[PPT] - CKM 2006 CKM 2006 Extracting CKM phase from phase from PowerPoint Presentation

SLIDE 1

Extracting CKM Extracting CKM phase from  phase from  B B±

±

  K K±

± 

+

+ 

-

and

and B B0

0, B

, B0

0 

 K KS

S 

+

+ 

-

Ignacio Bediaga, Gabriel Guerrer,

Ignacio Bediaga, Gabriel Guerrer, Jussara Miranda Jussara Miranda

CBPF – Rio de Janeiro , Brazil CBPF – Rio de Janeiro , Brazil

1 ) Feasibility of |A| 1 ) Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit 2 ) Extracting  2 ) Extracting 

CKM 2006 CKM 2006

1 1

hep-ph/0608268 hep-ph/0608268

Gabriel Guerrer - guerrer@cbpf.br Gabriel Guerrer - guerrer@cbpf.br

15/12/2006 15/12/2006

SLIDE 2

2 2 ,

2 vs 3 body amplitudes

B B0

K*(1430) K*(1430)+

+ 

-

K

Ks

s 

(770) (770)0 K Ks

s f

f0

0(980)

(980)

K Ks

s 

c0

c0

K Ks

s 

+

+ 

-

15/12/2006

15/12/2006

B B0

K K+

+ 

-

a e

a e i

i  

K*(890) K*(890)+

+ 

-

a

aj

j e

e i

i 

j

j

x

BW

BWj

j(E)

(E)

Gabriel Guerrer

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

m mj

j

SLIDE 3

3 3 ,

Analysis Formalism* Analysis Formalism*

Gabriel Guerrer

A(x) =

A(x) =  i

i

a ai

i e

e i

i  i

i

S

Si

i J J(x)

(x)

a ai

i

→ → magnitude magnitude , ,  i

i

→ → strong + weak phases strong + weak phases x = { s x = { sl

l m m , s

, sm n

m n }

} → → Dalitz variables Dalitz variables

s sl m

l m =

(p = (pl

l   +

p + pm

m  )

)2

2 =

m = ml

l 2 2 +

m + mm

m 2 2 +

2 E + 2 El

lE

Em

m – 2 p

– 2 pl

l p

pm

m cos

cos  l m

l m

S Si

i J J

→

→form factors x

form factors x BW BW x angular term (spin J) x angular term (spin J)

*AKA Isobaric Model *AKA Isobaric Model

15/12/2006 15/12/2006

all interm states all interm states

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 4

4 4 ,

Toy Model Toy Model

Gabriel Guerrer

A =

BW A = BW1

1 +

+ r r e e i

i   BW

BW2

2

Phase space (Dalitz Plot) points distribution

Phase space (Dalitz Plot) points distribution

∝

|A| |A|2

2 = |BW

= |BW1

1|

|2

2+

+ r r 2

2 |BW

|BW2

2|

|2

2 +

+ + 2 + 2r r cos cos   Re BW Re BW1

1 BW

BW2

2 * * + 2

+ 2r r sin sin   Im BW Im BW1

1 BW

BW2

2 * *

interference interference

1 1 2 2

DP DP

15/12/2006 15/12/2006

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 5

5 5 ,

Toy Model Toy Model

Gabriel Guerrer

r r= 1, = 1,



   0 .. 2 0 .. 2 

surface univocally defined by the set of parameters

surface univocally defined by the set of parameters { {

r

r, ,  

}

15/12/2006 15/12/2006

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 6

given a set of points modelled by A :

given a set of points modelled by A :

PDF PDF = = 1 1 | |BW

BW1

1 +

+ r r e e i

i   BW

BW2

2 |

|2

2

M = ∫ ds M = ∫ ds13

13ds

ds23

23 |A|

|A| 2

2

Likelihood Fit Likelihood Fit : : r, r,  



 extracted extracted

Fit of Isobaric amplitudes in 3 body decays has been

Fit of Isobaric amplitudes in 3 body decays has been successfully used in many analysis from BaBar, Belle, Focus, etc successfully used in many analysis from BaBar, Belle, Focus, etc

ex:

ex:  (500) discovery, Fermilab E791, Phys Rev Lett (500) discovery, Fermilab E791, Phys Rev Lett 86 86, 770 , 770

6 6 ,

Fitting |A| Fitting |A|2

2

Gabriel Guerrer

M M

ex: r= 1.2, ex: r= 1.2, =1 =1

15/12/2006 15/12/2006

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 7

s s12

12

s s13

13

s s12

12

s s13

13

7 7 ,

B

B0

0 

 K Ks

s 

+

+ 

-

resonances

resonances

Gabriel Guerrer

B B0

K*(890) K*(890)



 K*(1430) K*(1430)



 K Ks

s 

(770) (770)0 K Ks

s f

f0

0(980)

(980) K Ks

s 

c0

c0

K Ks

s

 +

+

 -

1

1 2 2 3 3

15/12/2006 15/12/2006

B B0

K*(890) K*(890)



 K*(1430)  K*(1430)  K Ks

s 

(770) (770)0 K Ks

s f

f0

0(980)

(980) K Ks

s 

c0

c0

|A| |A|2

2

|A'| |A'|2

2

+

+
+
+
+
+
+
+

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 8

8 8 ,

B

B0

0 

 K Ks

s 

+

+ 

-

amplitudes

amplitudes

Gabriel Guerrer

time independent time independent

B B0

0 

 K

Ks

s 

+

+ 

-

: A,

: A, B B0

0 

 K

Ks

s 

-



+

+ : A'

: A'

time dependence time dependence

  B B0

0/ B

/ B0

0 mixing

mixing

Prob. (t=

0) B

Prob. (t=

0) B0   (t= t) K (t= t) KS

S 

+

+ 

-

M (t)=

e M (t)= e-(

(

/2-iM)t /2-iM)t[A cos(

[A cos( m t/2) – i q/p A' sen( m t/2) – i q/p A' sen( m t/2)] m t/2)]

Prob. (t=

0) B

Prob. (t=

0) B0   (t= t) K (t= t) KS

S 

+

+ 

-

M' (t)=

e M' (t)= e-(

(

/2-iM)t /2-iM)t[A' cos(

[A' cos( m t/2) – i p/q A sen( m t/2) – i p/q A sen( m t/2)] m t/2)]

15/12/2006 15/12/2006

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 9

9 9 ,

Good news Good news

Gabriel Guerrer

if | p/q| = 1 if | p/q| = 1

Prob. ( B
Prob. ( B0

0 or

r B

B0

0 

 K Ks

s 

+

+ 

-

)

) ∝ ∝ |M(t)| |M(t)|2

2+|M'(t)|

+|M'(t)|2

2 =

= e e- t



t

 ( |A|

( |A|2

2+|A'|

+|A'|2

2 )

)

mixing effects cancels out! mixing effects cancels out! time independent amp time independent amp 



NO TAGGING NO TAGGING

G. Burdman
G. Burdman et al

et al, Phys Rev , Phys Rev 45 45, 187 , 187

15/12/2006 15/12/2006

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 10

10 10 ,

In practice In practice

Gabriel Guerrer

DATA DATA B B0

0 +

B + B0

15/12/2006 15/12/2006

|A| |A|2

2

|A'| |A'|2

2

Is possible to extract parameters Is possible to extract parameters separately from A and A' in a joint sample? separately from A and A' in a joint sample?

{ { r r1

1 ,

,  

1 1 , ...}

, ...} { { r r2

2 ,

,  2

2 , ...}

, ...}

? ?

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 11

11 11 ,

In practice In practice

Gabriel Guerrer

DATA DATA B B0

0 +

B + B0

15/12/2006 15/12/2006

| A| | A|

2 2

| A'| | A'|

2 2

N N1

1

N N2

2

? ?

Yes! Yes!

reason reason: different, non-overlap : different, non-overlap interferences interferences 



different surfaces different surfaces

also possible to extract the number of also possible to extract the number of events N events N1

1, N

, N2

2 of each set, measuring

f each set, measuring

direct CPV direct CPV

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 12

12 12 ,

Fit |A|

Fit |A|2

2 +

+ |A'| |A'|2

2 how to

how to

Gabriel Guerrer

PDF PDF = =

1 1 { | S { | S1

1+

+ r r1

1e

e i

i 1 1  S

S2

2 +...

+...| |2

2 +

+| | r r S S1

1 +

+ r r2

2e

e i

i 2 2  S

S3

3 +...

+...| |2

2 }

} M M1

1 = ∫ds

= ∫ds13

13ds

ds23

23 |A|

|A| 2

2, M

, M2

2 = ∫ds

= ∫ds13

13ds

ds23

23 |A'|

|A'| 2

2

Likelihood Fit Likelihood Fit

r

r1

1 ,

,  

1 1 ,

, r r2

2 ,

,  2

2 ,

, r r , ... , ...

→

→ univocally extracted univocally extracted r r

→

→ scale, fundamental for measuring scale, fundamental for measuring N N1

1and

and

N

N2

2

N N1

1 ,

, N N2

2 →

→ N N1

1 /

/ N N2

2 =

= M M1

1 / M

/ M2

2

M M1

1+ M

+ M2

2

15/12/2006 15/12/2006

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 13

13 13 ,

Feasibility Feasibility test test

Gabriel Guerrer

We generated and fitted 100 samples of

We generated and fitted 100 samples of 100K 100K B B0

0 +

B + B0

0 events each, using the method discussed

events each, using the method discussed previously previously

The input resonances magnitudes and phases

The input resonances magnitudes and phases were inspired in BaBar results were inspired in BaBar results hep-ex:0507004 hep-ex:0507004

The errors that will be shown are

The errors that will be shown are RMS RMS from the from the 100 sample distributions 100 sample distributions

15/12/2006 15/12/2006

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 14

14 14 ,

Feasibility Feasibility test test

Gabriel Guerrer

decay B0 / B0 input fitted c0 Ks a0 / b0 0.3 / 0.3 Fixed / (0.3 ± ± 0.03) 0 / 0  3.78 / 3.78 fixed / fixed K*(890)  a1 / b1 1.17 / 1.3 (1.17 ± ± 0.06) / (1.30 ± ± 0.01) 1 / 1  0.4 / 5.98 (0.41 ± ± 0.08) / (5.99 ± ± 0.07) K*(1430)  a2 / b2 2.45 / 2.72 (2.45 ± ± 0.11) / (2.72 ± ± 0.13) 2 / 2  0.375 / 6.0 (0.39 ± ± 0.08) / (6.00 ± ± 0.06) 0 Ks a3 / b3 0.6 / 0.6 (0.60 ± ± 0.04) / (0.60 ± ± 0.04) 3 / 3  1.2 / 1.2 (1.22 ± ± 0.09) / (1.20 ± ± 0.07) f0 Ks a4 / b4 1.03 / 1.03 (1.02 ± ± 0.06) / (1.04 ± ± 0.05) 4 / 4  2.3 / 2.3 (2.30 ± ± 0.07) / (2.30 ± ± 0.08)

N

N1

1 / N

/ N2

2 =

0.84 = 0.84 ± ± 0.12 0.12

small errors

small errors

15/12/2006 15/12/2006

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 15

15 15 ,

Belle results Belle results

Gabriel Guerrer

Recently, Belle released the final result for the

Recently, Belle released the final result for the untagged amplitude analysis of B untagged amplitude analysis of B0

0

K Ks

s

+

+

-

:

: hep-ex: 0610081 hep-ex: 0610081

Against the theoretical previsions, they assume

Against the theoretical previsions, they assume no CP violation, i.e. no CP violation, i.e. A(x,y) A(x,y)

=

= A'(y,x) A'(y,x)

They comment about measuring an average.

They comment about measuring an average. This technical difficulty would be avoided if they This technical difficulty would be avoided if they made the joint fit as proposed here made the joint fit as proposed here

15/12/2006 15/12/2006

1 ) 1 ) Feasibility of |A| Feasibility of |A|2

2 +|A'|

+|A'|2

2 fit

fit

SLIDE 16

16 16 ,

Extracting  Extracting 

Gabriel Guerrer

Two step Two step

Analyse

Analyse B

B±

±

K K±

±

+

+

-

to extract

to extract penguin penguin amplitude and amplitude and phase from phase from K*

K* resonances

resonances

Analyse joint (not-tagged)

Analyse joint (not-tagged) B

B0

0, B

, B0

0

K Ks

s

+

+

-

,

, using the using the B

B±

±

penguin to extract penguin to extract tree tree parameters and  parameters and 

Depends on Depends on

Possibility to measure independently B

Possibility to measure independently B0 and and B B0 parameters in parameters in the joint sample (we can do it as shown before) the joint sample (we can do it as shown before)

3 widely accepted hypothesis (we can test them)

3 widely accepted hypothesis (we can test them)

2 ) 2 ) Extracting Extracting  

15/12/2006 15/12/2006

SLIDE 17

17 17 ,

B B±

±

K K±

±

+

+

-

contributions

contributions

Gabriel Guerrer

B B±

±

K*(890) K*(890)0

0 

±

± : a

: ap

p e

e i

i  p

p

B B±

±

K*(1430) K*(1430)0

0 

±

± : a'

: a'p

p e

e i

i  p

p'

'

B B±

±

K K±

± ,

, f f0

: A, B

: A, B B B±

±

K K±

± 

c0

c0 :

: a at

t e

e i

i  t t

1 1st

st hypothesis

hypothesis

: : K*

K* from

from B

B±

±

has only penguin contribution

15/12/2006 15/12/2006

2 ) 2 ) Extracting Extracting  

SLIDE 18

18 18 ,

B

B0

0

K Ks

s

+

+

-

contributions

contributions

Gabriel Guerrer

B B0

0

K*(890) K*(890)+

+ 

-

:

: a at

t e

e i (

i ( t

t +

)  + )  +

+

a

ap

p e

e i

i  p

p

B B0

0

K*(1430) K*(1430)+

+ 

-

:

: a' a't

t e

e i (

i ( t

t'

' + )  + )  +

+

a'

a'p

p e

e i

i  p

p'

'

B B0

0

K Ks

s ,

, f f0

: A', B'

: A', B' B B0

0

K Ks

s 

c0

c0 :

: a at

t e

e i

i t t

2 2nd

nd hypothesis

hypothesis

: penguin from : penguin from B

B0

K*

is the same of

is the same of B

B±

±

15/12/2006 15/12/2006

2 ) 2 ) Extracting Extracting  

SLIDE 19

19 19 ,

2 2nd

nd hypothesis

hypothesis

Gabriel Guerrer

➔penguin from

penguin from B B±

± K*

K*

is the same of B

is the same of B0

➔Flavour SU(3) symmetry

Flavour SU(3) symmetry

u u b s d d g W+

B B±

±

d d b s u u g W+

B B0

15/12/2006 15/12/2006

2 ) 2 ) Extracting Extracting  

SLIDE 20

20 20 ,

 c0

c0

Gabriel Guerrer

amplitudes and phases are always measured relative to a

amplitudes and phases are always measured relative to a fixed one fixed one

to compare amplitudes and phases from

to compare amplitudes and phases from B B0

0 and

and B B±

±, we

, we must measure them relative to the same anchor must measure them relative to the same anchor

we choose the

we choose the  c0

c0 , because we expect the same

, because we expect the same contribution to contribution to B B±

± and B

and B0

0, based on its graphic

, based on its graphic

u, d u, d b c c s W+

3 3rd

rd hypothesis

hypothesis

: : 

c0

c0

is the same is the same for for B

B±

±

and and B

B0

15/12/2006 15/12/2006

2 ) 2 ) Extracting Extracting  

SLIDE 21

21 21

Idea Idea

Gabriel Guerrer

B B±

±

K*(890)

K*(890)0



±

±:

: a ap

p e

e i

i  p p

B B0

0

K*(890)

K*(890)+

+ 

-

:

: a ap

p e

e i

i  p p +

+ a at

t

e e i

i  

B B0

0

K*(890)

K*(890)-



+

+ :

: a ap

p e

e i

i  p p +

+ a at

t

e e i

i  

knowing knowing penguin penguin   can extract can extract a at

t ,

,  ,

 ,

a

at

t

and



 for model consistency, we must measure for model consistency, we must measure a at

t=

= a

at

t

 = =t

t +

 +   = =t

t - 



15/12/2006 15/12/2006

2 ) 2 ) Extracting Extracting  

SLIDE 22

22 22

 

Gabriel Guerrer

The ability of measuring The ability of measuring   is related to the value of is related to the value of   and the ratio* and the ratio* r = a r = at

t / a

/ ap

p

In our Monte Carlo 100x100k test samples we input: In our Monte Carlo 100x100k test samples we input:   = 69 = 69o

, r =

0.45 , r = 0.45 and measure: and measure:

  = = ( (  -



) / = 2 ) / = 2 69 69o

±

±

5 5o

* divergent theoretical previsions: Beneke,Neubert Nucl. Phys B675, 333(2003) and

Buras et al, Phys. Rev.Lett 92 101804 (2004)

15/12/2006 15/12/2006

We can measure it We can measure it

2 ) 2 ) Extracting Extracting  

SLIDE 23

23 23 ,

Hypothesis Hypothesis

Gabriel Guerrer

test test in the charged fit, check if magnitude in the charged fit, check if magnitude ( (K* K*



+

+) =

) = magnitude magnitude ( (K* K*



-

)

) BaBar confirmed this hypothesis : hep-ex/0507004 BaBar confirmed this hypothesis : hep-ex/0507004 test test a at

t

(B (B0

0)

) = = a at

t (B

(B0

0)

) test test Γ Γ = = Γ Γ = = Γ Γ

Based on theoretical papers Based on theoretical papers

➔ C. W. Chiang

C. W. Chiang et al,

et al, Phys. Rev.

Phys. Rev. D69

D69, 034001 (2004) , 034001 (2004)

➔ M. Beneke and M. Neubert, Nucl. Phys,

M. Beneke and M. Neubert, Nucl. Phys, B675

B675, 333 (2003) , 333 (2003) If one fails If one fails   interesting anyway, unexpected physical effects ! interesting anyway, unexpected physical effects !

1 1st

st hypothesis

hypothesis : : K*

K* from

from B

B±

±

has only penguin contribution has only penguin contribution 2 2nd

nd hypothesis

hypothesis : penguin from : penguin from B

B±

±

K*

is the same of B

is the same of B0 3 3rd

rd hypothesis:

hypothesis: 

c0

c0 is the same

is the same for for B

B±

±

and and B B0

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B0 →Ks c0 B0 →Ks c0 B± →K± c0 2 ) 2 ) Extracting Extracting  

SLIDE 24

24 24 ,

Conclusion Conclusion

Gabriel Guerrer

Joint fits to non tagged B

Joint fits to non tagged B0

0 B

B0

0 data samples can be made

data samples can be made and this is a general result that be applied to other channels: and this is a general result that be applied to other channels: B B0 → →  +

+

-



0

0 , B

, Bs

s→

→D D0

0 K

K+

+K

K-

, D

, D0

0 →

→ K Ks

s 

+

+ 

-

...

...

With 100K evts and all the hypothesis mentioned we

With 100K evts and all the hypothesis mentioned we measure measure   within within 5 5o

We can measure

We can measure direct CP direct CP asymmetry in B asymmetry in B0

0,B

,B0

0 →

→ K Ks

s 

+

+ 

-

We can measure

We can measure r = a r = at

t / a

/ ap

p

and and  

t t -





p p



c0

c0 is used as reference. If f

is used as reference. If f0

0 is dominated by ss component

is dominated by ss component , it could be used as anchor and this method applied at , it could be used as anchor and this method applied at current B factories statistics current B factories statistics

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2 ) 2 ) Extracting Extracting  