Introduction Measure properties of unitarity triangle to test CKM - - PowerPoint PPT Presentation

SLIDE 1

Results On φ2 From e+e− Colliders

Pit Vanhoefer on behalf of the Belle Collaboration Max-Planck-Institut f¨ ur Physik, M¨ unchen pvanhoef at mpp.mpg.de

BELLE

(ρ,η)

(1,0)

φ φ φ

1 2 3

V

udV ub

* V

cdV cb

*

| | | |

V

udV ub

* V

cdV cb

*

| | | |

V

tdV tb

* V

cdV cb

*

| | | |

φ2/α: Decays covered in this talk

a) B → ππ b) B → ρρ c) B0 → (ρπ)0 d) B0 → a±

1 π∓

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

1

SLIDE 2

Introduction

• Measure properties of unitarity triangle to test CKM mechanism: 2 sides, 3 angles
• Time-dependent decay rate of a B or a ¯

B meson decaying into common CP eigenstate P(∆t) = e−|∆t|/τB0 4τB0

• 1 + q
• SCP sin(∆md∆t) + ACP cos(∆md∆t)
• 3

φ

3

φ

2

φ

2

φ

d

m ∆

K

ε

K

ε

s

m ∆ &

d

m ∆

ub

V

1

φ sin 2

(excl. at CL > 0.95) < 0

1

φ

• sol. w/ cos 2

excluded at CL > 0.95 2

φ

1

φ

3

φ

ρ

• 1.0
• 0.5

0.0 0.5 1.0 1.5 2.0

η

• 1.5
• 1.0
• 0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 Winter 12

CKM

f i t t e r

• ACP : direct CP violation (= −CCP )
• SCP : mixing induced CP violation
• q: flavor of Btag, q = +1 for Btag = B0
• τB0: B life time
• ∆md: mass difference of BH and BL
• ∆t: decay time difference of BCP and Btag

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

2

SLIDE 3

Mixing Induced ✟✟✟✟

✟

CP

• φ2 = arg

VtdV ∗

tb

VubV ∗

ud

• accesible through mixing induced✟

✟ CP in b → u transitions,

e.g. interference between B → π+π−

b d d u u d

ub

V

* ud

V

+

W

→

and B → ¯

B → π+π−

d b b d t t W W B B

td

V

tb

V

td

V

tb

V b d d u u d

ub

V

* ud

V

+

W

ր

+

B

CP

f B B

CP

f B

CP

mixing induced

—— ————

B B

fCP V

ub ud

V

*

V

ub ud

V* V V

*

tb td

2

ρ fCP= ρ π π,

x

⇒ at tree level: SCP = sin(2φ2), ACP = 0

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

3

SLIDE 4

Living With Pollution

b → u (ρ, π, ...) at Tree level: SCP = sin(2φ2) and no direct ✟ ✟ CP (ACP = 0)

BUT more amplitudes (penguins) can contribute with different weak/strong phases

b d u u d d

ub

V

* ud

V

+

W

⇒ φ2

b d d d d d g

+

W

tb

V

* td

V

t

penguin pollution ⇒ ∆φ2, ACP

⇒ measured observable φeff

2

= φ2 + ∆φ2 → extraction of ∆φ2 with isospin analysis is possible SCP =

• 1 − A2

CP sin(2φeff 2

)

with ACP = 0 possible

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

4

SLIDE 5

Recover φ2

• extraction of ∆φ2 with isospin analysis (remove penguin pollution)

for unflavored isospin triplets, e.g. ρ, π Bose statistics:⇒ I=0,2 (final states); tree I=0,2; penguin: I=0 only (gluon) allows to formulate relations of the decay amplitudes A e.g. ¯

A+− = A( ¯ B → ρ+ρ−)

• 1

√ 2A+− + A00 = A+0

• 1

√ 2 ¯

A+− + ¯ A00 = ¯ A−0

2

φ ∆ 2

+-

A 2 1

00

A

+-

A 2 1

00

A

A =

+0

A

• M. Gronau and D. London, PRL 65 3381 (1990)
• A+0 = ¯

A−0 (no penguin) ⇒ geometrical considerations reveal ∆φ2

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

5

SLIDE 6

Data Samples

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

6

SLIDE 7

B → π+π−

BaBar PRD 87 052009(2013)

467 × 106B ¯ B pairs

t (ps) ∆

• 6
• 4
• 2

2 4 6

Events / ps

20 40 60 80 100 120 140 160

t (ps) ∆

• 6
• 4
• 2

2 4 6

Events / ps

20 40 60 80 100 120 140 160

BABAR

Preliminary

t (ps) ∆

• 6
• 4
• 2

2 4 6

Events / ps

20 40 60 80 100 120 140 160

t (ps) ∆

• 6
• 4
• 2

2 4 6

Events / ps

20 40 60 80 100 120 140 160

t (ps) ∆

• 6
• 4
• 2

2 4 6

Asymmetry

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1

t (ps) ∆

• 6
• 4
• 2

2 4 6

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1

Sπ+π−

CP

= −0.68 ± 0.10 ± 0.03 Aπ+π−

CP

= +0.25 ± 0.08 ± 0.02

Belle arXiv:1302.0551

772 × 106B ¯ B pairs

Events / (1.5 ps)

50 100 150 200 250 300

q = +1 q = -1

t (ps) ∆

• 7.5
• 5
• 2.5

2.5 5 7.5

B

+N

B

N

B

• N

B

N

• 0.5

0.5

BELLE

PRELIMINARY

Sπ+π−

CP

= −0.636 ± 0.082 ± 0.027 Aπ+π−

CP

= +0.328 ± 0.061 ± 0.027 ⇒ clear mixing induced✟ ✟ CP and presence of penguins

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

7

SLIDE 8

B → π+π−

World averages

CCP = −ACP

π+ π- SCP

HFAG

CKM 2012

• 1
• 0.9
• 0.8
• 0.7
• 0.6
• 0.5
• 0.4
• 0.3

BaBar

arXiv:1206.3525

• 0.68 ± 0.10 ± 0.03

Belle

CKM2012 preliminary

• 0.64 ± 0.08 ± 0.03

LHCb

LHCb-CONF-2012-007

• 0.56 ± 0.17 ± 0.03

Average

HFAG correlated average

• 0.65 ± 0.06

H F A G H F A G

CKM 2012 PRELIMINARY

π+ π- CCP

HFAG

CKM 2012

• 0.8
• 0.6
• 0.4
• 0.2

0.2

BaBar

arXiv:1206.3525

• 0.25 ± 0.08 ± 0.02

Belle

CKM2012 preliminary

• 0.33 ± 0.06 ± 0.03

LHCb

LHCb-CONF-2012-007

• 0.11 ± 0.21 ± 0.03

Average

HFAG correlated average

• 0.29 ± 0.05

H F A G H F A G

CKM 2012 PRELIMINARY

π+ π- SCP vs CCP

Contours give -2∆(ln L) = ∆χ2 = 1, corresponding to 60.7% CL for 2 dof

• 0.8
• 0.6
• 0.4
• 0.2
• 0.8
• 0.6
• 0.4
• 0.2

SCP CCP

BaBar Belle LHCb Average

H F AG H F A G

CKM 2012 PRELIMINARY

⇒ good agreements between experiments (prev. tension removed)

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

8

SLIDE 9

B → π0π0

BaBar PRD 87 052009(2013)

467 × 106B ¯ B pairs

)

2

(GeV/c

ES

m

5.2 5.22 5.24 5.26 5.28

)

2

Events / ( 5 MeV/ c

50 100 150

)

2

(GeV/c

ES

m

5.2 5.22 5.24 5.26 5.28

)

2

Events / ( 5 MeV/ c

50 100 150

background substracted

Belle PRL 94 181803 (2005)

275 × 106B ¯ B pairs B ¯ B mES = Mbc =

• E2

beam − p2 B

BaBar Belle

B(B0 → π0π0) × 106 1.83 ± 0.21 ± 0.13 2.3+0.4 +0.2

−0.5 −0.3

Aπ0π0

CP

0.43 ± 0.26 ± 0.05 0.44+0.53

−0.52 ± 0.17

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

9

SLIDE 10

B± → π±π0

BaBar PRD 76 091102 (2007)

383 × 106B ¯ B pairs )

2

(GeV/c

ES

m 5.24 5.26 5.28 200 400 600 800 )

2

(GeV/c m 5.24 5.26 5.28 200 400 600 800 )

2

(GeV/c m 5.24 5.26 5.28 )

2

Events/(3.3MeV/c 200 400 600 800

π

±

π π

±

K

(a)

background substracted

Belle arxiv:1210.1348 (2012)

772 × 106B ¯ B pairs

signal enhanced

∆E(GeV ) Mbc(GeV/c2) ∆E = EBrec − Ebeam

BaBar Belle

B(B± → π±π0) × 106 5.02 ± 0.46 ± 0.29 5.86 ± 0.26 ± 0.38 Aπ±π0

CP

0.03 ± 0.08 ± 0.01 0.043 ± 0.043 ± 0.007

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

10

SLIDE 11

B → ππ

φ2/α constraints

(deg)

2

φ

20 40 60 80 100 120 140 160 180

p-value

0.0 0.2 0.4 0.6 0.8 1.0

CKM12 (prel.)

CKM

f i t t e r

(BABAR) π π → B (Belle) π π → B (WA) π π → B CKM fit

C K M

f i t t e r CKM12 (prel.)

C K M

f i t t e r CKM12 (prel.)

Belle: φ2 ∈ [85.0◦, 148.0◦] , Babar: α ∈ [71◦, 109◦], WA: φ2/α = (87.1+17.5

−7.8 )◦

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

11

SLIDE 12

B → ρρ

• B → ρρ

ρ → ππ

• S → VV decay

֒ → superposition of CP even and

• dd states

֒ → separation through helicity analy-

sis helicity basis:

B

ρ0 ρ0

π

+

π

+

π

+

π

+

π

+

π

+

π

+

π

+

π

+

π

+

π- π-

θHel

θHel

φ

• fL: fraction of longitudinal polarization(LP

, pure CP even final states)

1 Γ d2Γ d cos θ1

Held cos θ2 Hel = 9

4

• fL cos2 θ1

Hel cos2 θ2 Hel + 1 4(1 − fL) sin2 θ1 Hel sin2 θ2 Hel

• naiv SM expectation: fL ∼ 1 − m2

V

m2

B ∼ 1 difficult to predict for color-suppressed mode

B0 → ρ0ρ0

• smaller statistics(exp.) less penguin pollution compared to B → ππ

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

12

SLIDE 13

B0 → ρ+ρ−Helicity

BaBar PRD 76 052007 (2007) 384 million B ¯

B pairs

)

i

θ cos(

• 0.5

0.5

Events / (0.188)

100 200

(c)

Belle PRL 96 171801 (2006) 275 million B ¯

B pairs

BaBar Belle

B(B0 → ρ+ρ−) × 106 (25.5 ± 2.1+3.6

−3.9)

(22.8 ± 3.8+2.3

−2.6)

fL 0.992 ± 0.024+0.026

−0.013

0.941+0.034

−0.040 ± 0.030

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

13

SLIDE 14

B0 → ρ+ρ−

BaBar PRD 76 052007 (2007) 384 million B ¯

B pairs ∆t distribution and asymmetry

Events / 2 ps 10 20 30 Events / 2 ps 10 20 30 (a) Events / 2 ps 10 20 30 Events / 2 ps 10 20 30 (b)

t (ps) ∆

• 6
• 4
• 2

2 4 6 Asymmetry

• 1
• 0.5

0.5 1 t (ps) ∆

• 6
• 4
• 2

2 4 6 Asymmetry

• 1
• 0.5

0.5 1

(c)

SCP = −0.17 ± 0.20+0.05

−0.06

ACP = −0.01 ± 0.15 ± 0.06

Belle PRD 76 011104 (2007) Update to 535 million B ¯

B pairs ∆t distribution and asymmetry

10 20 30 40 50 60 70

• 5

5

∆t (ps) Events / (1.25 ps)

(a)

10 20 30 40 50 60 70

• 5

5

∆t (ps)

(b)

∆t (ps) Events / (1.25 ps)

• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6

• 6
• 4
• 2

2 4 6

(c)

∆t (ps) Raw Asymmetry / (2.5 ps)

SCP = +0.19 ± 0.30 ± 0.07 ACP = +0.16 ± 0.21 ± 0.07

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

14

SLIDE 15

B0 → ρ+ρ−

World average

ρ+ ρ- SCP

HFAG

LP 2007

• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8

BaBar

PRD 76 (2007) 052007

• 0.17 ± 0.20 +
• .

. 5 6

Belle

PRD 76 (2007) 011104 0.19 ± 0.30 ± 0.07

Average

HFAG correlated average

• 0.05 ± 0.17

H F A G H F A G

LP 2007 PRELIMINARY

ρ+ ρ- CCP

HFAG

LP 2007

• 0.6
• 0.4
• 0.2

0.2 0.4

BaBar

PRD 76 (2007) 052007 0.01 ± 0.15 ± 0.06

Belle

PRD 76 (2007) 011104

• 0.16 ± 0.21 ± 0.07

Average

HFAG correlated average

• 0.06 ± 0.13

H F A G H F A G

LP 2007 PRELIMINARY

ρ+ ρ- SCP vs CCP

Contours give -2∆(ln L) = ∆χ2 = 1, corresponding to 60.7% CL for 2 dof

• 0.4
• 0.2

0.2 0.4

• 0.4
• 0.2

0.2 0.4 SCP CCP

BaBar Belle Average

H F AG H F A G

LP 2007 PRELIMINARY

Good agreements between experiments

ACP (= −CCP ) ≈ 0 → small penguin contribution

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

15

SLIDE 16

B0 → ρ0ρ0

BaBar PRD 78, 071104 (2008) 465 million B ¯

B pairs

)

2

(GeV/c

ES

m 5.25 5.26 5.27 5.28 5.29

)

2

Events / ( 0.0018 GeV/c

10 20 30 40 50

(a)

)

2

(GeV/c

π π

m 0.6 0.7 0.8 0.9 1

)

2

Events / ( 0.02 GeV/c

10 20 30 40 50

(b)

S00LP

CP

= 0.3 ± 0.7 ± 0.2 A00LP

CP

= −0.2 ± 0.8 ± 0.3

Belle arXiv:1212.4015 772 million B ¯

B pairs

Events / (0.04)

10 20 30 40 50 60 70 80 90

]

2

) [GeV/c

• π

+

π (

2

m

0.6 0.8 1

Residuals Normalised

• 4
• 2

2 4

fL: Belle vs BaBar

fL00

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

p-value

0.0 0.2 0.4 0.6 0.8 1.0

CKM12 (prel.)

CKM

f i t t e r

fL00 measurement (Babar) fL00 measurement (Belle) fL00 (meas. not in fit)

2.1σ tension

BaBar Belle (preliminary)

B(B0 → ρ0ρ0) × 106 0.92 ± 0.32 ± 0.14 1.02 ± 0.30 ± 0.22 fL 0.75+0.11

−0.14 ± 0.04

0.21+0.18

−0.22 ± 0.11

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

16

SLIDE 17

B0 → ρ0(±)ρ0

B0 → ρ0ρ0 from Belle

Events / (0.1)

20 40 60 80 100 1

)

H

Θ cos(

• 1
• 0.5

0.5 1

Residuals Normalised

• 4
• 2

2 4 6

10 × ) ρ ρ → B(B

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

L

f

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 5 10 15 20 25 30 35 40

2

mES

) (GeV/c 5.26 5.27 5.28 5.29

2 )

Events / ( 0.001 GeV/c 20 40

2

5.26 5.27 5.28 5.29 ) Events / ( 0.001 GeV/c 20 40 Data ρ

+

ρ f

+

ρ Bkgs B B q q (a)

B0 → ρ±ρ0

BaBar Belle journal PRL 102 141802 (2009) PRL 91 221801 (2003) N(B ¯

B) ×106 465 85 B(B0 → ρ±ρ0) × 106 23.7 ± 1.4 ± 1.4 31.7 ± 7.1+3.8

−6.7

fL 0.950 ± 0.015 ± 0.006 0.948 ± 0.106 ± 0.021 A±0

CP

0.054 ± 0.055 ± 0.010 0.00 ± 0.22 ± 0.03

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

17

SLIDE 18

B → ρρ

φ2/α constraints

(deg)

2

φ

20 40 60 80 100 120 140 160 180

p-value

0.0 0.2 0.4 0.6 0.8 1.0

CKM12 (prel.)

CKM

f i t t e r

(BABAR) ρ ρ → B (Belle) ρ ρ → B (WA) ρ ρ → B CKM fit

• small penguin contribution
• best environment for con-

straining φ2 with 1st gen- eration B-factories Belle: φ2 = (84 ± 13)◦ , Babar: α = (92.4 ± 6.4)◦ , WA: φ2/α = (89.9+5.4

−5.3)◦

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

18

SLIDE 19

B0 → (ρπ)0

Not a CP eigenstate, need to consider the 4 flavour-charge configurations Corresponding isospin analysis has 12 unknowns compared to 6 for CP eigenstates

• U/I fomalism instead of quasi-two-body(Q2B)

→ 27 real free parameters

can be related to ACP and SCP parameters

• Dalitz plot sensitive to strong and weak phases of the

interfering ρ resonances (A. Snyder and H. Quinn, PRD 48 2139 (1993))

5 10 15 20 25 30 5 10 15 20 25 30

m2(π+π0) (GeV/c2)2 m2(π–π0) (GeV/c2)2

1 2 3 4 5 22 23 24 25 26 27

B0→ π+π–π0 (kin.) interference regs.

⇒ possible to constrain φ2 without ambiguity explicitly in the analysis !

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

19

SLIDE 20

B0 → (ρπ)0

NEW BaBar arXiv:1304.3503 (2013) 471 million B ¯

B pairs

Mass projections

)

2

) (GeV/c

• π

+

π m(

1 2 3 4 5 20 40 60 80 100 120

)

2

) (GeV/c π

+

π m(

1 2 3 4 5 20 40 60 80 100 120 140

)

2

) (GeV/c π

• π

m(

1 2 3 4 5 50 100 150 200

Belle PRL 98 221602 (2007) 449 million B ¯

B pairs

Mass projections

50 100 150 200 0.6 0.8 1 1.2 1.4 m+ (GeV/c2) Events / 0.05GeV/c2 50 100 150 200 0.6 0.8 1 1.2 1.4 m- (GeV/c2) Events / 0.05GeV/c2 20 40 60 80 100 120 0.6 0.8 1 1.2 1.4 m0 (GeV/c2) Events / 0.05GeV/c2

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

20

SLIDE 21

B0 → (ρπ)0

World averages for B0 → ρ±π∓

ACP is time and flavour-integrated CP asymmetry

ρ+-π-+ ACP

HFAG

ICHEP 2008

• 0.26 -0.24 -0.22 -0.2
• 0.18 -0.16 -0.14 -0.12
• 0.1 -0.08 -0.06 -0.04 -0.02

BaBar

PRD 76 (2007) 012004

• 0.14 ± 0.05 ± 0.02

Belle

PRL 98 (2007) 221602

• 0.12 ± 0.05 ± 0.04

Average

HFAG correlated average

• 0.13 ± 0.04

H F A G H F A G

ICHEP 2008 PRELIMINARY

ρ+-π-+ C

HFAG

ICHEP 2008

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3

BaBar

PRD 76 (2007) 012004 0.15 ± 0.09 ± 0.05

Belle

PRL 98 (2007) 221602

• 0.13 ± 0.09 ± 0.05

Average

HFAG correlated average 0.01 ± 0.07

H F A G H F A G

ICHEP 2008 PRELIMINARY

ρ+-π-+ S

HFAG

ICHEP 2008

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3

BaBar

PRD 76 (2007) 012004

• 0.03 ± 0.11 ± 0.04

Belle

PRL 98 (2007) 221602 0.06 ± 0.13 ± 0.05

Average

HFAG correlated average 0.01 ± 0.09

H F A G H F A G

ICHEP 2008 PRELIMINARY

NEW Babar Result arXiv:1304.3503 (2013)

Param Value ± stat ± syst ACP −0.100 ± 0.029 ± 0.021 C 0.016 ± 0.059 ± 0.036 S 0.053 ± 0.081 ± 0.034 A+−

CP

0.09+0.05

−0.06 ± 0.04

A−+

CP

−0.10 ± 0.08+0.04

−0.05

A+−

CP = − ACP +C+ACP ∆C 1+∆C+ACP C

A−+

CP = ACP −C−ACP ∆C 1−∆C−ACP C

∆C:

rate asymmetry if ρ± formed from spectator or not

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

21

SLIDE 22

B0 → (ρπ)0

World averages for B0 → ρ0π0 ρ0π0 C

HFAG

ICHEP 2008

• 1

1 2

BaBar

PRD 76 (2007) 012004

• 0.10 ± 0.40 ± 0.53

Belle

PRL 98 (2007) 221602 0.49 ± 0.36 ± 0.28

Average

HFAG correlated average 0.30 ± 0.38

H F A G H F A G

ICHEP 2008 PRELIMINARY

ρ0π0 S

HFAG

ICHEP 2008

• 1.2
• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1 1.2 1.4

BaBar

PRD 76 (2007) 012004 0.04 ± 0.44 ± 0.18

Belle

PRL 98 (2007) 221602 0.17 ± 0.57 ± 0.35

Average

HFAG correlated average 0.12 ± 0.38

H F A G H F A G

ICHEP 2008 PRELIMINARY

NEW Babar Result arXiv:1304.3503 (2013)

Param Value C00 0.19 ± 0.23 ± 0.15 S00 −0.37 ± 0.34 ± 0.20 f00 0.092 ± 0.011 ± 0.009

f00 fraction of ρ0π0 in (ρπ)0

———————————————————————————————– Babar’s result submitted to PRD Belle is working on final update Good agreement between experiments but difficult mode with current statistics

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

22

SLIDE 23

B0 → (ρπ)0

φ2 scan

• Solid line: incl. isospin constraints (B and ACP of B+ → ρ+π0, ρ0π+)
• Dotted line: Use B0 → (ρπ)0 results only

BaBar

50 100 150

Α deg

0.25 0.5 0.75 1

• scan not robust with current statistic

Belle

0.2 0.4 0.6 0.8 1 30 60 90 120 150 180 1−C.L. φ2 (degrees) C.L.=68.3%

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

23

SLIDE 24

B0 → (ρπ)0

φ2/α constraints (not incl. NEW Babar result)

(deg)

2

φ

20 40 60 80 100 120 140 160 180

p-value

0.0 0.2 0.4 0.6 0.8 1.0

WINTER 12

CKM

f i t t e r

(BABAR) π ρ → B (Belle) π ρ → B (WA) π ρ → B CKM fit

• difficult to pin down φ2

with B0 → (ρπ)0now

• ne solution for φ2 with higher statistics possible, → higher luminosity experiments

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

24

SLIDE 25

B0 → a1(1260)± π∓

Flavour non-specific final state

⇒ 5CP parameters

Babar, PRL 97, 051802 (2006).

t (ps) ∆

• 5

5 Asymmetry

• 0.5

0.5

(c)

t (ps) ∆

• 5

5 Asymmetry

• 0.5

0.5 20 40

(b)

20 40 20 40

(a)

20 40

Events / 1 ps

SCP = +0.37 ± 0.21(stat) ± 0.07(syst)

Belle, PRD 86, 092012 (2012).

t (ps) ∆

• 6
• 4
• 2

2 4 6

Events / (2.5 ps)

50 100 150 200 250 300 350 400 450

q = +1 q = -1

BELLE

t (ps) ∆

• 6
• 4
• 2

2 4 6

• Fit

+N

+ Fit

/N

• Fit
• N

+ Fit

N

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4 0.5

SCP = −0.51 ± 0.14 (stat) ± 0.08 (syst)

First evidence of mixing induced CP violation in

B0 → a1(1260)± π∓ decays(3.1σ)

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

25

SLIDE 26

Summary

• recent results on B → π+π− and B → ρ0ρ0 from Belle and on B → (ρπ)0 from Babar
• tightest constraint from B → ρρ, best potential in B → (ρπ)0

(frequentist)

(deg)

2

φ

20 40 60 80 100 120 140 160 180

p-value

0.0 0.2 0.4 0.6 0.8 1.0

CKM12 (prel.)

CKM

f i t t e r

(BABAR) π ρ / ρ ρ / π π (Belle) π ρ / ρ ρ / π π (WA) π ρ / ρ ρ / π π CKM fit

φ2/α = (88.5+4.7

−4.4)◦

(bayesian)

] ° [ α

60 80 100 120 140

Probability density

0.05 0.1

winter13

SM fit

φ2/α = (88.7 ± 3.1)◦

• some final results still anticipated
• LHCb entered the game, Belle2 under construction

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

26

SLIDE 27

Summary

BACKUP

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

27

SLIDE 28

B0 → a1(1260)± π∓

reconstructed in 4 charged pion final state arXiv:1205.5957 PRELIMINARY Difficulties from huge continuum background and other 4 pion backgrounds Extract branching fraction from 4 discriminating variables

∆E

Events / (0.008 GeV)

20 40 60 80 100 120 E (GeV) ∆

• 0.1 -0.06 -0.02 0.02

0.06 0.1

Residuals Normalized

• 2

2

Blue: 4π background Fisher discriminant

Events / (0.1)

100 200 300 400 500 F

• 3
• 2
• 1

1 2

Residuals Normalized

• 2

2

Red: Continuum

3π mass

)

2

Events / (0.036 GeV/c

2 4 6 8 10 12 14 16 18 20 22 )

2

(GeV/c

π 3

m 0.85 1.03 1.21 1.39 1.57 1.75

Residuals Normalized

• 2

2

Blue: a1, Red: a2

3π helicity

Events / (0.04)

2 4 6 8 10 12 14

π 3

H

• 1
• 0.6
• 0.2

0.2 0.6 1

Residuals Normalized

• 2

2

Blue: a1, Red: a2

B(B0 → a1(1260)± π∓) × B(a±

1 (1260) → π±π∓π±) = (11.1 ± 1.0 (stat) ± 1.4 (syst)) × 10−6

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

28

SLIDE 29

B0 → a1(1260)± π∓

Flavour non-specific final state⇒ 5CP parameters arXiv:1205.5957, PRELIMINARY

t (ps) ∆

• 6
• 4
• 2

2 4 6

Events / (2.5 ps)

50 100 150 200 250 300 350 400 450

q = +1 q = -1

BELLE

t (ps) ∆

• 6
• 4
• 2

2 4 6

• Fit

+N

+ Fit

/N

• Fit
• N

+ Fit

N

• 0.5
• 0.4
• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4 0.5

SCP = −0.51 ± 0.14 (stat) ± 0.08 (syst)

First evidence of mixing induced CP violation in

B0 → a1(1260)± π∓ decays(3.1σ)

) ° (

eff 2

φ

• 50

50 100 150

1 - CL

0.2 0.4 0.6 0.8 1

68%

φeff 2 = 1 4

• arcsin
• SCP +∆S
• 1−(CCP +∆C)2
• +

arcsin

• SCP −∆S
• 1−(CCP −∆C)2
• φeff

2

scan: 4 solutions at 1σ level,

φeff

2

= [−25.5◦, −9.1◦], [34.7◦, 55.3◦], [99.1◦, 115.5◦]

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

29

SLIDE 30

B0 → a1(1260)± π∓

non CP eigenstate - final state, need to consider 4 flavour-charge configurations (q, c) P(∆t, q, c) = (1 + cACP ) e−|∆t|/τB0 8τB0

• 1 + q
• (SCP + c∆S) sin ∆md∆t − (CCP + c∆C) cos ∆md∆t
• ACP : Time and flavour-integrated direct CP violation

CCP : Flavour-dependent direct CP violation SCP : Mixing-induced CP violation ∆C: Rate asymmetry between configurations where a1 does not and does contain the spectator quark ∆S: Strong phase difference between configurations

where a1 does not and does contain the spectator quark

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

30

SLIDE 31

B0 → (ρπ)0

Time and amplitude differential decay rate,

d3Γ d∆tds+ds− ∝ e−|∆t|/τB0

• (|A3π|2 + | ¯

A3π|2) − q(|A3π|2 − | ¯ A3π|2) cos ∆md∆t + 2qℑ q pA∗

3π ¯

A3π

• sin ∆md∆t
• |A3π|2 ± | ¯

A3π|2 =

• κ∈{+,−,0}

|fκ|2U ±

κ +

• κ<σ∈{+,−,0}

2(ℜ[fκf ∗

σ]U ±,ℜ κσ

− ℑ[fκf ∗

σ]U ±,ℑ κσ )

ℑ q pA∗

3π ¯

A3π

• =
• κ∈{+,−,0}

|fκ|2Iκ +

• κ<σ∈{+,−,0}

(ℜ[fκf ∗

σ]Iℑ κσ + ℑ[fκf ∗ σ]Iℜ κσ)

27 coefficients U, I determined from a fit to data

f: Form factors and line shapes

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

31

SLIDE 32

B0 → (ρπ)0

U ±

κ = |Aκ|2 ± | ¯

Aκ|2 U ±,ℜ

κσ

= ℜ[AκA∗

σ ± ¯

Aκ ¯ A∗

σ]

U ±,ℑ

κσ

= ℑ[AκA∗

σ ± ¯

Aκ ¯ A∗

σ]

Iκ = ℑ[ ¯ AκA∗

κ]

Iℜ

κσ = ℜ[ ¯

AκA∗

σ − ¯

AσA∗

κ]

Iℑ

κσ = ℑ[ ¯

AκA∗

σ + ¯

AσA∗

κ]

e+2iφ2 = ¯ A+ + ¯ A− + 2 ¯ A0 A+ + A− + 2A0

Convert to Quasi-two-body parameters For B0 → ρ±π∓

ACP = U +

+ − U + −

U +

+ + U + −

CCP = 1 2 U −

+

U +

+

+ U −

−

U +

−

• , SCP = I+

U +

+

+ I− U +

−

∆C = 1 2 U −

+

U +

+

− U −

−

U +

−

• , ∆S = I+

U +

+

− I− U +

−

For B0 → ρ0π0

ACP = −U − U + , SCP = 2I0 U +

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

32

SLIDE 33

B → K1Aπ

4-fold ambiguity for φeff

2

φeff

2

= 1 4

• arcsin
• SCP + ∆S
• 1 − (CCP + ∆C)2
• + arcsin
• SCP − ∆S
• 1 − (CCP − ∆C)2
• Can measure |∆φ2| using SU(3) symmetry involving B0 → a1K, B → K1Aπ decays
• M. Gronau and J. Zupan, PRD 73 057502 (2006)

BaBar, 454 million B ¯

B pairs

Amplitude analysis of WA3 data taken by ACCMOR collaboration Needed to determine Kππ model First measurement!

B(B0 → K1(1270)+π− + K1(1400)+π−) = 3.1+0.8

−0.7 × 10−5 (7.5σ)

B(B+ → K1(1270)0π+ + K1(1400)0π+) = 2.9+2.9

−1.7 × 10−5 (3.2σ)

Relative contributions also determined PRD 81 052009 (2010)

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

33

SLIDE 34

B → K1Aπ

Solve system of inequalities,

cos 2(φ±

2, eff − φ2) ≥

1 − 2R0

±

• 1 − A± 2

CP

cos 2(φ±

2, eff − φ2) ≥

1 − 2R+

±

• 1 − A± 2

CP

R0

+ ≡

¯ λ2f 2

a1 ¯

Γ(K+

1Aπ−)

f 2

K1A ¯

Γ(a+

1 π−) ,

R0

− ≡

¯ λ2f 2

π ¯

Γ(a−

1 K+)

f 2

K ¯

Γ(a−

1 π+)

R+

+ ≡

¯ λ2f 2

a1 ¯

Γ(K0

1Aπ+)

f 2

K1A ¯

Γ(a+

1 π−) ,

R+

− ≡

¯ λ2f 2

π ¯

Γ(a+

1 K0)

f 2

K ¯

Γ(a−

1 π+)

λ2 = |Vus|/|Vud| = |Vcd|/|Vcs| ¯ Γ: averaged decay rates, fi: decay constants

Calculate bound on |∆φ2| ≡ |φeff

2 − φ2| from

|φeff

2 − φ2| ≤ (|φ+ 2, eff − φ2| + |φ− 2, eff − φ2|)/2

|∆φ2| < 11◦(13◦) at 68% (90%) CL

Solution nearest SM expectation, φeff

2

= (79 ± 7 ± 11)◦

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

34

SLIDE 35

B → π+π−

• S→SS, simultanious fit including B0 → π+π−, K±π∓, K+K−

New results

• 6D fitter: ∆E, Mbc, L+

K/π, L− K/π, Fs/b and ∆t

L±

K/π: likelihood to be a K for a π mass hypothesis for pos./neg. charged tracks

Fs/b: event shape dependent variable

)

2

Events / (0.0025 GeV/c

10 20 30 40 50 60 70 )

2

(GeV/c

bc

M 5.24 5.25 5.26 5.27 5.28 5.29 5.3

Residuals Normalised

• 2

2

Events / (0.1)

50 100 150 200 250

q /q B B

F

• 3
• 2
• 1

1 2

Residuals Normalised

• 2

2

Events / (0.1)

• 1

10 1 10

2

10

π K/ +

L 0.2 0.4 0.6 0.8 1

Residuals Normalised

• 2

2

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

35

SLIDE 36

B0 → π+π−

Downward fluktuation within the last 240 million B ¯

B pairs

Belle result for the last 236.995e+06 BBbar pairs.

ACP (B0 → π+π−) = 0.06 ± 0.10 SCP (B0 → π+π−) = −0.62 ± 0.13

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

36

SLIDE 37

Polarization: Helicity Basis

2 different polarizations, longitudinal(LP , CP even) and transversal(TP , CP even & odd)

fL: fraction of L pol,through helicity analysis (SM: fL ∼ 1) B

ρ0 ρ0

π

+

π

+

π

+

π

+

π

+

π

+

π

+

π

+

π

+

π

+

π- π-

θHel

θHel

φ

θHel: angle between the B0 and the π+ flight directions in the ρ frame

Hel

π π π π

s s sz sz

LP TP

Helicity

Θ cos

• 1
• 0.6
• 0.2

0.2 0.6 1

Events / (0.02)

1000 2000 3000 4000 5000 6000 7000 8000 9000

Helicity

Θ cos

• 1
• 0.6
• 0.2

0.2 0.6 1

Events / (0.02)

2000 4000 6000 8000 10000

1 Γ d2Γ d cos θ1

Held cos θ2 Hel = 9

4

• fL cos2 θ1

Hel cos2 θ2 Hel + 1 4(1 − fL) sin2 θ1 Hel sin2 θ2 Hel

• Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

37

SLIDE 38

B → π+π−

PRELIMINARY New results on full data set

• simultanious fit of branching ratios and CP

asymmetries

NB0→π+π− = 2886 ± 82 (stat)

——————————————————-

• previous Belle result: (450 × 106B ¯

B pairs)

Sπ+π−

CP,prev. = −0.61 ± 0.10 ± 0.04

Aπ+π−

CP,prev. = +0.55 ± 0.08 ± 0.05

new analysis is consistent on same dataset ’downward fluctuation’ with last 200 × 106

B ¯ B pairs

Events / (1.5 ps)

50 100 150 200 250 300

q = +1 q = -1

t (ps) ∆

• 7.5
• 5
• 2.5

2.5 5 7.5

B

+N

B

N

B

• N

B

N

• 0.5

0.5

BELLE

PRELIMINARY

Sπ+π−

CP

= −0.636 ± 0.082 ± 0.027 Aπ+π−

CP

= +0.328 ± 0.061 ± 0.027

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

38

SLIDE 39

B0 → ρ0ρ0

Full Projection

Events / (0)

500 1000 1500 2000 2500

E [GeV] ∆

• 0.1
• 0.05

0.05 0.1

Residuals Normalised

• 4
• 2

2 4

PRELIMINARY New results Signal enhanced projections

B0 → ρ0ρ0, B0 → f0ρ0, 4π final states, B ¯ B bkg, total non-peaking bkg, total

Events / (0.01)

50 100 150 200 250

E [GeV] ∆

• 0.1
• 0.05

0.05 0.1

Residuals Normalised

• 4
• 2

2 4

Events / (0.04)

10 20 30 40 50 60 70 80 90

]

2

) [GeV/c

• π

+

π (

1

m

0.6 0.8 1

Residuals Normalised

• 4
• 2

2 4

Events / (0.1)

20 40 60 80 100

1

)

H

Θ cos(

• 1
• 0.5

0.5 1

Residuals Normalised

• 4
• 2

2 4

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

39

SLIDE 40

B0 → ρ0ρ0

visually seperate B0 → ρ0ρ0 from B0 → f0ρ0 with projections into

ρ0ρ0window

Events / (0.01)

10 20 30 40 50 60 70

E [GeV] ∆

• 0.1
• 0.05

0.05 0.1

Residuals Normalised

• 4
• 2

2 4

Events / (0.1)

2 4 6 8 10 12 14 16 18 20 22 24 1

)

H

Θ cos(

• 1
• 0.5

0.5 1

Residuals Normalised

• 4
• 2

2 4

f0ρ0 window

Events / (0.01)

10 20 30 40 50 60 70 80

E [GeV] ∆

• 0.1
• 0.05

0.05 0.1

Residuals Normalised

• 4
• 2

2 4

Events / (0.1)

5 10 15 20 25 30 35 40 1

)

H

Θ cos(

• 1
• 0.5

0.5 1

Residuals Normalised

• 4
• 2

2 4

• ρ0ρ0, f0ρ0, 4π fs, B ¯

B bkg

—————————————————————— Interference is treated as a systematic uncertainty, dominant source for B0 → ρ0ρ0.

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

40

SLIDE 41

φ2

PRELIMINARY New results

φ2 scan from isospin analysis in the ππ and the ρρ(LP) system

) ° (

2

φ

30 60 90 120 150 180

1 - CL

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ππ

68%

• B → ππ, using Belle results only
• exclude: 23.8◦ < φ2 < 66.8◦ (at 1σ)
• exclude: |∆φ2| > 44.25◦

) ° (

2

φ

30 60 90 120 150 180

1 - CL

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

68%

ρρLP

φ2 = (91.0 ± 7.2)◦ ∆φ2 = (0 ± 5.4)◦

• B → ρρ, using the LP fraction of

B(B0 → ρ0ρ0)|LP = (0.21 ± 0.36) × 10−6

from this measurement, world averages otherwise

Pit Vanhoefer(MPI)

φ2 from e+e− colliders

FPCP 2013

41