Paola Garosi(University of Siena & INFN Pisa)

Seventh meeting on B Physics Orsay, October 04th-05th 2010

Measurements of theCKM angle γ

2Favored b → c transition Color suppressed b → u transition A1 ~ VcbVus

* ~ λ3 A2 ~ VubVcs* ~ λ3 rB e-iδB e-iγ

CKM γ angle through B→DK decays

γ can be extracted exploiting the interference between the processesb → c us (B- → D0 K-) and b → ucs (B- → D0 K-), when D0 and D0 decay to thesame final state

CKM matrix CP violation if η≠0

Using B→DK decays is the cleanest way to measure γ: - tree-level amplitude only - no theoretical uncertanties

3

Current situation for the γ anglemeasurement using B- → D0 K-

γ (deg) = 71 [+21 -25]

• GGSZ (Giri-Grossmann-Soffer-Zupan) method ([PRL78,3257, PRD68,054018])

that uses the B± → D K± decays with the D0 and D0 reconstructed into three-body finalstate. For example the D0 → K0

s π+ π-

• GLW (Gronau-London-Wyler) method ([PLB253,483 PLB265,172])

that uses the B± → D K± decays with DCP decay modes. DCP+ → π+ π-, K+ K-

and DCP- → K0s π0, K0

s ω, K0s φ.

• ADS (Atwood-Dunietz-Soni) method ([PRL78,3257;PRD63,036005])

that uses the B± → D K± decays with D reconstructed in the doubly Cabibbo suppressedD0

DCS → K+ π-

It is the least well-known angle of the CKM

triangle nowadays!

4

GGSZ method

5

GGSZ methodUses the B-→[K0

s π+ π-] K- decay (large statistics)

Need:- Dalitz plot of D0 decay products as function of:- Precise model of the D0 amplitude (to separate resonances from interference)

s+ = M2(K0S π+)

s- = M2(K0S π-)

+ rB ei(+γ+δB)

B+→B- ⇒ +γ→-γ, s-↔s+, D0↔D0

- Dalitz plot of B+/B- events as function of:- Gaussian-distributed,- uncorrelated

- Fit on B+/B- to obtain rB, δB and γ

x±=rB cos(δB±γ)y±=rB sin(δB±γ)

6

BaBar GGSZ result (468M BB)(arXiv:1005.1096, accepted by Phys. Rev. Lett. (August 2010))

Used D→KSππ and D→KSKK

Combining the three results:

7

Belle GGSZ result (657M BB)(A. Poluektov et al., PRD 81, 112002 (2010))

B→DK B→D*KCombining the two results:

They want to update the analysis using a model-indipendent strategy

D0→K0Sπ+π− from

D*→D0 πsoft

8

GGSZ summary

• Still dominated by statistical error.• Improved model and reduced model error from Babar.• Still model error hard to quantify. Will limit the precision offuture high-statistics measurements using this method.

Average results:

9

GLW method

10

From theory:

RCP± = 1 + rB2 ± 2rB cosδB cosγ

ACP± = 2rB sinδB sinγ/RCP±

GLW method

!

RCP ± =

"(B#$ D

CP ±

0K

#) + "(B

+$ D

CP ±

0K

+)

["(B#$ D

0K

#) + "(B

+$ D

0K

+)]/2

!

ACP ± =

"(B#$ D

CP ±

0K

#) #"(B

+$ D

CP ±

0K

+)

"(B#$ D

CP ±

0K

#) + "(B

+$ D

CP ±

0K

+)

!

R =B(B

"# D

0K

") + B(B

+# D

0K

+)

B(B"# D

0$") + B(B

+# D

0$ +)

!

R± =B(B

"# D

CP ±

0K

") + B(B

+# D

CP ±

0K

+)

B(B"# D

CP ±

0 $") + B(B

+# D

CP ±

0 $ +)

RCP± ~ R±/R

Direct CP violation in B → DCPK modes (DCP+ → π+ π-, K+ K- and DCP- → K0

s π0, K0s ω, K0

s φ.)

4 observables

3 are independent(ACP+RCP+ = -ACP-RCP-)and 3 unknowns (rB, γ, δB)

We neglect a termrB|VusVcd/VudVcs| ~ 0.01

- very clean method- small asymmetry, sensitivity to γ proportional to rB

11

BaBar GLW result (467M B B)(arXiv:1007.0504, accepted by Phys. Rev. D (August 2010)

~ 480 B→DCP+K events

RCP+ = 1.18 ± 0.09 ± 0.05ACP+ = 0.25 ± 0.06 ± 0.02

~ 500 B→DCP-K events

RCP- = 1.07 ± 0.08 ± 0.04ACP- = -0.09 ± 0.07 ± 0.02

• Direct CPV at 3.6σ in B→DCP+K decays • Most precise measurement of ACP± and RCP± • x± competitive with Dalitz-analysis results

12

Belle GLW result (275M B B)(arXiv:hep-ex/0601032v3, PRD 73, 051106, 2006)

B+ B-

B+ B-

~ 140 B→DCP+K events

RCP+ = 1.13 ± 0.16 ± 0.08ACP+ = 0.06 ± 0.14 ± 0.05

~ 150 B→DCP-K events

RCP- = 1.17 ± 0.14 ± 0.14ACP- = -0.12 ± 0.14 ± 0.05

13

GLW at CDF: first measurement at a hadron collider (L=1fb-1)(Phys.Rev.D81:031105,2010)

Selection of DCP+ modes: - cuts optimized minimizing the expected statistical uncertainty on ACP

B- → D0CP+ π- → [K K] π- L = 1fb-1 B- → D0

CP+ π- → [π π] π- L = 1fb-1

Fit procedure:

Implementation of a Likelihood FIT using• kinematics (masses and momenta) and• particle identification (dE/dx)information to determine the signalcomposition(K - π separation: 1.5 σ for p > 2 GeV/c)

D0π mass vs momentum imbalance α

If Pt < PD0 α = 1 - Pt/PD0 > 0If Pt >= PD0α = - (1 - PD0/Pt) <= 0

14

Results

Yield (B → DCP+K) ~ 90 (1 fb-1)!

RCP + =1.30 ± 0.24(stat) ± 0.12(syst)

ACP + = 0.39 ± 0.17(stat) ± 0.04(syst)

15

GLW method: Summary

B→DK B→DK

B→DKB→DK

16

ADS method

17

ADS ObservablesDirect CP violation in B → DDCSK modes

Observables

From theory:RADS(K) = rD

2 + rB2 + 2rBrD cos(δB+δD) cosγ

AADS(K) = 2rBrD sin(δB+ δD)sinγ/RADS(K)

!

AADS(MAX) =

2rBrD

rB

2+ r

D

2

Sizeableasymmetries maybe found also forB → DDCS π

D0CF→K-π+, D0

DCS→K+π-

- expected large CP asymmetry- results have to be combined with other methods to obtain γ measurement

18

BaBar ADS result (467M BB)(arXiv:1006.4241, accepted by Phys. Rev. D (September 2010))

~ 20 B→DDCSK events, with a significance of ~2σ

B→DDCSπ reconstruction

B→DDCSK reconstruction

~ 80 B→DDCSπ events

19

Belle ADS result (772M BB)(preliminary shown at CKM2010)

B→DDCSπ reconstruction

B→DDCSK reconstruction

Evidence of B→DDCSK, with a significance of 3.8σ

20

First measurement of AADS and RADSat a hadron collider using 5 fb-1

ADS method at CDF

21

CF and DCS samples (L = 5fb-1)

B- → D0CF π-→ [K- π+] π- B- → D0

DCS π-→ [K+ π-] π-

Cuts optimization Crucial step towardthe DCS modes

• Maximize the quantity on CF sample.

!

S

1.5 + B(arXiv:0808063v2)

22

B candidate D0 candidate

• LxyB/errLxyB ≥ 12• |IPB| ≤ 0.005 cm• Pointing angle ≤ 0.15• Isolation(R=0.4) ≥ 0.7• Isolation(R=1) ≥ 0.4• χ2

3D ≤ 13

• Lxy wrtB ≥ 0.01 cm• ΔR(D-track from B) ≤ 1.5• ΔID(KfromD-πfromD) ≥ -1.• |cos(θ*)D| ≤ 0.6• 1.8495 ≤ MD(HP k-π) ≤ 1.8815• MD(HP π−k) ≥ 1.9045 & MD(HP π−k) ≤ 1.8265• MD(HP k-πfromB) ≥ 1.9045 & MD(HP k-πfromB) ≤ 1.8265

Optimized selection

angle between the 3Dmomentum of B and thedecay axis

!

ID(h) =dE /dx(h) " dE /dxexp(#)

dE /dxexp(K) " dE /dxexp(#)

θ*D = angle between the D0

in the CM of the B and theflight direction of B

LxyB

IPB

Lxy wrtB

Remove D0→ππ events

23

B candidate D0 candidate

• LxyB/errLxyB ≥ 12• |IPB| ≤ 0.005 cm• Pointing angle ≤ 0.15• Isolation(R=0.4) ≥ 0.7• Isolation(R=1) ≥ 0.4• χ2

3D ≤ 13

• Lxy wrtB ≥ 0.01 cm• ΔR(D-track from B) ≤ 1.5• ΔID(KfromD-πfromD) ≥ -1.• |cos(θ*)D| ≤ 0.6• 1.8495 ≤ MD(HP k-π) ≤ 1.8815• MD(HP π−k) ≥ 1.9045 & MD(HP π−k) ≤ 1.8265• MD(HP k-πfromB) ≥ 1.9045 & MD(HP k-πfromB) ≤ 1.8265

Optimized selection

Reduce contaminationfrom three bodydecay (B+→h+h-h+)

Exploit the powerful 3D silicon-tracking to resolve multiple verticesalong the beam direction and to reject fake tracks. Backg. reduces x2,small inefficiency on signal (<10%).

η - φ spaceB

!

I(B) =pT (B)

pT (B) + pT (i)i"

24

CF and DCS after cut optimization

B- → D0DCS π-

B- → D0CF π-→ [K- π+] π- B- → D0

DCS π-→ [K+ π-] π-

Use of an unbinned maximum likelihood fit (combined on CF and DCSmodes) to separate signals contribution using: mass information particle identification (dE/dx with K-π separation: 1.5 σ for p > 2 GeV/c)

Fit procedure

25

Results

B- → D0DCS π-→ [K+ π-] π-B+ → D0

DCS π+→ [K- π+] π+

Yield (B → DDCSK) = 34 ± 14 (5 fb-1)Yield (B → DDCSπ) = 73 ± 16 (5 fb-1)

Significance for all DCSsignal (DDCSπ + DDCSK) > 5 σ

!

RADS (") = 0.0041± 0.0008(stat) ± 0.0004(syst)

AADS (") = 0.22 ± 0.18(stat) ± 0.06(syst)

RADS (K) = 0.0225 ± 0.0084(stat) ± 0.0079(syst)

AADS (K) = #0.63 ± 0.40(stat) ± 0.23(syst)

• First measurement ofAADS and RADS at a hadroncollider, with a goodprecision!

26

Summary of results

B→Dπ

B→Dπ

B→DK

B→DK

27

Conclusions• BaBar updated Dalitz, GLW and ADS measurements using thefull dataset (468M BB)

• Dalitz: γ = 68 ± 14 ± 4 ± 3• GLW: direct CPV at 3.6σ in B→DCP+K decays• ADS: hint of ADS signals in B→DDCSK (2σ)

• Belle updated Dalitz and ADS measurements using 657M and772M BB (full dataset)

• Dalitz: γ = 78.4 ± 10.8 ± 3.6 ± 8.9• ADS: evidence of ADS B→DDCSK (3.8σ)

B-factories used almost all data available, expected no significantupdates.

• CDF has demostrated capability of hadron colliders with B tocharm decay.

• New ADS results (5 fb-1) competitive with B-factories• We expect significant improvement soon, double data-set by 2011.(expected 10-12 fb-1)• Prospective to extend the run of CDF, further double statistics.

28

BACK-UP

29

The CDF II detectorTRACKING system:• DRIFT CHAMBER96 layers (|η|<1)

→ 1.5σ π/K separation by dE/dx

• SILICON TRACKER7 layers (1.5-22cm from beam pipe)

→ I.P. resolution 35 µm at 2 GeV

→ σ(pT)/pT2 ~ 0.015% (c/GeV)

TRACKING TRIGGER system:• Chamber track processor at L1,2D tracks in COT, pT > 1.5 GeV

• Silicon Vertex Trigger at L2,2D tracks pT > 2 GeV,Impact Parameter measurement (triggeron events containing long lived particles)

30

From an LHCb study: resolution on γ (assuming 2fb-1)

4°-10°B → ππ,KK13°tagged, A(t)KKπBS→DSK

DalitzADS+GLW4-body “Dalitz”4-body “Dalitz”DalitzADS+GLWADS+GLWMethod

15°KSππB+→DK+

15°KKππB+→DK+

under studyKπππB+→DK+

7°-10°Kπ + KK + ππB0→DK*0

under studyKSππB0→DK*0

under studyKπB+→D*K+

5°-15°Kπ +KK/ππ + KπππB+→DK+

σ(γ)D modeB mode

Signal only,no accept.effect

WhenstatisticsbecomessufficientlylargetoactuallyseetheB‐>DKDCSdecay,themostsensitivemethodformeasuringgammabecomesADS(+GLW),notDalitz.

31

To reject most of the physicalbackgrounds, narrow fit windows[5.17,6.5]

Separating DK from other modes

MC

DATA

The only significant physics backgroundsare B-→D0π- and B- →D0*π-

B- → D0CF π-→ [K- π+] π-

32

Implementation of a Likelihood FIT using masses and particleidentification (dE/dx) information to determine the signalcomposition

Separation by Particle ID

K - π separation: 1.5 σ forp > 2 GeV/c

33

ADS: cuts definition

Pointing angle = angle between the momentum 3D of B andthe decay axis

cos(θ*)D = angle between the D0 in the CM of the B and

the flight direction of B

ΔID = ID(KD) - ID(πD) where

!

ID(h) =dE /dx(h) " dE /dxexp(#)

dE /dxexp(K) " dE /dxexp(#)

34

Results

6±828±1144±1229±10DCS

785±49727±478804±1038873±103CF

B- →DK-B+ →DK+B- →Dπ-B+ →Dπ+D mode

B- → D0DCS π-→ [K+ π-] π-B+ → D0

DCS π+→ [K- π+] π+

Yield (B → DDCSK) = 34 ± 14 (5 fb-1)Yield (B → DDCSπ) = 73 ± 16 (5 fb-1)

Significance for all DCSsignal (DDCSπ + DDCSK) > 5 σ

35

Results: physics backgroundPhysics background for DCS:

4±3B0→D0*- e+ νe

18±4B-→K-π+ π-

4±3B-→D0 K-, D0→X90±13B-→D0 π-, D0→X3±3B-→D0* π-, D0*→D0γ/π0

YieldDecay

B- → D0DCS π-→ [K+ π-] π-B+ → D0

DCS π+→ [K- π+] π+

36

ADS: Systematics

37

ADS: Likelihood

• pdfi(M,ID) = pdfi(M) *pdfi(ID)• Fitted parameters

– b CF, DCS = background fraction for CF and DCS– fπ, CF, DCS = B->D0 π fraction for CF and DCS signal– c = fD* /fπ (equal for CF and DCS)– f[X]π = fraction of B->D0 π, D0->X in DCS reconstruction (constrained from MC)– f[X]K = fraction of B->D0K, D0->X in DCS reconstruction (constrained from MC)– fKππ = fraction of B->K- π+ π- in DCS reconstruction (constrained from MC)– fB0 = fraction of B0->D*- e ν in DCS reconstruction (constrained from MC)

Analogous expressions for negative charges

38

Selection of DCP modes

B- → D0CP+ π- → [K K] π- L = 1fb-1 B- → D0

CP+ π- → [π π] π- L = 1fb-1

We optimized the cuts by minimizing theexpected statistical uncertainty on ACP

Select the sub-sample where theB-pion is a trigger track(kinematics differ according towhich tracks trigger, need aseparate fit for the rest)

• Isol > 0.65• chi3D < 13• |d0_B| < 0.007 cm• Sig_LxyB > 12

• LxyD_B > 0.01 cm• LxyD > 0.04 cm• ΔR = (Δφ2 + Δη2)1/2 < 2

39

Fit for B- → D0 π-/K- fractions SIMULTANEOUSLY in:D0

flav, D0CP → KK, D0

CP → ππ modes.

GLW: Likelihood

Likelihood =

ΠkNevents [(1-b) * (fπ Fπ (α, Ptot, MD0π, dE/dx) + fD BGD (α, Ptot, MD0π, dE/dx)

+ (1-fπ - fD) FK (α, Ptot, MD0π, dE/dx)) + b BGcomb (α, Ptot, MD0π, dE/dx)]

b = fraction of the background measured with respect to all the eventsfπ = fraction of B → D0 π with respect to the total signal (common to the twoDCP modes)fD = fraction of B → D0* π with respect to the total signal (common to theflavor and the DCP modes)

Fi (α, Ptot, MD0π, ID) = pdf(MD0π|α, Ptot) pdf(α,Ptot) pdf(dE/dx| α, Ptot)

Write masses with different particle assignments as functions of asingle mass + appropriate kinematics variables α, Ptot

40

Fi (α, Ptot, MD0π, ID) = pdf(MD0π|α, Ptot) pdf(α,Ptot) pdf(dE/dx| α, Ptot)

GLW:Likelihood

Mass term• Signal shape from MC(including FSR)• Background shape:exponential function freein the fit

Momentum term• Signal shape from MC• Background shapefrom data sideband

PID termSignal andbackgroundshapes fromD0 → K-π+

41

Implementation of a Likelihood FIT using kinematics(masses and momenta) and particle identification(dE/dx) information to determine the signal composition

Separation by kinematics and Particle ID

D0π mass vs momentum imbalance α

If Pt < PD0 α = 1 - Pt/PD0 > 0 If Pt >= PD0 α = - (1 - PD0/Pt) <= 0

K - π separation: 1.5 σ forp > 2 GeV/c

42

GLW: Systematics

43

Cross-check: kaon PID selection

A requirement onthe PID variablewas applied tosuppress the Dπcomponent andfavor the DKcomponent.

B → D0CP+ π → [K K] π L = 1fb-1

B → D0CP+ π → [π π] π L = 1fb-1

44

Tevatron is great for rare B decay searches:• Enormous b production cross section, x1000times larger than e+e- B factories• All B species are produced (B0, B+, Bs, Λb…)

The Tevatron

But:• The total inelastic x-section is a factor 103

larger than σ(b b)• The BRs of rare b-hadron decays are O(10-6) orlowerTherefore interesting events must be extractedfrom a high track multiplicity environment

CDF

Detectors need to have:• Very good tracking and vertex resolution• Highly selective trigger