

Line: 1 to 1

 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

The aims for the asymmetry fitter are the following

Changed:
<
<
• Perform basic checks of current fitting package with toy data for Bd and Bs asymmetries.
• Add proper time pdf to the fitting package
>
>
• Perform basic checks of current fitting package with toy data for Bd and Bs asymmetries (see below).
• Add proper time pdf to the fitting package (started looking at this below).

• Add Bs→KK pdf to fit package
• Alter the parameters that are being varied by the minimiser to d, θ and γ
Line: 18 to 18

### 2. Bs → K K

50 datasets were generated with 6099 events per data set using 0.68 bs2KK (sf3=1 and ssb = 0.68) and 0.32 combinatoric background ( mass distribution ). The asymmetry fitter was used to fit for Bs asymmetries only with sf3'=0.68 and obtained the following Adir for Bd and Amix for Bs which in numbers are:
Adir Bs - input was 0.1 and fitted was 0.0811 ± 0.0275
Amix Bs - input was 0.25 and fitted was 0.1799 ± 0.0346

>
>
Ran a job with 100 data sets with 6000 events per data set using 0.664 Bs2KK and 0.336 combinatoric background.

Adir Bs - input was 0.1 and fitted was 0.06436 ± 0.00630 ( AdirBs)
Amix Bs - input was 0.25 and fitted was 0.1721 ± 0.0076 ( AmixBs)

Now ran the same job as above but removed the Gaussian smearing of the proper time in the toy data generation and re-ran the job and got the exact same asymmetries and uncertainties. This should make a difference surely? Still looking in to it.

### 3. Bd → π π and Bd → K π

50 data sets were generated with 6099 events per data set using 0.68 bd2pipi and bd2Kpi (sf1=sf2=0.5 and ssb = 0.68) and 0.32 combinatoric background ( mass distribution ).The asymmetry fitter was used to fit for Bd asymmetries only with sf1'=sf2'=0.34 and obtained the following Adir for Bd and Amix for Bd which in numbers are:
Adir Bd - input was 0.38 and fitted was 0.298 ± 0.206
Amix Bd - input was 0.61 and fitted was 0.660 ± 0.062

Line: 28 to 34
Amix Bd - input was 0.61 and fitted was 0.6811 ± 0.0019 ( AmixBd) and Laurence got 0.655 ± 0.024
Changed:
<
<
The asymmetry plot is shown here . However the pull plots are still showing a large bias in the mean of the pull plot (the widths are approximately ok). What's causing the bias in the pull plots? It is not present in the first case when on ly B2pipi and combinatoric background are used....looking in to this now.
>
>
The asymmetry plot is shown here . However the pull plots are still showing a large bias in the mean of the pull plot (the widths are approximately ok). What's causing the bias in the pull plots? It is not present in the first case when only B2pipi and combinatoric background are used....looking in to this now. Interesteingly, in an earlier version of Laurence's thesis he has numbers like mine then they suddenly got really good. Waiting to hear back from him to see if he can remember what he changed.

### 4. Bd → π π, Bd → K π and Bs → K K

50 datasets were generated with 6099 events per data set using all 3 channels with sf1=sf2=sf3=0.333 and ssb = 0.68) and 0.32 combinatoric background ( mass distribution ). The asymmetry fitter was used to fit for Bd asymmetries only with sf1'=sf2'=sf3'=0.226 and obtained the following Adir for Bd and Amix for Bd which in numbers are:
Adir Bd - input was 0.38 and fitted was 0.4917 ± 0.0638
Amix Bd - input was 0.61 and fitted was 0.6852 ± 0.0456
Then re-ran the asymmetry fitter for the Bs asymmetries and found;
Adir Bs - input was 0.1 and fitted was 0.0416 ± 0.0606 ( AdirBs)
Amix Bs - input was 0.25 and fitted was 0.1505 ± 0.0598( AmixBs)

>
>

### 5. Full toy data sample

-- AlisonBates - 2010-08-06
Line: 60 to 67

 META FILEATTACHMENT attachment="AdirBigJob2BddecaysCB.gif" attr="" comment="" date="1281343361" name="AdirBigJob2BddecaysCB.gif" path="AdirBigJob2BddecaysCB.gif" size="14588" stream="AdirBigJob2BddecaysCB.gif" tmpFilename="/usr/tmp/CGItemp24241" user="AlisonBates" version="1" attachment="AmixBigJob2BddecaysCB.gif" attr="" comment="" date="1281343382" name="AmixBigJob2BddecaysCB.gif" path="AmixBigJob2BddecaysCB.gif" size="14485" stream="AmixBigJob2BddecaysCB.gif" tmpFilename="/usr/tmp/CGItemp24320" user="AlisonBates" version="1" attachment="AsymPLotBigJob2BddecaysCB.gif" attr="" comment="" date="1281343417" name="AsymPLotBigJob2BddecaysCB.gif" path="AsymPLotBigJob2BddecaysCB.gif" size="10241" stream="AsymPLotBigJob2BddecaysCB.gif" tmpFilename="/usr/tmp/CGItemp24278" user="AlisonBates" version="1"
>
>
 META FILEATTACHMENT attachment="AmixBs2KKCBwithsmearing.gif" attr="" comment="" date="1281353531" name="AmixBs2KKCBwithsmearing.gif" path="AmixBs2KKCBwithsmearing.gif" size="14465" stream="AmixBs2KKCBwithsmearing.gif" tmpFilename="/usr/tmp/CGItemp24427" user="AlisonBates" version="1" attachment="AdirBs2KKCBwithsmearing.gif" attr="" comment="" date="1281353541" name="AdirBs2KKCBwithsmearing.gif" path="AdirBs2KKCBwithsmearing.gif" size="14349" stream="AdirBs2KKCBwithsmearing.gif" tmpFilename="/usr/tmp/CGItemp24470" user="AlisonBates" version="1"

#### Revision 22010-08-09 - AlisonBates

Line: 1 to 1

 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

Line: 22 to 22
50 data sets were generated with 6099 events per data set using 0.68 bd2pipi and bd2Kpi (sf1=sf2=0.5 and ssb = 0.68) and 0.32 combinatoric background ( mass distribution ).The asymmetry fitter was used to fit for Bd asymmetries only with sf1'=sf2'=0.34 and obtained the following Adir for Bd and Amix for Bd which in numbers are:
Adir Bd - input was 0.38 and fitted was 0.298 ± 0.206
Amix Bd - input was 0.61 and fitted was 0.660 ± 0.062
Changed:
<
<
Now using 150 data sets with 100k events per data set using bd2pipi and bd2Kpi (sf1= 0.845 and sf2=0.155 and ssb = 0.664, see Laurence's thesis, page 183). The asymmetry fitter was used to fit for Bd asymmetries with sf1'=0.561 and sf2'=0.103 and obtained the following:
Adir Bd - input was 0.38 and fitted was 0.4241 ± 0.0017 ( AdirBd) and Laurence got 0.407 ± 0.033
Amix Bd - input was 0.61 and fitted was 0.6818 ± 0.0018 ( AmixBd) and Laurence got 0.655 ± 0.024
The asymmetry plot is shown here . The pull plots show a large bias. The only difference was the large mass window I used (4800 - 5800 MeV) compared with Laurence (5229 - 5329 MeV). Hence I have re-run the same signal fractions in a 5fb-1 job (300 data sets with 100k events per data set) with the much tighter mass window and found the following:
>
>
Now using 150 data sets with 100k events per data set using bd2pipi and bd2Kpi (sf1= 0.845 and sf2=0.155 and ssb = 0.664, see Laurence's thesis, page 183). The asymmetry fitter was used to fit for Bd asymmetries with sf1'=0.561 and sf2'=0.103 and obtained the following:
Adir Bd - input was 0.38 and fitted was 0.4241 ± 0.0017 ( AdirBd) and Laurence got 0.407 ± 0.033
Amix Bd - input was 0.61 and fitted was 0.6818 ± 0.0018 ( AmixBd) and Laurence got 0.655 ± 0.024
The asymmetry plot is shown here . The pull plots show a large bias. The only difference was the large mass window I used (4800 - 5800 MeV) compared with Laurence (5229 - 5329 MeV). Hence I have re-run the same signal fractions in a 5fb-1 job (288 data sets with 100k events per data set) with the much tighter mass window and found the following:

Changed:
<
<
Adir Bd - input was 0.38 and fitted was 0. ± 0. ( AdirBd) and Laurence got 0.407 ± 0.033
>
>
Adir Bd - input was 0.38 and fitted was 0.4245 ± 0.0022 ( AdirBd) and Laurence got 0.407 ± 0.033

Changed:
<
<
Amix Bd - input was 0.61 and fitted was 0. ± 0. ( AmixBd) and Laurence got 0.655 ± 0.024
>
>
Amix Bd - input was 0.61 and fitted was 0.6811 ± 0.0019 ( AmixBd) and Laurence got 0.655 ± 0.024

Changed:
<
<
The asymmetry plot is shown here .
>
>
The asymmetry plot is shown here . However the pull plots are still showing a large bias in the mean of the pull plot (the widths are approximately ok). What's causing the bias in the pull plots? It is not present in the first case when on ly B2pipi and combinatoric background are used....looking in to this now.

### 4. Bd → π π, Bd → K π and Bs → K K

50 datasets were generated with 6099 events per data set using all 3 channels with sf1=sf2=sf3=0.333 and ssb = 0.68) and 0.32 combinatoric background ( mass distribution ). The asymmetry fitter was used to fit for Bd asymmetries only with sf1'=sf2'=sf3'=0.226 and obtained the following Adir for Bd and Amix for Bd which in numbers are:
Adir Bd - input was 0.38 and fitted was 0.4917 ± 0.0638
Amix Bd - input was 0.61 and fitted was 0.6852 ± 0.0456
Then re-ran the asymmetry fitter for the Bs asymmetries and found;
Adir Bs - input was 0.1 and fitted was 0.0416 ± 0.0606 ( AdirBs)
Amix Bs - input was 0.25 and fitted was 0.1505 ± 0.0598( AmixBs)

Line: 57 to 57

>
>
 META FILEATTACHMENT attachment="AdirBigJob2BddecaysCB.gif" attr="" comment="" date="1281343361" name="AdirBigJob2BddecaysCB.gif" path="AdirBigJob2BddecaysCB.gif" size="14588" stream="AdirBigJob2BddecaysCB.gif" tmpFilename="/usr/tmp/CGItemp24241" user="AlisonBates" version="1" attachment="AmixBigJob2BddecaysCB.gif" attr="" comment="" date="1281343382" name="AmixBigJob2BddecaysCB.gif" path="AmixBigJob2BddecaysCB.gif" size="14485" stream="AmixBigJob2BddecaysCB.gif" tmpFilename="/usr/tmp/CGItemp24320" user="AlisonBates" version="1" attachment="AsymPLotBigJob2BddecaysCB.gif" attr="" comment="" date="1281343417" name="AsymPLotBigJob2BddecaysCB.gif" path="AsymPLotBigJob2BddecaysCB.gif" size="10241" stream="AsymPLotBigJob2BddecaysCB.gif" tmpFilename="/usr/tmp/CGItemp24278" user="AlisonBates" version="1"

#### Revision 12010-08-06 - AlisonBates

Line: 1 to 1
>
>
 META TOPICPARENT name="WebHome"

# B2hh GFact Asymmetry Fitting page

The aims for the asymmetry fitter are the following

• Perform basic checks of current fitting package with toy data for Bd and Bs asymmetries.
• Add proper time pdf to the fitting package
• Add Bs→KK pdf to fit package
• Alter the parameters that are being varied by the minimiser to d, θ and γ
• Move to MC data/ real data (Bd) for first looks. So far 0.3fb-1 data is enough for asymmetry fitter

Most of the following is on my web page http://ppewww.physics.gla.ac.uk/~alison/B2hh.html where all the attached files are there and work. I have now stopped using my web page and will now just post all my results here.

## Basic Checks with asymmetry fitter

### 1. Bd → π π

50 datasets were generated with 6099 events per data set using 0.68 b2pipi (sf1=1 and ssb = 0.68) and 0.32 combinatoric background (MassDistribution) mass distribution. The asymmetry fitter was used to fit for Bd asymmetries only with sf1'=0.68 and obtained the following:
Adir Bd - input was 0.38 and fitted was 0.3953 ± 0.0476 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.6503 ± 0.0311 ( AmixBd)
Then re-ran same job with 150 data sets with 2000 events per data set and fitted for the following:
Adir Bd - input was 0.38 and fitted was 0.4338 ± 0.0196 ( AdirBd)
Amix Bd - input was 0.61 and fitted was 0.6619 ± 0.0197 ( AmixBd)
The asymmetry plot is shown here .

### 2. Bs → K K

50 datasets were generated with 6099 events per data set using 0.68 bs2KK (sf3=1 and ssb = 0.68) and 0.32 combinatoric background ( mass distribution ). The asymmetry fitter was used to fit for Bs asymmetries only with sf3'=0.68 and obtained the following Adir for Bd and Amix for Bs which in numbers are:
Adir Bs - input was 0.1 and fitted was 0.0811 ± 0.0275
Amix Bs - input was 0.25 and fitted was 0.1799 ± 0.0346

### 3. Bd → π π and Bd → K π

50 data sets were generated with 6099 events per data set using 0.68 bd2pipi and bd2Kpi (sf1=sf2=0.5 and ssb = 0.68) and 0.32 combinatoric background ( mass distribution ).The asymmetry fitter was used to fit for Bd asymmetries only with sf1'=sf2'=0.34 and obtained the following Adir for Bd and Amix for Bd which in numbers are:
Adir Bd - input was 0.38 and fitted was 0.298 ± 0.206
Amix Bd - input was 0.61 and fitted was 0.660 ± 0.062

Now using 150 data sets with 100k events per data set using bd2pipi and bd2Kpi (sf1= 0.845 and sf2=0.155 and ssb = 0.664, see Laurence's thesis, page 183). The asymmetry fitter was used to fit for Bd asymmetries with sf1'=0.561 and sf2'=0.103 and obtained the following:
Adir Bd - input was 0.38 and fitted was 0.4241 ± 0.0017 ( AdirBd) and Laurence got 0.407 ± 0.033
Amix Bd - input was 0.61 and fitted was 0.6818 ± 0.0018 ( AmixBd) and Laurence got 0.655 ± 0.024
The asymmetry plot is shown here . The pull plots show a large bias. The only difference was the large mass window I used (4800 - 5800 MeV) compared with Laurence (5229 - 5329 MeV). Hence I have re-run the same signal fractions in a 5fb-1 job (300 data sets with 100k events per data set) with the much tighter mass window and found the following:

Adir Bd - input was 0.38 and fitted was 0. ± 0. ( AdirBd) and Laurence got 0.407 ± 0.033

Amix Bd - input was 0.61 and fitted was 0. ± 0. ( AmixBd) and Laurence got 0.655 ± 0.024

The asymmetry plot is shown here .

### 4. Bd → π π, Bd → K π and Bs → K K

50 datasets were generated with 6099 events per data set using all 3 channels with sf1=sf2=sf3=0.333 and ssb = 0.68) and 0.32 combinatoric background ( mass distribution ). The asymmetry fitter was used to fit for Bd asymmetries only with sf1'=sf2'=sf3'=0.226 and obtained the following Adir for Bd and Amix for Bd which in numbers are:
Adir Bd - input was 0.38 and fitted was 0.4917 ± 0.0638
Amix Bd - input was 0.61 and fitted was 0.6852 ± 0.0456
Then re-ran the asymmetry fitter for the Bs asymmetries and found;
Adir Bs - input was 0.1 and fitted was 0.0416 ± 0.0606 ( AdirBs)
Amix Bs - input was 0.25 and fitted was 0.1505 ± 0.0598( AmixBs)

-- AlisonBates - 2010-08-06