Measuring α with the B-factories

Adrian BevanSCIPP 17th Feb ‘04

Outline

•CP Violation in Meson Decay & measuring α

• Experiments and Techniques

• measurements in the B meson system:

B→ππ from Belle and BaBarprospects from B→ρρ

• Conclusions

Why is CP Violation interesting?• The universe is matter dominated!

• Cosmology requires C and CP Violation

• Known levels of CP Violation in K0 and B0 decays is O(9) orders of magnitude too small to explain matter dominance!

New Physics to discover

Need B factories to study CP Violation in B meson decay

Precision tests of the SM and search for new physics

Work towards a deeper understanding of CP Violation mechanism

Diagrams of interest for CP Violation have interactions of the form

, ,iq u c t=

, ,jq d s b=

W +

ijV

The couplings, Vij, form a 3×3 matrix: The CKM Matrix

CP Violation in meson decay

32

4

23

2 2

(1 / 2 )1 / 2 ( )

(1 ) 1

ub

cd cs

td t

ud u

ts

s

cb

b

A iV VV V

VV VV A

A OV AV i

λ λλ λ

λ ρ η

λ ρλ

ηλ

λ

− = ≈ − − +

−

−

− −

CP Violating phase present

Single Complex Phase Describing CP Violation in meson decay

Unitarity gives † † 1VV V V= =

Orthogonality of V gives 6 closed triangles

~ 0.22~ 0.8~ 0.2 0.27~ 0.28 0.37

Aλ

ρη

−−

2 triangles have all sides with the same order in λkaon system is not one of theseinteresting one for the Bd/u system is “The Unitarity Triangle”

| |

| |

itd td

iub ub

V V e

V V e

β

γ

−

−

=

=

mixing

The “Unitarity Triangle”

0 0B B* * * 0ud cd cub tdb tbV V V VV V+ + =

α

βγ(1,0)(0,0)

(η,ρ) *

*td tb

tcd cb

V V RV V

=*

*ub ud

bcd cb

V V RV V

=

* , ,,...

B D DKK

ππ→

, ,B ππ ρπ ρρ→

0

* *

/ ,

, ,...SB J K

D D K

ψ

ϕ

→

For neutral mesons; K, B, D • strong eigenstates are not CP eigenstates

• mass eigenstates are an admixture of different strong eigenstates

• particle ↔ antiparticle (mixing), ∆f = 2

Neutral Meson Phenomenology

(mixing is very suppressed in the Standard Model for D mesons)

0 01 1( ), ( )2 2H L H LB B B B B B

p q= + = −

mass eigenstates=CP eigenstatesif no CP Violation in mixing (q/p=1)

if q/p≠1 have CP Violationin mixing;

e.g. εK=2.3x10-3

H L

H L

B B

B B

m M M∆ = −

∆Γ = Γ − Γ

0 0

0 0

2 2 1

H

L

B p B q B

B p B q B

p q

= +

= −

+ =

CP even

CP odd

CP Violation at the B-factories

Υ(4s) run at 10.58GeV CMSto produce B pairs

(on-peak)

• Correlated B pair decay into charged and neutral B mesons

• Run 40 MeV below the Υ(4s) O(12%) of the time to characterise continuum(light quark: u,d,s,c) background from e+e- collisions.

• Need asymmetric beam energies for CP violation study

0 0

0.110.10~ 1.09 0.08B B

B B

ff

+ − +− ± (PDG 2002)

•9GeV e- on 3.1GeV e+

•Υ(4S) boost: βγ=0.56

BaBar

run 1

run

2

run

3

run

4

Peak Lumi:

Performance snapshot from 10th Feb ‘04

Belle

Performance snapshot from 10th Feb ‘04

Total Lumi: 193.478 /fb

Peak Lumi:

Estimate 350/fb by July ‘05

• Three interference effects:– CP violation in mixing (|q/p| ≠ 1)

– (direct) CP violation in decay (|A/A| ≠ 1)

– CP violation in interference of mixing and decay (Imλ ≠ 0)

0B

0B

CPf

0 0 0 0Pr( ) Pr( )B B B B→ ≠ →

0 0Pr( ) Pr( )B f B f→ ≠ →

time dependent effect -- ∆m

time dependent effect -- ∆m

time integrated effect – number counting

Observing CP violation at the Υ(4S)

Analyse time evolution of B0B0 system (assume ∆Γ=0):

C P

C P

C P

ff

f

Aqλp A

= ⋅

0

4

04

( , ) 1 sin ( ) cos( )

( , ) 1 sin ( ) cos( )C P

C P

C P

C P

tphys C P d d

tphys C P d

f

f

f

f d

f B f t e m t m t

f

S

SB f t

C

Ce m t m t

− Γ ∆Γ

− Γ ∆Γ

→ ∆ = + ∆ ∆ − ∆ ∆ → ∆ = − ∆ ∆ + ∆ ∆

Indirect CP violation S ≠ 0

C P

C P

C P

2f

f 2f

1 | λ |1 | λ |

C−

=+

C P

C P

C P

ff 2

f

2 Im λ1 | λ |

S =+

Direct CP violation C ≠ 0

00

0 0

( ( ) ) ( ( ) )( )

( ( ) ) ( ( ) )

sin( ) cos( )

physphysCP

phys phys

B t f B t fA t

B t f B t f

S m t C m t

Γ → −Γ →=

Γ → +Γ →

= ∆ ∆ − ∆ ∆

( ) ( )( ) ( )CP

Br B f Br B fABr B f Br B f

→ − →=

→ + →

CP Asymmetries & Observables

Time integrated CP asymmetry

(e.g. charged B decay)

Direct CP Violation

Direct and Indirect CP Violation

Time dependent CP asymmetry

(e.g. neutral B decay)

Interesting Observable: ACP

Interesting Observables: S, C

Ingredients of a CP analysis:

1) Event Selection:

2) Flavour Tagging

3) Vertex Reconstruction

Need to determine proper time difference between the tag B, BTAG, and the reconstructed ‘CP’ B, BCP.

(BCP is not always a CP eigenstate)

Need good understanding of detector resolution for ∆t=tCP-tTAG

Determine the flavour of the selected B candidate – is it a B0 ora B0? Issues: Use the other B in the event

tagging efficiency: signal, B backgroundmis-tag probability Dilutionasymmetry in tag efficiency for continuum background

Select events: discriminate against any B backgroundand continuum background from e+e- → qq

B Flavour Tagging

• Tagging algorithm with physics-based neural networks– Inputs include leptons, kaons, slow-π (from D*), and high-momentum

tracks– Outputs combined and categorized by mistag probability (w)

• 5 mutually exclusive hierarchical categories:• Lepton – isolated high-momentum leptons

• Kaon I – high quality kaons or correlated K+ and slow-π-

• Kaon II – lower quality kaons, or slow-π

• Inclusive – unidentified leptons, poor-quality kaons, high-momentum tracks

• Untagged – no flavour information is used

b sc

−

K-cl

eane

rsi

gnal

larg

er

mis

tag

prob

66% of events havesome flavour information

Q = ε(1-2w)2 = (28.4 ± 0.7)%

efficiency mistag probability

Tagging: example of rare B decay: h+h-

• Tagging efficiency is very different for signal and background

• Strong bkg suppression in categories with the lowest mistag prob (Lepton/Kaon)

• plots shown are for h+h-, a rare decay with significant backgrounds.

81/fb B→ h+h- sample split by tagging category

mES (GeV/c2)

Lepton

mES (GeV/c2)

Kaon I

mES (GeV/c2)

Kaon II

mES (GeV/c2)

Inclusive

0

10

20

30

5.2 5.30

20

40

60

80

5.2 5.3

0

50

100

150

5.2 5.30

50

100

150

5.2 5.3

150

100

Vertex Reconstruction

Resolution function parameters obtained from data for both signal and background– Signal from sample of fully reconstructed B

decays to flavour eigenstates: D*(π, ρ, a1)– Background from data sideband sampe

(or float in fit)

Beam spot

Interaction Point

BCP VertexBCP daughters

Exclusive BCP reconstruction

BTAG direction

TAG tracks, V0s

zBTAG Vertex

czt 1

βγ∆

≈∆

B → ππ

Example in B → ππ

e+e-→ qq

∆t (ps)

•∆z resolution dominated by tag side (other B)

•Average ∆z resolution ~180µm

•Average ∆z ~260 µm

without the boost would have ∆z~30µm …

e.g. CLEO

without the boost would have ∆z~30µm …

e.g. CLEO

The CKM Angle α

0B ρπ→

0B ππ→

0B ρρ→

Interesting modes to measure α

need to perform an Isospin analysis of branching ratios of B0 and B0 to 2π final states to determine shift in α due to the presence of penguin (loop) diagrams

ππκαα += 22 eff

doing a ‘quasi 2 body analysis’ – will eventually have to analysethe whole Dalitz plot – thus enabling the extraction of α.

In analogy to these modes one needs to analyse the time dependence of this decay and extract α from an isospin analysis of each of the three partial waves (L=0,1,2) in the final state (full angular analysis not required)

The shift in α from penguin diagrams is better constrained than in ππ!the time evolution of π+π− gives the shifted value of α

CP Violation in B0 → π+π−

mixing decay

Tree (T) Level:

)2sin(0

2

α

λ

ππ

ππ

αππ

===

SC

e i

* *

**tb td

tb td

ud ub

ud ub

V VV VV V VVππλ =

)2sin(1

)sin(

eff2

/1

/12

α

δ

λ

ππππ

ππ

αππ γδ

γδ

CS

C

e ii

ii

eeTP

eeTPi

−=

∝

= −+

+

With Penguins (P):

0 0 0 0B & Bπ π π π+ +→ →• Need to measure the weak phase α

• can use isospin relations to extract shift

• penguins are significant: P/T~0.3

u,c,t

W

The Isospin Analysis:

Need to measure decay of Band B to

final states in order to determine the shift

0 0 0, ,π π π π π π± ±∓

( ), ( ) ( )

A A B fA CP A A B f

= →

= = →)Br()Br(2

)Br()Br()Br(cos0

00210

ππππ

ππ−ππ+ππ=φ

+−+

−++Measure φ (φ’) for B(B) from

φ φ′

Established Measurements

Recently Observed

Can bound the shift on α using BR(B±→ π± π0) and BR(B0→π0π0)

( )( )

0 0 02

0

Bsin ( )

Beff

Br

Br

π πα α

π π+ +

→− ≤

→Grossman Quinn bound

effα α φ φ′− = −illustration using B→ππ

0

0

( )

( )

( ) (| | ) | | ),( ) (| | ) | | ),

1 | / |1 | / |

T P

T P

i ii

i ii

ii

i

A B T e e P eA B T e e P e

P T eeP T e

δ δγ

δ δγ

δ γα

ππ δ γ

π π

π π

λ

+ −

+ − −

+

−

→ = − +

→ = − +

+=

+

2

2

[sin 2 2 | | sin( ) cos

| | sin 2 ] / ,[2 | | sin( )sin ] / ,

1 2 | | cos( ) cos |

/

//

/ / |

P T

P TP T

P T P

S

RC R

R T

ππ

ππ

ππ ππ

ππ

β

ββ

α α

α

αβ

δ

δ

δ

= + −

−= +

= − + +

convention taken fromM.Gronau and J.L.RosnerPhys. Rev. D65, 093012 (2002)

Alternative: Model Dependent Constraints on the CKM angle α

P Tδ δ δ≡ −

4 parameters

|P/T| 0.15-0.45 (representative) Theory ~0.3β 21.3 - 25.9deg (Belle & BaBar combined)δ strong phase difference not known

( ) ( )( ) ( )

0 0

0 0( )

sin( ) cos( )

tag tag

tag tag

d d

N B N BA t

N B N B

S m t C m t

ππ

ππ ππ

−∆ ≡

+

= ∆ ∆ − ∆ ∆

0.40 0.22 0.030.19 0.19 0.050.107 0.041 0.013K

SCA

ππ

ππ

π

= − ± ±

= − ± ±

= − ± ±

Presented at LP ‘03 π+π− results for S and C

4.105.125.373.8730.249.265

±=±=±=

KK

K

NNN

π

ππ

124×106 B pairs, 113 /fb

No significant signal for CPV yet with these data

0B

0B

0

10

20

30

40

∆t (ps)

π+π

− y

ield

(c) q = +1q = −1

0

20

40

60

∆t (ps)

Eve

nts

/(1

.25

ps) (a) q = +1 Total

π+π−

qq– + Kπ

5-5 00

20

40

60

∆t (ps)E

ve

nts

/(1

.25

ps) (b) q = −1 Total

π+π−

qq– + Kπ

5-5 0

-1

0

1

∆t (ps)

Asym

metr

y

(d)

B → π+π−

-Cππ = +0.77 ±0.27(stat) ±0.08(syst)Sππ = −1.23 ±0.41(stat) (syst)+0.08

−0.07

3.1σ

0B 0B

PRD 68 012001 (2003)

Belle’s result on 78/fb

78° ≤ α ≤ 152°

Evidence for CP ViolationResult slightly unphysicalErrors from toy MCModel dept α

assumptions on δT-P, |P/T|, β

data set II (62fb−1)

Improvements in the analysis; includemore efficient continuum suppression algorithm (π0π0)2D fit in ∆E-MBC plane

Sππ

-C=Aππ

2 2physical bound: 1S C+ ≤

data set I (78fb−1)

New Result From Belle: 140/fb, 152×106 B -pairs

ResultsAππ = +0.58 ±0.15(stat) ±0.07(syst)Sππ = −1.00 ±0.21(stat) ±0.07(syst)

Belle140fb−1

1529 ev. (all LR-r

regions)

Observation of CP Violation in B ππ (5.2 σ)Evidence for direct CPV (3.2 σ)

Toy MC Confirms Result is ReasonableInput: (Aππ, Sππ) = (0,0)Belle result almost impossibleprobability ~ 0.1 ppm

Input: (Aππ, Sππ) = maximum likelihood point in the physical regionBelle result no problemprobability ~ 27%

107 experiments (140fb-1 each) 107 experiments (140fb-1 each)

Belle

BaBar

So how do these results compare?

Belle and BaBarmoving closer together as more data added

Belle nearing physical region

only about 1.9σdifference

Belle error now from data

2eff1 sin(2 )S Cππ ππ α= −

-C=Aππ

Model Dependent constraint on α

90° ≤ α ≤ 146° (95.5% CL)for |P/T|=0.45(conservative)

|P|/(|T|+|P|)

δ(deg)

α(deg)

Small Penguin contribution ruled out by this measurement

Isospin Analysis: limiting factor is B0→π0π0

• Small signal; BR ~2×10-6

• qq and ρπ0 background

)2

(GeV/cES m5.2 5.22 5.24 5.26 5.28

)

2E

vent

s / (

2.5

MeV

/ c

0

5

10

(a)

Significance including

systematic errors = 4.2σ0 01413

0 0 0 6

46 3

( ) (2.1 0.6 0.3) 10

N

BR Bπ π

π π

+−

−

= ±

→ = ± ± ×

Phys.Rev.Lett. 91 (2003) 241801

F bin0 2 4 6 8 10

Eve

nts/

1.0

1

10

102

(c)

124×106 B pairs

δα<500

ππ Isospin analysis• 4-fold ambiguity• needs all 3 modes + CP asymmetry measurements• needs a lot more data to get a precision measurement!

now

2006

B ππ→

Belle: B→π+π-

( ) ( ) ( )0| |/(1 ) ( )sin ( )cosX

CPt

XB X XXXf t e SA Cm t C m tSρ τ

ρ ρρρ

± − ∆ ∆ = ± ± ∆ ∆ ∆ − ± ∆ ∆ ∆ ∓

related to α

direct CPV

•ρK is self taggingCρK, SρK, ∆SρK =0, ∆CρK =-1

•large expected:ACP(ρπ) & ACP(ρK)

6

1.3 61.2

( ) (22.6 1.8 2.2) 10( ) (7.3 1.3) 10

B BB B K

ρ π

ρ

± −

± + −−

→ = ± ± ×

→ = ± ×

∓

∓

0 / : Not A CP EigenstateB Kρπ ρ→

BF From Winter ’03 (82/fb)

804.2 ±49.2signal events

doing analysis in region near ρDalitz Plot analysis goal

cos( ) sin( )C m t S m tρπ ρπ− ∆ ∆ + ∆ ∆

~123×106 B pairsLP ‘03 result (113 /fb)

2.4σ

Aρπ+−

Aρπ−+ Difficult to relate to α without DP analysis

The Future for α

α from B→ππ is limited by theoretical interpretation- isospin analysis needs a Super B Factory- But can still get model dependent constraint

B→ρπ need a Dalitz plot analysis to reallyunderstand what is going on

B→ρρ - the new kid on the block

By the end of the current generation of the B-factories we should expect to see combinations of measurements from these modes…

0B ρ ρ+ −→

• final state is dominated by CP even helicity amplitude

• smaller penguin pollution than ππ or ρπ!

• larger BF than ππ: (e.g. factorisation predicts ×2.5 larger)

• promising alternative to ππ and ρπ for getting a precise measure of α

2

21 VL

B

mfm

−∼expect now experimentally confirmed…

Assume Grossman Quinn Bound

(ignores possible I=1 amplitudes)

( )( )

0 0 0, 0

002

00 Bsin ( ) 16 (90% C.L.)

BL

e fL

Lf

Br

Br

f

fρρ

ρ ρα α

ρ ρ+ + +

< → >− ≤ =

→

Measuring α with B→ρρ

Grossman Quinn Bound: 013 (68% C.L.)δα ≤

Similar precision to αeff as for ππ (see BaBar physics book)Model free measurement of α soon!

Electro-Weak PenguinsIsospin Symmetry Breaking

Gluonic penguin pollution: δα

Problems:Angular analysis

Interference

longitudinal polarisation is O(1) – simplifies measurement

Not yet estimated

Current expectation O(50) theoretical uncertainty – will improveSee: Ciuchini , CKM Planning Workshop @ slac Fall ‘03

BaBar Method:

• Optimised analysis for longitudinal polarisation componentSo have to work on reducing B and continuum backgroundfor large cosθH

• only have to fit time dependence for longitudinal polarisationbut deal with transverse and longitudinal

• Consider exclusive charmless and inclusive charm B backgrounds (~3K events)(about 16% of total background)

• large continuum background (~22K events)can fit shape on data so don’t need to rely on MC

Likelihood Fit:B Background

⇒We use 7 distinct PDFsfor the 7 main modes (with an asterisk and arrow in table).

⇒The fraction of b→ c decays is determined with the generic B0B0

and B+B- MC.

⇒For the Five-body decays we use the JetSet estimation (from charmless cocktail).

⇒The BF of the other modes are measured or estimated from isospin symmetries .

38

(simplified form – also have tagging dilution factor and resolution to consider)

0 0

0 0

| |/

( )

| |/

( )

( ) (1 sin( ) cos( ))4

( ) (1 sin( ) cos( ))4

tLong

B B

tTran

B

Long Long

Tran TrB an

ef t m t m t

ef t m tS C

S

m t

Cτ

τ

τ

τ

− ∆

− ∆

∆ = ± ∆ ∆ ∆ ∆

∆ = ± ∆ ∆ ∆ ∆

∓

∓

Time Dependence is:

Analysis in final stage of reviewjournal draft in preparationexpect a hep-ex soon

• For now vary S and C for transverse component between ±1 as systematic

• main systematics:CPV in background (dominates)PDF shapes in likelihoodSVT Local Alignment

• currently working on 82/fb – plan to update to run1-3 soon

Thanks to Andreas Höcker & Lydia Roos for plots

Blind Plot

summer 042006

Blind Projections• Assume that α~110 degrees (near the CKM best fit result)• Project current sensitivity by ×2.4 and ×6 in stats

Caveats: • I=1 amplitudes could contribute at the level of 5% (see Falk et al; PRD69 011502)• Interference needs to be treated properly.• Electroweak penguins could give up to a 5 degree correction on this

CL = 0.317

Can also get rid of some ambiguity:Isospin Analysis has 4 fold ambiguity – inputs:

0 0 000 0, , , , , ,BF BF BF C S SC+− +− +− +−

CPV in interference unique to ρρ I-spin analysis

If BF00 is small Grossman Quinn bound; limit δα

If BF00 is large do isospin analysis:measure S and C & resolve 2 solutions

S00 constrains this angleδα

Same as ππ I-spin analysis

Conclusions

α will ultimately be measured to O(5-100) at B factories

Belle’s new result established CPV in B→ππ and is our best indication of direct CPV outside of the kaon system!

isospin analysis of ππ limited by knowledge of penguin diagramsδα<500 as of now

can get model dependent limits on α

focus moving to ρπ and ρρ for longer term at current machines (theoretically cleaner)

expect measurement from ρρanalysis soon watch hep-ex

90° ≤ α ≤ 146° (95.5% CL) [Belle]