Transcript B d →π + π

Status of the Glasgow B→hh
analysis
CP Working group γ from loops
15th October 2010
Paul Sail, Lars Eklund and Alison Bates
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
2
Data selection
•
•
Run on 2 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
3
B→hh
Bd→K+π-
Bd→π+π-
Bd→Kπ
Bd→K-π+
Bs→K+K4
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).
5
Fit for signal fractions
• The signal fractions are fitted for by maximising
this total likelihood to find P(class)
f (m, PID)   f (m, PID | class )  P(class )
class
Total likliehood
PDF for each class
Prob for each class
• The signal probability used in subsequent fits is
Mass distribution
for each class
f (m, PID | class )  P(class )
P(class | m, PID) 
f (m, PID)
Prob. of a particular event
being in each decay class
Total mass PDF
6
Signal fraction Fitter
• Details on the signal fraction fitter
7
Mass distribution
• Add the plot of the overlapping mass
distributions
8
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
9
*the pull means are showing a slight bias but this is not a true bias, as will be discussed in the next slide
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
Bd→π+πBd→K+πBd→π+KBs→K+K-
• The bias in absolute numbers is less than 0.1 % if more than 1000 events
10
are used, below that number a measurable bias is seen.
Sensitivity to number of events…
continued
Bd→π+πBd→K+πBd→π+KBs→K+K-
• The sigma of the pull distribution seems fairly independent
of the number of events.
11
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
12
Asymmetry fitter
• Currently implemented analytical PDFs using
the following expressions for the time class
models

t
f (t , q,t min | Bd   )  Ne [1  q (1  2 ){ Adir cos( mt )  Amix sin( mt )}]


t
f (t , q,t min | Bd  K )  Ne  [1  q(1  2 ) Adir cos( mt )]
1
1
f (t , q, t min | Bs  KK )  N ' e (   ) [(e t  1)  A (e   1)  q (1  2 w){ Adir cos( mt )  Amix sin( mt )}]
2
2
t
t
f (t , q, t min | Combinatoric )  f short
e
 short
2 shorte
t min
 short
 f long
e
 long
t min
2 longe
 long
13
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 14
Time distribution for Bd→π+π-
15
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
1
t
f (t | t min , signal )  N e  [cosh

t
t
 A sinh
]
2
2
[1  q (1  2 )( Adir cos( mt )  Amix sin( mt ))](t  t min ) 
1
e
2
(t 't ) 2
2 2
Which results in the new PDF for Bs→K+K-:
t
f (t , q, t min )  Ne  [{cosh(
q (1  2 )
 Adir
e
2
 Amix
 m 2 2
2
q (1  2 )
e
2i
 m 2 2
2
t
t  t min
t
t  t min
)F (
)  A sinh(
)F (
)}
2

2

{e imt F (
t  t min
 mi )  e imt F (
t  t min
 mi )  e imt F (
{e imt F (


t  t min
 mi )}
t  t min
 mi )}]


16
New Bs→K+K- PDF
New PDF
Old PDF
Now need to implement this new
PDF in G-Fact and run the
asymmetry fitter and study the
improvement in the Bs asymmetries
17
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
18
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.
19
Thanks
20
Bias in pulls using just statistical
uncertainties
21
22
Example Asymmetry fits
23