Recent Results on CP Violation from Belle

March 17, 2003 CPV at Belle

Particle Physics SeminarCaltech

Daniel Marlow Princeton University

March 17, 2003

Talk Outline

• Introduction• KEK-B & Belle• Mixing• Indirect CP Violation Measurement/Analysis

– Gold plated mode– Other sin2ϕ1 Modes

• B0→π+π-

• Conclusion

The Kobayashi-Maskawa Mixing Scheme

Where the second matrix is the Wolfenstein parameterization.

0* =++ ∗∗tbubtsustdud VVVVVV

Quark mixing is described via

The “d b” unitarity relation yields 3* λAVV ubtd ≈+

⎥⎥⎥

⎢⎢⎢

−−−−−

−−≅

⎥⎥⎥

⎢⎢⎢

1)1(21

ληρλλλλ

ηρλλλ

VVVVVVVVV

tbtstd

cbcscd

ubusud

The Unitarity Triangle

3λAVtd

( )ηρ ,

( )0,1

3λAVub

λAVV tsus

The gold-plated mode determines the angle which is also called .

1≈≈ tbud VV

KEK B Asymmetric Collider

•Two separate ringse+ (LER) : 3.5 GeVe− (HER) : 8.0 GeV

•ECM : 10.58 GeV at Υ(4S)•Luminosity

•target: 1034 cm-2s-1

•achieved:8.3x1033cm-2s-1

•±11 mrad crossing angle •Small beam sizes:

σy ≈3 µm; σx ≈ 100 µm

asymmetric e+e− collider

KEKB Performance

Reported here

Integrated/day

Total Integrated~78 fb-1

KEKB/PEP II Luminosity Bakeoff

1934 pb-13091 pb-17 day

108 fb-1119 fb-1Integrated

309 pb-1462 pb-124 hour

117 pb-1159 pb-1Shift

PEP-IIKEKB

1233 scm 103.8 −−× 1233 scm 101.5 −−×

As of ~March 15, 2003 Comparisons not quite apples to apples.

µ / KL detection14/15 lyr. RPC+Fe

Tracking + dE/dxsmall cell + He/C2H5

CsI(Tl) 16X0

Aerogel Cherenkov cnt.n=1.015~1.030

Si vtx. det.3 lyr. DSSD

TOF counter

SC solenoid1.5T

8GeV e−

3.5GeV e+

Belle Detector

An international collaboration involving about 10 Countries, 50 Institutes, & 250 People

The BELLE Collaboration

Mixing

( ) ( )[ ]022

(0 sincos)( BeiBetB mimtmtimi φ−∆∆)/2Γ−− +×=

Neutral B’s exhibit the fascinating phenomenon of mixing, which is where we will start the story.

Flavor TaggingAs noted, in IDCPV measurements, one needs to know the flavor of the spectator B0. This information can also be used for mixing studies.

• Track level tags

• High momentum leptons

• Medium momentum K±

• High-momentum π± (from e.g., )

• Low-momentum π± (from D*’s).

• Need to take into account multiple tags and correlations.

+−→ π(*)0 DB

Flavor Tagging: “Hamlet”

yreliabilit tag 10 ;1 ⇔<<±= rq

MixingBtdtb

Fd BVV

mmSmmfGm

6 ⎟⎟⎠

⎞⎜⎜⎝

⎛=∆ η

[ ])cos(14

tmetP dB

∆∆+=∆

∆−

[ ])cos(14

tmetP dB

∆∆−=∆

∆−

Mixing measurements can be done by counting “same-sign” decays or by observing the timing distributions, or both.

XB +→ l0 XB −→ l0

mll±⇔""OS−−++⇔ llll or ""SS

MixingThere are various ways to determine the flavor of the decaying B0. In one method, one side of the event is fully reconstructed using known hadronic decay modes, such as B0→D*−π+

and the other side is tagged using standard flavor tagging algorithm. Timing distributions are then plotted for same-flavor (SF) and opposite-flavor (OF) subsamples.

Summary of Mixing Results

0.528±0.017±0.011HamletB0→D*-π+Hadronic

0.505±0.017±0.020High-pt l±B0→D*-π+D*- →D0π-

Partial reconstruction

0.494±0.012±0.015HamletB0→D*-l+νSemi-leptonic

0.503±0.008±0.010High-pt l±High-pt l±Dilepton

∆md (ps-1)TagSignalMethod

But What About the CP Violating Phase?

( ) ( )[ ]022

(0 sincos)( BeiBetB mimtmtimi φ−∆∆)/2Γ−− +×=

As noted, it is there, but we can’t get at it in a standard mixing measurement since it disappears when we “project out” the flavor eigenstates.

Indirect CP Violation

( ) ( )[ ]02

0 sincos )( 1 BieBtB mtimt ∆−∆ +∝ φ

( ) ( )[ ]02

20 cos sin)( 1 BBietB mtmti ∆∆ +∝ φ

[ ]000 2

1 BBB ±≅±

LKJB Ψ→+ /0

CP Eigenstates

SKJB Ψ→− /0

CP odd CP even

Indirect CP ViolationIf we choose ϕ1=45o, then ie i ±=± 12 ϕ

( ) ( ) 02

sincos

tBmtmt ∆∆ +

( ) ( ) 02

cossin

tBmtmt ∆∆ +−

Indirect CP Violation

mt∆2π π

)(tΓ No mixing [ ]φξτ

2sin)sin(1

∆±×

=Γ−

0B0B f

π mt∆2π

)(tA0B

Mixing Coefficient

Interference from mixing.

CP eigenvalue

The Measurement

+µtag

0DNeed to:

•Measure momenta

•ID leptons & K’s

•Measure vertices

−e +e

Analysis Flowchart

Muon Identification

µµµ

side- tagplus

/+−+

The dilepton decay modes are a big part of the reason of why the “gold-plated” modes are given that name.

The gaps are instrumented with RPCs.

J/Ψ Reconstruction

• Require one lepton to be positively identified and the other to be consistent with lepton hypothesis.

• For e+e-, add any photon within .05 of electron direction.

29 fb-1

B Reconstruction

*cand EEE −≡∆

2*beam ⎟

⎞⎜⎝

⎛−= ∑ pEmbcr

29 fb-1 sample

CP Even Mode (B→J/ΨKL) Reconstruction

KL hits

LKJB Ψ→ /0• Assume(2-body) kinematics.

• Look for KL recoiling from J/ψ

• hits in RPCs

• cluster in ECL

• Remove positively tagged background modes: J/ψK+ , J/ψK* , etc.

• Plot

LKJB Ψ→ /0

*LKJB ppp rr

B→J/ΨKL Reconstruction

*LKJB ppp rr

78 fb-1 Sample

Charmonium CP Mode Summary

78 fb-1 Sample

Flavor TaggingTwo measures of tagging performance:

• ε = efficiency

• w = wrong-tag fraction

• r = 1 – 2w

Amplitude of mixing oscillation depends on w

)21( w−

01.027.0eff ±=ε

Vertexing

+µtag

0D−e +e

Reality

Cartoon

The B lifetime is of the same order as the vertex resolution, so the effect is quite subtle.

Effect of Resolution

∆tThe resulting signature of CP violation is mainly a mean shift between the B0 and B0 samples.

Unsmeared theory Resolution

Smearing

Test of Vertex Resolution0*0 / KJB Ψ→

Fitting

)()'( sigsig tRttPLi ∆⊗∆−∆= )1( bgf−×

bgbgbg )()'( ftRttP ×∆⊗∆−∆+

[ ])sin(2sin)21(12

sig tmwqetP fB

∆∆−−=∆∆−

ϕξτ

Signal

)()1(2

bkg tfeftPbg

∆−+=∆∆−

δτ τ

τ Background

Response function

The Fitted Result: 78 fb-1 Sample

035.0074.0719.02sin 1 ±±=ϕ

033.0067.0741.02sinBaBar cf ±±=β

Time-Dependent Asymmetry

One can plot the excess/deficit on a bin-by-bin basis. The plots to the right are notcorrected for dilution effects (wrong tagging, background, etc.).

78 fb-1 Sample

What if |λ|≠1 ?

If |λ| is allowed to float, (i.e. a cos(∆m t) term)

074.0720.02sin 1 ±=φThe CPV asymmetry is ~unchanged.

026.0049.0950.0 ±±=λ

In general we have

Note: if |λ|≠1, then the gold-plated mode isn’t really gold plated.

78 fb-1 Sample

Other ϕ1 Modes b→sss

In the SM, the phase for these decays is ~0, so the IDCPV asymmetry should be ~sin2ϕ1 and no direct CPV. Given the anomalously large rate, however, there might be more to the story . . .

500 108.5)'( −×=→ KBB η

Other ϕ1 Modes b→sssπ+π−

B0 η’KSπ+π−η, ργ

π+π−

B0 φKSK+K−

π+π−

B0 K+K−KS(K+K−≠φ)

Mbc (GeV/c2) Mbc (GeV/c2) Mbc (GeV/c2)

BELLE-CONF-0225

SφK = −0.73±0.64±0.22

AφK = −0.56±0.41±0.16

−SKKK = +0.49±0.43±0.11

AKKK = −0.40±0.33±0.10

+0.33−0.00+0.00−0.26

−Sη’K = +0.71±0.37

Aη’K = +0.26±0.22±0.03

+0.05−0.06

Uncertainty in CP ± fractionsw = (3 )%+16

(−)S sin2φ1 in b ccs(=0.719±0.074±0.035)

Raw Asymmetries

PreliminaryPreliminary

Other ϕ1 Modes: b→sss

Onward to φ2

φ1φ3

Measuring 2φ2=2(π- φ1- φ3)

)(2sin)sin(

)(2sin)sin( )()()()()(

φφξ

+∆∆−=

+∆∆−=→Γ+→Γ→Γ−→Γ

tmfBfBfBfBtA

CP−+= ππffor

With just one amplitude, CP violating phases will remain hidden. With two, they are revealed in a simple way. Three, alas, is not even better.Ideal Case

Measuring 2φ2

Interference between the tree level and penguin decay graphs is a little bit too much of a good thing!

[ ]) sin(14

+∆∆+=∆Γ∆−

tmSqetB

τtmA ∆∆cosππ

Mean shift between q=+1 and q=-1 samples.

Population difference between the q=+1 and q=-1 samples.

22sin and 0 then penguin, no If φππππ == SA

Particle ID

for π+π–,

π eff. = 0.91

K fake rate = 0.10

Flavor TaggingUse inclusive flavor-specific properties and correlations

Inclusive Leptons:high-p l−

intermed-p l+

Inclusive Hadrons:high-p π+

intermed-p K+

low-p π−

BB-mixing fit flavor tag performance(“class 6” has the least dilution).

mixing amplitude wrong tag fraction

class 1 class 2

class 3 class 4

class 5 class 6Classify events based on expected dilution

Continuum Suppression

LLRL L

LRmin 0.825

continuumπ+π−

(MC)class 1 class 2

class 3 class 4

class 5 class 6

Construct likelihood based on:

• Event topology

• Modified Fox-Wolfram

• Fisher Discriminant

• Angular distribution of B flight direction

The likelihood cut depends on the flavor-tagging class.

Kinematic Selection

mπ±→ KB0

825.0<LR

−+→ ππ0B

825.0>LR

Vertexing

B0 D+π−, D*+π−, D*+ρ−, J/ψKS and J/ψK*0

B0 lifetime1.551±0.018(stat) ps

Time resolution (rms)1.43ps

(PGD02: 1.542±0.016 ps)

• Same method as sin2ϕ1 analysis

• Resolution determined mainly by tag-side vertex

evts M 85 BB

∆t Spectra & Fit Results

08.041.023.108.027.077.0

±±−=±±+=

Cross Checks

B0 →K+π– control sample

020406080

100120140160180

-0.2 0 0.2 0.4

∆E (GeV)

-0.2 0 0.2 0.4

∆E (GeV)

1371 candidates

Positively-identified kaons (opposite use of PID)

LR > 0.825 LRmin < LR ≤ 0.825

Mixing fit using B0→K+π−

∆md=0.55 ps-1+0.05−0.07

Consistent withthe world average(0.489±0.008) ps-1

PDG2002(OF−

ππ : τB=(1.42 ± 0.14) ps

Kπ : τB=(1.46 ± 0.08) ps

BG shape fit

Lifetime Measurementsc.f. (PDG2002)(1.542 ± 0.016) ps

Evidence that background treatment is correct

Null Asymmetry Tests

Null asymmetry

A = −0.015±0.022S = 0.045 ±0.033

SKπ = 0.08 ± 0.16

AKπ =-0.03 ± 0.11

MC/Fit Linearity Check

Monte Carlo pseudo experiments are used to check various things. In particular, we studied the linearity of the fitting procedure and the determination of the statistical error.

Statistical Error

The log likelihood functions are not well behaved (parabolic), which is not surprising since the central values lie outside of the physically allowed region.

Statistical ErrorThe MINOS errors are significantly smaller than the toy-MC pull distributions. After considerable internal discussion, we decided to adopt the larger MC errors as the most indicative of the actual statistical uncertainty.

Green arrows indicate MINOS errors.

How Often Are We Outside the Physical Region?

Probability that we have fluctuation equal to or larger than the fit to data(input values at the physical boundary)

Physical regionAππ2 + Sππ2 ≤ 1

Events outside physical region: 60.1% Events outside ellipse: 16.6%

822.0 0.539 ; vs −== ππππππππ SASA

Systematic Uncertainties

−0.055+0.044−0.048+0.058Background fractions

−0.013+0.010−0.020+0.019Resolution function

−0.002+0.007−0.015+0.003Background shape

−0.022+0.022−0.014+0.021τB, ∆md, AKπ

−0.016+0.015−0.021+0.026Wrong tag fraction

−error+error−error+error

+0.016

+0.044

−0.07+0.08−0.08Total

−0.020+0.052−0.021Fit bias

−0.012+0.037−0.054Vertexing

source

* Actual estimations were done before seeing the fit result, as we adopted a blind analysis technique.

Confidence Regions; Evidence for CP Violation

• Feldman-Cousins frequentistapproach.• Acceptance regions obtained from MC pseudo-experiments.•Systematic errors also included.• Confidence Level (CL) at each point is calculated.

CL for CP conservation: 3.4σ

Future Prospects (as seen in the past!)

Summary & Conclusions• CP violation in the B system has been observed at the >6σ level.

• We see an indication of CP violation in B→π+π- decay.

• The KEKB accelerator is working very well and now holds the world record for instantaneous and integrated luminosity.

035.0074.0719.02sin 1 ±±=ϕ

08.041.023.1 08.027.077.0 ±±−=±±+= ππππ SA

Additional Slides

Answers to FAQsQ: Is the anomalous result due to a problem in PID ?

A: Checks on the PID have been done:

• the amount of Kπ background obtained in the ∆E fit to the ππ sample is consistent with that is expected from the Kπ yield and miss-id probability.

• The fits are repeated with the Kπ fraction varied by estimated uncertainty (±20%). The change of A is +0.003/-0.007 and S +-0.037 which is included in sys. error.

• We repeat the fit to the sample with tighter PID requirement and different Delta-E cuts, where Kpibackground is different. These give consistent results.

Answers to FAQs

Q: Are the fit errors or results biased when the true value is near the physical boundary ?

•We confirmed with MC pseudo-experiments that there is no sizable bias in the fit results. We conservatively include a possible fit bias near the physical boundary in the systematic error; the values are +0.05/-0.02 for Sππ and ±0.02 for Aππ

• Fit errors (MINOS errors), which are subject to bias in this region, are not used to calculate the confidence intervals.

Answers to FAQsQ: What happens if the result is constrained to lie in the physical region?

A: The result is the point with the largest likelihood at the boundary (A=0.57, S=-0.82), which is close to the closest point to our fit result (A=0.53, S=-0.83).

Answers to FAQs

Q: Why have the errors remained the same size even though the data size was doubled?

• We now use rms values of fit output distributions from MC pseudo-experiments.

• In the previous result, we quoted MINOS errors from the fit.

Answers to FAQsQ: How do you know the background parameterization is correct?

A: We obtained parameters for continuum background by fitting to sideband events. Continuum MC show that the distribution in sideband is same as that in signal region.

Q: How do we know that we have parameterized the tails of distributions?

A: The lifetime fits results for ππ and Kπ are consistent with world averages, indicating that the ∆t distribution is correctly parameterized.

A: for the ∆E shape, double Gaussians were used for both ππand Kπ, yielding results consistent with the single-Gaussianfits.functions for both pipi and Kpi shapes.

Answers to FAQs

Q: Are the fit values of Aππ and Sππ (anti-) correlated?

A: No. The correlation coefficient for the data is 0.02. Morever, the toy MC results shows no clear correlation between Aππ and Sππ.

Answers to FAQs

A: What do you obtain when you fit events with B0 and B0 tags separately?

Q: Since A is mainly determined by the counting asymmetry of signal yields between, B0 and B0 tags, when fitting these samples separately, we fix Aππ to 0.77 and fit for Sππ . The result is

The results are consitent with the standard fits at the 2σ level.

034.025.0

059.043.0 for 97.0 and for 57.2 BSBS +

−+− −=−= ππππ

Answers to FAQs

Q: It looks like it is the background asymmetry that has fluctuated. Could that explain the result?

A: Statistical fluctuations in the background are accounted for in the statistical error. We also confirm null asymmetry with sideband data that is dominated by continuum.

It is true, however, that an overestimate of the background (and other dilution effects) could artificially increase the apparent asymmetry.

Answers to FAQsQ: Are Belle and BaBar consistent?

A: The values are

Which is a difference of 2.6σ when taken in quadrature. Stranger things have happened.

BaBar 04.025.030.0 and 05.034.002.0 Belle 08.027.077.0 and 08.041.023.1

±±=±±=±±=±±−=

ππππ

Answers to FAQsQ: Can the asymmetry be traced to a detector-dependent asymmetry in the particle ID? (This question was posed by Blair Ratcliff.)

Comment: this effect is potentially dangerous, since there is a “magnification” of the asymmetry in the events that feed across from the Kπ to the ππchannel.

This effect is still under discussion within Belle, so what is said here should be considered preliminary.

Answers to FAQsQ: Can the asymmetry be traced to a detector-dependent asymmetry in the particle ID (cont’d)?

ππππ

ηΓΓ∆

≈ KKA2

Where the A’ππ is an apparent counting asymmetry resulting from feed across from B→Kπ decays and ∆ηKπ is a detector induced asymmetry in the rates for K+ and K- faking π+ and π- This magnification results because misID fakes directly enter the B→ππ sample.

πηK∆

• Due to dilution effects, the maginfication is actually more like 2.5, rather than the 4 that one would expect from the measured BRs.

• The charge asymmetry in Belle appears to be very small (surprisingly so), and has conservatively been taken to be <1% based on direct measurements. For example, Brendan Casey’s thesis gives

310)1.19.0()()()()( −

×±−=+−

KNKNKNKN

• Due to dilution effects, the maginfication is actually more like 2.5, rather than the 4 that one would expect from the measured BRs.

• The charge asymmetry in Belle appears to be very small (surprisingly so), and has conservatively been taken to be <1% based on direct measurements. For example, Brendan Casey’s thesis gives

310)1.19.0()()()()( −

×±−=+−

KNKNKNKN

Detector Charge Asymmetry

Answers to FAQs

B→K(*)l+l-

FCNC decays likeB→K(*)l+l- have a long and important history in particle physics. In the SM, they are forbidden at the tree level, but occur through penguins and loops, which are potentially sensitive to beyond-the-SM contributions.

60 fb-1 Sample

B→K(*)l+l-

610)06.016.058.0( )(

×±±

=→ llKBBR

C.L. 90% 104.1 )(

→ llKBBR

Both results consistent with SM expectations.

B→π+π- Checks

Likelihood Plots

12sin ϕ

0LK Detection

∑± =

−=hi

iS PPP,

4missγ

Inclusive “KL’s”

Vertexing

• Common track requirements– # of associated SVD hits > 2– Use run-dependent IP

• For CP-side, use J/ψ l+l- tracks– Reject poorly fit events.

• For Tag-side, use tracks with:– |δz|<1.8mm, |σz|<500 µm, |δr|<500 µm– Iterate: discard worst track until fit is acceptable.

• Require |zCP - ztag|<2 mm (≈10τB)

Test of Vertex Resolution0*0 / KJB Ψ→

The Data

The first order effect is a mean shift between positively and negatively tagged samples (Summer ’01 sample).

30 fb-1

sample

Sources of Systematic Error

±0.035Total

±0.007∆md and τB0 errors

±0.007Fit biases

±0.010KL background fraction

±0.014Resolution function

±0.015Flavor tagging

±0.022Vertex algorithm

Subsample Dependence

Comparison to other sin2ϕ1Measurements

It looks like CDF had it right!

Ψ’ Modes

Both leptons tagged.

29 fb-1 sample

Other Charmonium Modes

M(l+l−γ) − M(l+l−)

1st observationof inclusiveB→ χc2 X

29 fb-1 sample

Mixing

The effect of the mixing is readily evident when the asymmetry is plotted as a function of ∆t.

Other ϕ1 Modes: b→ccd

00 / πΨ→ JB 00 / ρΨ→ JB

Belle-Conf-0209

Other ϕ1 Modes: b→ccd

06.039.025.0 08.049.093.0

±±−=±±=−

AS78 fb-1 Sample

After cut on Mbc

The background situation is more difficult.

In the 42 fb-1 sample, we have observed an asymmetry in the rate for vs.At present, this is only a ~3σ effect, but if it persists with higher statistics, it will represent the first observation of direct CP violation in the B system.

−+→ ππ0B −+→ ππ0B

[ ]) sin(1)(/

+∆∆±=∆Γ∆−

tmSet fB

tmC ∆∆cosππ

Mean shift between q=+1 and q=-1 samples.

Population difference between the q=+1 and q=-1 samples.

Recent Results on CP Violation from Belle

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