Status of the Glasgow B→hh analysis

CP Working group γ from loops14th October 2010

Paul Sail, Lars Eklund and Alison Bates

2

Overview

• Data selection

• Introduce Glasgow’s newly developed fitting package called G-Fact.

• Signal fraction fit results on toy data including sensitivity study on the number of events.

• Asymmetry fitter using the mass fitter signal fractions as input.

• Summary and outlook

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Data selection• Run on X pb-1 from Real Data + Reco06-Stripping10-Merged• List of selection cuts:

– min(piplus_MINIPCHI2, piminus_MINIPCHI2)>30– max(piplus_MINIPCHI2, piminus_MINIPCHI2)>100– min(piplus_PT, piminus_PT)>1500– max(piplus_PT, piminus_PT)>3000– max(piplus_TRACK_CHI2NDOF,piminus_TRACK_CHI2NDOF)<4– B0_PT>2000– B0_IPCHI2_OWNPV<8 && B0_DIRA_OWNPV>0.99995– B0_FDCHI2_OWNPV>625– B0_OWNPV_CHI2/B0_OWNPV_NDOF<1.6

• PID Cuts– piplus_PIDmu<5 && piminus_PIDmu<5 && piplus_PIDe<2.5 &&

piminus_PIDe<2.5 && piplus_PIDp<-1 && piminus_PIDp<0– piplus_PIDK<0– piminus_PIDK<0– piplus_PIDK>0– piminus_PIDK>0

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5

G-Fact

• Glasgow has developed a stand alone fitting package called G-Fact (Glasgow Fitter of ACp and Time) which can– Fit for the signal fraction– Then either fit for

• lifetimes or

• Adir,mix(B(d,s)→hh).

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Signal Fraction Fitter

• Using Toy MC Data

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Fit for signal fractions

• The signal fractions are fitted for by maximising this total likelihood to find P(class)

• The signal probability used in subsequent fits is

class

classPclassPIDmfPIDmf )()|,(),(

),(

)()|,(),|(

PIDmf

classPclassPIDmfPIDmclassP

PDF for each class Prob for each class

Prob. of a particular event being in each decay class Total mass PDF

Mass distribution for each class

Total likliehood

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Signal fractions

Use a toy data sample with 1000 data sets, 100k events each data set

Decay True s/f [%]

Initial value [%]

Mean fit value [%]

Sigma fit value [%]

Pull mean*

Pull sigma

Bd→π+π- 8.47 10 8.45 0.13 -0.13±0.03 1.02±0.02

Bd→K+π- 17.82 15 17.84 0.14 0.12±0.03 0.99±0.03

Bd→K-π+ 14.58 15 14.58 0.13 -0.02±0.03 1.01±0.03

Bs→K+K- 8.47 10 8.47 0.10 0.01±0.03 1.02±0.03

Bs→K+π- 1.62 1 1.62 0.07 -0.03±0.04 0.96±0.03

Bs→K-π+ 0.72 1 0.71 0.05 -0.32±0.03 1.01±0.02

Bd→π+π-π0 15.0 10 14.98 0.16 -0.11±0.03 1.02±0.02

Combinatoric 33.32 38 35.02

*the pull means are showing a slight bias but this is not a true bias, as will be discussed in the next slide

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Sensitivity to number of events• The mean of the pull distribution for the fitted s/f seems to show a bias for

large data samples• However, the bias in absolute numbers is shown below

– absolute bias = pull mean * statistical error of fit

• The bias in absolute numbers is less than 0.1 % if more than 1000 events are used, below that number a measurable bias is seen.

Bd→π+π-

Bd→K+π-

Bd→π+K-

Bs→K+K-

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Sensitivity to number of events… continued

• The sigma of the pull distribution seems fairly independent of the number of events.

Bd→π+π-

Bd→K+π-

Bd→π+K-

Bs→K+K-

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Sensitivity to initial values• A study has been performed to test how sensitive the signal fraction

fitter is to the initial values given to the fit. Initial values were generated randomly in the following ranges, – Bd→π+π- [0.02,0.279]– Bd→K+π- [0.125,0.428]– Bd→K-π+ [0.099,0.354]– Bs→K+K- [0.061,0.25]– Combinatoric [0.11,0.35]

• Conclusions– Statistical error is independent of initial fit input values, as expected.– Mean of the pull is distributed over ±0.1 for all signal classes and initial

values for #events>1000– Bias in pull mean in absolute numbers is

• Less than 0.1% if #events > 1000• Less than 0.5% if #events > 100

– Sigma of the pull distribution is independent of #events and initial values

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Asymmetry fitter

• Currently implemented analytical PDFs using the following expressions for the time class models

long

long

short

short

t

long

t

longt

short

t

short

mixdirts

dirt

d

mixdirt

d

e

ef

e

eficCombinatortqtf

mtAmtAwqeAeeNKKBtqtf

mtAqNeKBtqtf

mtAmtAqNeBtqtf

minmin

22

)|,,(

)}]sin()cos(){21(2

1)1(

2

1)1[(')|,,(

)]cos()21(1[)|,,(

)}]sin()cos(){21(1[)|,,(

min

)(min

min

min

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CP asymmetry fitterUsing Toy MC Data

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Asymmetry Fits• Using a toy data sample which contained

– Generated s/fs of 24% Bd2pipi, 20% Bd2Kpi and 21%Bs2KK events with the rest being combinatoric background. SSB = 0.65

– Fit signal fractions used in asymmetry fitter obtained from the signal fraction fitter– 1000 data sets with 100k events.

Generated Asymmetry

Fit input Asymmetry

Mean fitted Asymmetry

Sigma of Fitted Asymmetry

Adir(Bd→π+π-) 0.38 0.32 0.380±0.002 0.061±0.002

Amix(Bd→π+π-) 0.61 0.69 0.604±0.002 0.048±0.001

Adir(Bs→K+K-) 0.1 0.15 0.088±0.002 0.057±0.001

Amix(Bs→K+K-) 0.25 0.3 0.194±0.002 0.057±0.001

Bd asymmetries are very well fitted

Bs asymmetries are not so well fitted since there is no proper time resolution modelled in the fitted as yet and there is a Gaussian smearing in the generation

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Time distribution for Bd→π+π-

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Improved Bs→K+K- asymmetry fitter• Currently the Bs→K+K- asymmetry fitter has no proper time resolution

modelled. We have just completed the calculation for the analytical expression for the normalised PDF

2

2

2

)'(

min

min

2

1)())]sin()cos()(21(1[

]2

sinh2

[cosh1

),|(

tt

mixdir

t

ettmtAmtAq

tA

teNsignalttf

Which results in the new PDF for Bs→K+K-:

)}]()({2

)21(

)}()({2

)21(

)}()2

sinh()()2

[{cosh(),,(

minmin2

minmin2

minminmin

22

22

imtt

Feimtt

Feei

qA

imtt

Feimtt

Feeq

A

ttF

tA

ttF

tNetqtf

mtimtim

mix

mtimtim

dir

t

17

New Bs→K+K- PDF

Now need to implement this new PDF in G-Fact and run the asymmetry fitter and study the improvement in the Bs asymmetries

New PDF Old PDF

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Summary

• Selection from data looks good• Developed new fitting package, G-Fact, for

B→hh decays– Signal fractions fits are good – sensitivity on number of events and initial fit

parameters studied using signal fraction fitter– Asymmetry fitter well developed and tested– Lifetime fitter exists and has been extensively tested

in charm area but soon will be developed in B→hh

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Outlook• Signal fraction fitter

– Verify on MC– Run on real data

• Need to study current PID PDFs which are currently extracted from MC

• Need to compare mass PDFs from data and MC to extract offsets and scale factors

• Implement Λb decays into background

• Asymmetry fitter– Implement and test new analytical PDF for Bs decays– Re-express the 4 currently independent asymmetries in terms of

d, θ and γ• Lifetime fitter

– Start rigorous testing in B→hh decays.

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Thanks

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Bias in pulls using just statistical uncertainties

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Back-up Slide

• Input parametersfor analytic expressions…– Send to Paul on Tuesday

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Example Asymmetry fits