unitarity triangle 2 angles at babarbeach2008.sc.edu/.../sessions/martinez-vidal.talk.pdfbeach 2008,...

BEACH 2008, 22-28 June, 2008 F. Martínez-Vidal , Unitarity Triangle angles at BaBar 1

Unitarity Triangle angles at BaBar

F. Martínez-Vidal

IFIC – Universitat de València-CSIC

g, f3

a, f2

b, f1

2

The matrix and the “db” Unitarity

Triangle angles

• In the Standard Model (SM), the CKM matrix elements Vij describe the (complex)

electroweak couplings of the W± to quarks

• The 6 unitarity conditions can be represented with triangles in a complex plane

– One only has roughly equal-length sides “db” Unitarity Triangle

β

-i

-i

γ1 1

1 1 1

1 1

e

e

* * * 0ub ud cb cd tb tdV V V V V V

CKM phases(in Wolfenstein convention)

(0,0)

( , )

(1,0)

2 3

2 2

3 2

1 / 2 ( )

1 / 2

(1 ) 1

ub

t

ud us

cd cs cb

tbd ts

V V A i

V V V A

A

V

V i AV V

Wolfenstein parameterization:

4( )O

~ 0.23, ~ 0.8, ~ 0.2, ~ 0.4A

Non-zero phase implies CP violation

*

2

*( )ud ub

cd cb

V Vi i O

V V

3

Measuring the phases from CPV• CKM phases measurable when there are two paths to reach the same final state, and

strong phases do not vanish

• Text book example: interference between B0J/YKS (bccs) and B0

J/YKS

(bccs) decays allows determination of b

mixing decay mixing decay

2

2

1 | |0

1 | |

f

f

2

2Imsin 2

1 | | CP

f

f

f

C

P a

sym

met

ry

2/ ip q e

f

f

f

q

p

Aλ

A

Next largest amplitude (l2) has same weak phase

Other CKM corrections are Cabibbo suppressed O(l4)

and depend on the CKM anglesf fS C

0 0

0 0

CP,

( ) ( )( ) cos( ) sin( )

( ) ( )f f

B fB f

f

B fB f

t tA t m t m t

t tC S

weak

we

strong

str

2 2 2

1 2 1 2

2 2 2

ong2 ak1 2 1

| ( ) | | | | | 2 | || |

|

(cos

c( ) | | | | |

)

( )|| o| s2 |

A B f A A A A

A B f A A A A

Uncertainty ~1%


Time dependent measurements in a nutshell

e-e

tagB 4S

Start the Clock

z ~250 mm

c

zt

1

Δt is a signed quantity

recB

Exclusive B Meson and vertex reconstruction

/J

0

SK

Tag vertex reconstruction

B-FlavorTagging

K

Tagging performance:

Q=e(1-2w)2~30%

~ 1 ps 170 mt

(9.0 GeV)(3.1 GeV)

(4 ) 0.55S

High-statistics self-tagging

“B-flavor” sample to

calibrate tagging

measure Dz resolution

Coherent B meson production (L=1)


Common experimental techniques

• Veto significant/potentially dangerous B decay backgrounds

• Resonance masses, decay angles, helicity in

PPV, VPP decays

• Suppress continuum e+eqq (q=u,d,s,c) background

using event topology (multivariate methods)

• Characterize B candidates using

– Beam-energy substituted mass

– Energy difference

• Maximum likelihood fits to mES,

E, Fisher, PID, Dt, tagging, etc

• Use sidebands and control samples

to check backgrounds

Search for a needle in a haystack

MeVbeammES7.2~~

MeVBEE 5010~ *


Final collisions 12:43pm,

Monday 7 Apr 2008

Runs 1-4

Runs 1-5


sin2b in b→ccs decays: “golden modes”PRL 99, 171803 (2007) 383M BB

sin2b in individual charmonium modes

CP-odd

CP-even

sin 2 0.714 0.032 0.018

| | 0.952 0.022 0.017


b→ccd decays: B0→J/yp0 and B0→D(*)+D(*)-

arXiv:0804.0896 [hep-ex]

accepted by PRL 466MBB

Penguins with additional phases could contribute

If not, SM predicts S=sin2b, C=0

NEW!

184±15

5

1.23 0.21 0.04

0.20

(1.69 0.14 0

0.19

.07)

0.0

0

3

1

S

C

BF

0.66 0.19 0.04

0.02 0.11 0.02

S

C

617±33

D(*)+D(*)- are consistent with bccs.

E.g. for D*+D*-:

PRD 76, 111102 (2007) 383M BB


• If single phase dominates, SM

predicts S=sin2b, C=0

• Dominant CKM factors as

in J/yKS

Penguin-dominated b→qqs (q=s,d) decays

• Sensitivity in the loop to New Physics effects

• No recent updates

• Systematic (non statistically significative) shift

with respect to charmonium persists

• SM (hadronic) corrections to single-phase-

dominance would in general predict opposite

shift

pen pen sin 2S S

B0

b

d

u, c, t

g

W+

f, h,

(KK)

s

s

s

dK0


Measuring a• Access to a from the interference of bu decay (g) with B0-B0 mixing (2b)

complicated by penguin contribution

– Need additional information to extract a

d

d

0B

*

tbV

tdV

b

b

0Bt

t

*

tdV

tbV** // tdtbtdtb VVVVpq

B0B0 mixing

d

u

dd

0B

/ubV

*

udV

b /u

Tree decay

ubudVVA *

d

u

dd

0B

/g

b

/u

tcu ,,

Penguin decay

tbtdVVA *

2 2 2

sin 2

0

CP CP CP

CP CP

CP

i i i

f f f

f f

f

q Ae e e

p A

S

C

22

2

| |

1 sin 2

sin

eff

f CP CP CPCP

CP CP CP

CP

i iii

f f fi i

f f f eff

f

T P e ee e

T P e e

S C

C

How can we

obtain

from αeff ?

( )

T(P) = tree (penguin) amplitude

d = dP-dT , strong phase difference

http://www.devil-linux.org/


Measuring a: dealing with penguins

• SU(2) isospin symmetry relates u and d quarks: mu ~ md

• Bhh can have I=0 or 2 but gluonic penguins only contribute to I=0 (by DI=1/2 rule)

– B+h+h0 (mediated DI=3/2) is pure I=2,

with negligible EW penguins (1-2o)

only tree amplitude

• Different Bhh final states can be related to

each other through isospin amplitudes

• These amplitude relations can be used to

constrain the penguin shift in time dependent measurement bounds |aeff-a|=k/2

• Need 6 samples: 4 tagged neutral decays + 2 charged decays

• Still a 8-fold ambiguity (mod 180o) (4-fold from k, 2-fold from 2a)

0 000 001 1 A

2 2A A A A A

00A A

22eff

21 sin(2 )hh hhS C

Gronau, London, PRL 65, 3381 (1990)Gronau/London analysis

http://www.devil-linux.org/


a from B0p

+p

-

• Simultaneous EML to B0p

+p

-, K+p

-, K+K-

0.60 0.11 0.03 (5.1 )

0.21 0.09 0.02 (2.2 )

S

C

Still, 2.1s

difference

on Cp+p-

with Belle

1139±49

PRL 99, 021603 (2007) 383M BB

)96( 116

Isospin analysis to extract a (6 unknowns)

• Use 00 0 00, , , , ,S C C BF BF BF

CPV well established in B0p

+p

-

Includes SU(3) constraints

on penguin amplitude from BS→K+K-

[Fre

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PRD 76, 091102 (2007) 383M BB


• First measurement of TD CP

asymmetries in r0r

0

6

,00

,00

0.70 0.14 0.05

(0.84 0.29 0.17) 1

0.5 0.9 0.2

0.4 0.9 .2

0

0

L

L

Lf

S

C

BF

BABAR Preliminary: arXiv:0708.1630

(2007) 427M BB

Favored Da=11.3o

NEW!

B0r

0r

0 and isospin analysis

[Fre

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00 00 00 0, , , , , ,S C C BF B BS F F

Nsig=85±28±17

3.6s

Isospin analysis to extract a

• Use


• First measurement of TD CP

asymmetries in r0r

0

6

,00

,00

0.70 0.14 0.05

(0.84 0.29 0.17) 1

0.5 0.9 0.2

0.4 0.9 .2

0

0

L

L

Lf

S

C

BF

BABAR Preliminary: arXiv:0708.1630

(2007) 427M BB

Favored Da=11.3o

NEW!

B0r

0r

0 and isospin analysis

[Fre

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00 00 00 0, , , , , ,S C C BF B BS F F

Nsig=85±28±17

3.6s

Isospin analysis to extract a

• Use

PRD 76, 052007 (2007) 383M BB

729±60

0.05

, 0.06

,

0.17 0.20

0.01 0.15 0.06

L

L

S

C

BEACH 2008, 22-28 June, 2008 15

a from B0p

+p

-p

0

• Isospin analysis not viable Isospin pentagon (6 tagged decays+4 charged)

• Better approach: TD p+p

-p

0 Dalitz analysis assuming isospin symmetry

– Amplitude A3pdominated by r+

p-,r-

p+,r

0p

0 and radial excitations

– Interference at equal masses-squared (in the corners)

provides the information on relative strong phases

0

3 0

0

3 0

A f A f A f A

A f A f A f A

0( )A A B

0

+

0

0

+

0B

0B

Snyder, Quinn, PRD 48, 2139 (1993)

PRD 76, 012004 (2007) 375M BB

74o < a < 132o @ 68.3%C.L.

[Fre

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i

i

A T e P

A T e P

Resolve some ambiguities


g from BD(*)K(*)

• Use interference between bcus and bucs decay processes

• Sensitivity to g driven by the ratio

– s(g)~1/rB , need to measure rB from data

• B0D(*)0K(*)0 self-tagged decays also used (rB~0.37), but both diagrams are color

suppressed

• 3 different

final states

*

*

| |( )0.37 ~ 0.1

( ) | |

cs ubB F F

us cb

V VA b ur c c

A b c V V

Giri, Grossman, Soffer, Zupan,

PRD 68, 054018 (1993)

Bondar, PRD 70, 072003 (2004)

Atwood, Dunietz, Soni,

PRL 78, 3257 (1997),

PRD 63, 036005 (2001)

Gronau, London, PLB 253, 483 (1991)

Gronau, Wyler, PLB 265, 172 (1991)


arxiv:0802.4052,

Accepted PRD 383M BB

NEW!

Updated B+D*K+ and B+DK+ GLW

B+DK+ B+

D*K+

ACP+ 0.27 ± 0.09 ± 0.04 -0.11 ± 0.09 ± 0.01

ACP- -0.09 ± 0.09 ± 0.02 +0.06 ± 0.10 ± 0.02

RCP+ 1.06 ± 0.10 ± 0.05 1.31 ± 0.13 ± 0.04

RCP- 1.03 ± 0.10 ± 0.05 1.10 ± 0.12 ± 0.04

2

00

( ) ( )1 2 cos cos

[ ( ) ( )] / 2

CP CPCP B B B

B D K B D KR r r

B D K B D K

( ) ( )2 sin sin /

( ) ( )

CP CPCP B B CP

CP CP

B D K B D KA r R

B D K B D K

CP CP CP CPA R A R

• Based on triangle relations of amplitudes inherent 8-fold ambiguity

Preliminary 383M BB

B±DK±

B-

149

B+

106


• The idea in pictures:

• B± Dalitz plot distribution depends on g, rb and d. Write Likelihood as a function of the cartesian coordinates x± and y±

– Likelihood is Gaussian and unbiased

• No ambiguities mod 180o, only usual mirror solution: (dB,g)(dB+p,g+p)

2 2 2 2 2 * *( , ) | | | | 2 Re[ ] Im[ ]D B D D D D Dm m A r A x A A y A A

B+D(*)K+ Dalitz

A(B-)=|A(B→D0K-)|×+rBei(-g+d

B)

m(KS p-)2

m(K

Sp

+)2

m(KS p-)2

m(K

Sp

+)2

2 2 0 2 2 2 2

2 2 0 2 2 2 2

( , ) ( ) ( , ) ( , )

( , ) ( ) ( , ) ( , )

B

B

i i

D B D

i i

D B D

A m m A B D K A m m r e e A m m

A m m A B D K A m m r e e A m m

2 2 0 2( )Sm m K

D0→Ks pp D0→Ks pp

Neglect D mixing and CP violation in D decays

+D0→KsKK, p0pp

cos( )

sin( )

B B

B B

x r

y r

k accounts for natural width of K*

h accounts for different parity of D*0D0

g wrt D0p

0


• As interference depends on Dalitz position requires modelization of

• Extract D0/D0 decay amplitudes from DP analysis of independent high-statistics cc

sample with flavor-tagged D0→KS p+p

-, KS K+K- decays from D*+→D0

p+

• For D→Kspp use 9 BW resonances + K-matrix formalism for pp and Kp S-waves

– K-matrix deals with broad, overlapping, multi-channel scalar resonances

487k Evts

purity:97.7%

69k Evts

purity:99.3%

arXiv:0804.2089 subm.

to PRD 383M BB

2 2( , )DA m m

NEW!

B+D(*)K+ Dalitz: analysis of D0/D0 decays

2/dof1.11

D0→

Ks p

pD

0

Ks K

K

2/dof1.09

First time!


Distance between (B+B-)

points is 2rB|sin 2g|

extract CL for g, rb and db from x±,y± with frequentist stat. procedure

B→D0K

CPV 2.2s

B→D0*K

CPV 2.5s

B→D0K*

CPV 1.5s

*

* 0.088

0.105

23

24

(DK) 0.086 0.035

(D K) 0.135 0.051

(DK ) 0.163

(76 )

B

B

s

r

r

kr

Includes exp. (5O) and

Dalitz (5O) errors

arXiv:0804.2089 subm.

to PRD 383M BB

B+D(*)K+ Dalitz: results

[Fre

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B-

B+

2g

rB-

rB+ 2 | sin | 0 direct CPVBr


Despite BaBar

errors on x,y are

comparable with

Belle, error on g

is worse: the

“1/rB effect”

Belle preliminary arXiv:0803.3375 657M BB

22 o

23

12 o

13

(76 5 5)

(76 4 9)

Comparison with Belle

*

( ) 0.086 0.035

( ) 0.135 0.051

B

B

r DK

r D K

stat exp model


• b in charmonium is a precision measurement

– d(sin2b)~0.035 (2%) approaching accuracy of SM calculations (~1%)

• All b measurements in many different channels are consistent

– Sensitivity to NP for some channels

Summary and Outlook






• a ultimately limited by penguin pollution

– da~10o now

– The decay modes Bpp,rr,rp consistent

and complementary

– Still more new channels being added

(e.g. Ba1p)

Summary and Outlook

CKM fitter group combination

13.5

5.7(83.5 )

Eur. Phys. J C 41, 1 (2005)

http://ckmfitter.in2p3.fr







– da~10o now


and complementary


(e.g. Ba1p)

• Being able to measure g at the B Factories

was unexpected

– rB ratios confirmed to be ~0.1 (and >0)

– dg~20o now, dominated by B+DK+ Dalitz

Summary and Outlook

My personal Dalitz+D(*)K GLW

combination

0.028

0.027

* 0.057

0.046

* 0.09

0.10

21

22

(DK) 0.090

(D K) 0.113

(DK ) 0.17

(72 )

B

B

s

r

r

kr







– da~10o now


and complementary


(e.g. Ba1p)

• Being able to measure g at the B Factories

was unexpected

– rB ratios confirmed to be ~0.1 (and >0)

– dg~20o now, dominated by B+DK+ Dalitz

• Measurement of all angles still statistically limited

• SM surviving all challenges from B Factories, so far

Summary and Outlook

unitarity triangle 2 angles at babarbeach2008.sc.edu/.../sessions/martinez-vidal.talk.pdfbeach 2008,...

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