CP VIOLATION IN B0S J/

CDF (and D0)

Joe BoudreauUniversity of Pittsburgh

≠

1

A very brief abstract of this talk first. The following topics will be developed:

CDF and D0 use B0s J/

to measure CKM phases. Wedetermine from this decay thequantity s.

This is in exact analogy to B factory measurement of the , an angle of the unitarity triangle.

The standard model makes very precise predictions for both angles.

But other new particles & processes,lurking potentially in quantum mechanicalloops such as box diagrams and penguin diagrams can change the prediction.

Vub*Vud Vtb

*Vtd

Vcb*Vcd

Vub*Vus

Vtb*Vts

Vcb*Vcs

s

2

THE “LOCAL” CONNECTION

Studies of CPV in B0

s J/ at the Tevatron go back to 2006, since then this has remained a “hot topic”.

Significant updates are in the works right now From the U.K. Oxford team are major players (Farrukh

Azfar and Louise Oakes); I recommend inviting them in the near future to deliver the punch line.

3

“NOTHING IS CREATED, NOTHING IS DESTROYED, EVERYTHING IS TRANSFORMED.”

e.g 2H + O H20

This maxim from the 18th century is wrong.

Here is a recipe to produce hydrogen

Lavoisier

4

A THOUGHT EXPERIMENT WITH A BOX OF NOTHING:

• Take a box of nothing.

• Heat it up to above the TEM, the temperature of the electroweak phase transition ~ 100 GeV

• Cool rapidly

• Open the box and you will find something… ordinary baryonic matter.

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6

CKM PHYSICS & COSMOLOGY

WMap measures:

The SM has all of the ingredients (Sakharov conditions) to generate the 100%Baryon Asymmetry of the Universe, but the quantity:

where J is the Jarlskog Invariant

Depends on quark Masses and on CPviolation, thus it can be studied “in thelaboratory”.

7

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

Vub*Vud + Vtb

*Vtd + Vcb*Vcd=0

The quantity “A” is the area of the“Unitarity Triangle”

Vub*Vud Vtb

*Vtd

Vcb*Vcd

W+

u

d

W+

u

s

W+

u

b

W+

c

d

W+

c

s

W+

c

b

W+

t

d

W+

t

s

W+

t

b

8

There are six unitarity triangles that can be formed, and all of themhave the same area:

The area of any one of these triangles quantifies how much CPviolation one gets (with three generations of quark).

9

There are 12 observed instances of CP violation.

1. Indirect CP violation in the kaon system (K)2. Direct CP violation in the kaon system ’/3. CP Violation in the interference of mixing and decay in B0 → J/ K0.4. CP Violation in the interference of mixing and decay in B0->’K0

5. CP Violation in the interference of mixing and decay in B0->K+K-Ks

6. CP Violation in the interference of mixing and decay in B0->+-

7. CP Violation in the interference of mixing and decay in B0->D*+D-

8. CP Violation in the interference of mixing and decay in B0->f0K0s

9. CP Violation in the interference of mixing and decay in B0->0

10. Direct CP Violation in the decay B0 K-+

11. Direct CP Violation in the decay B 12. Direct CP Violation in the decay B

# 3 is important to us because: predictions are precise. there is a similarity w/ the B0

s J/

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Very famous measurement of CP Asymmetries in B0J/ K0s

|B0>

|B0>

| J/ K0s >

Vub*Vud Vtb

*Vtd

Vcb*Vcd

BABAR, BELLE have used this decayto measure precisely the value of sin(2) an angle of the bd unitaritytriangle.

There was a fourfold ambiguityhttp://ckmfitter.in2p3.fr/

11

|B0>

|B0>

| P0 >

| P >

| P|| >

|+-K0s0>

Babar, Belle resolve an ambiguity in by analyzing the decay

B0 J/ K0* which is BV V and measures sin(2) and cos(2)

This involves complicated angular analysis (to be described)

J/ K0*

|B0>

Phys.Rev. D71 (2005) 032005

Phys.Rev.Lett. 95 (2005) 091601

12

|Bs0>

|Bs0>

| P0 >

| P >

| P|| >

|+-K+K->

J/

|Bs0> J/ is an almost exact analogy, except this system also

contains a difference in lifetime/width)

|Bs0>

13

b ds

cc

W WW

dB0 →J/ K0*

b ss

cc

W WW

sBs

0 →J/

The decay B0sJ/ obtains from the decay B0J/ K0* by the

replacement of a d antiquark by an s antiquark

We are measuring not the (bd) unitarity triangle but the (bs) unitarity triangle:

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

tbtstd

cbcscd

ubusud

VVV

VVV

VVV

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B0s→J/

• B0s→J/ is two particles decaying to three final states..

Two particles:

Three final states: J/ in an S wave CP EvenJ/ in a D wave CP Even

J/ in a P wave CP Odd

0 0 0,

0 0 0,

S L S S

S H S S

B p B q B

B p B q B

Light, CP-even, shortlived in SMHeavy, CP-odd, longlived in SM

A supposedly CP even initial statedecays to a supposedly CP oddfinal state…. like the neutral kaons

Measurement needs ≠0 but not flavor tagging.

The polarization of the two vectormesons in the decay evolves witha frequency of ms

Measurement needs flavor tagging, resolution, and knowledge of ms

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Time dependence of the angular distributions: use a basis of linear polarization states of the two vector mesons { S, P, D} { P, P||, P0 }

CP odd states decay to P

CP even states decay to P|| , P0

If [H,CP] ≠ 0

Then 0dCP

dt

•The polarization correlationdepends on decay time.

•Angular distribution of decayproducts of the J/ and the analyze the rapidly oscillatingcorrelation.ms~ 17.77 ps-1.

A. S. Dighe, I. Dunietz, H. J. Lipkin, and J. L. Rosner, Phys. Lett. B 369, 144 (1996),

184 hep-ph/9511363.

16

ˆ (sin cos ,sin sin ,cos )n

29ˆ( , , , ) | ( , ) |

16P t A t n

||0

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

2 2

A t A tA t A t i

An analysis of an oscillating polarization.

The measurement is a flavor-tagged analysis of time-dependent angulardistributions

17

The flavor-tagged analysis of B0s J/ is a post B0

s mixing analysis.

* phenomenologically related* same flavor tagging technology, too.* CP violation analysis needs ms from mixing analysis

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There are two states in the B0s system,

the so-called “Flavor eigenstates”

They evolve according to the Schrödinger eqn

0

0

s

s

B bs

B bs

a adi H

b bdt

2

iH M and M, Hermitian Matrices

M: Dispersive diagrams : Absorptive diagrams

u, c

u, c

B0s –B0

s Flavor Oscillations

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The magnitude of the box diagram gives the oscillation frequency m.

The phase of the diagram determines the complex number q/p, with magnitude of very nearly 1 (in the standard model).

0 0 0,

0 0 0,

S L S S

S H S S

B p B q B

B p B q B

0 0 0

2 2 2 22*

12 02 212

s s sF W B B B B tts tb

W

G M M B f MM S V V

M

22

122

mM

*

*Mi tb ts

tb ts

q V Ve

p V V

Mass eigenstates are superpositions of flavor eigenstates governed by constants p, q:

And an initially pure |B0s> evolves (oscillates)

mixing probability: /1( ) (1 cos( ))

2tP t e mt

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In general the most important components of a general purpose detector system, for B physics, is:

• tracking.• muon [+electron] id• triggering.

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CDF Detector showing as seen by the B physicsgroup.

Muon chambersfor triggering on the J/→+- and Identification.

Strip chambers,calorimeter for electron ID

Central outer trackerdE/dX and TOF system for particle ID r < 132 cm B = 1.4 T for momentum resolution.

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L00: 1.6 cm from the beam. 50 m strip pitch Low mass, low M-S.

For B0s mixing: SVXII can trigger

on hadronic decays!!

Excellent vertex resolution from three silicon subsystems:

SVX II ISL

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The D0 Silicon tracker…..

• surrounded by a fibre tracker at a distance 19.5 cm < r <51.5 cm

• now augmented by a high-precision inner layer (“Layer 0”)

• 71 (81) m strip pitch• factor two improvement in impact• parameter resolution

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Mixing is an important constraint on the Unitarity Triangle:

Mixing probability /1( ) (1 cos( ))

2tP t e mt

Mixing occurs when a B0s decays as a B0

s.

Decay to a flavor specific eigenstate tags the flavorat decay: B0

s Ds ; B0s Ds ; B0

s Ds l

One of three tagging algorithms tags the flavor at production.

Good triggering, full reconstruction of hadronic decays,excellent vertex resolution, and high dilution taggingare all essential for this measurement, which made news in 2006.

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Δms = 17.77 ± 0.10(sta) ± 0.07(sys) ps-1

|Vtd/Vts| = 0.2060 ± 0.0007 (exp) + 0.0081 – 0.0060 (theor)(PRL 97, 242003 2006)

Δms = 18.56 ± 0.87(stat) ps-1

(D0 CONF Note 5474)

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Two techniques for initial state “flavor tagging”

•b, b quarks are always produced in pairs;

b quark always opposite bb antiquark always opposite b

Flavor-specific decay modes (eg semileptonic decays) of the opposite side b, or jet charge can be used to determine the sign of the b quark on the opposite side.

•The fragmentation chain produces weak correlations between b quark flavor and the sign of nearby pions and kaons in the fragmentation chain

Procedure to select leading ±, K± can be optimized to obtain the highest quality tag.

27

Each tagger returns:

•A decision (B or B)•An estimate of the quality of that decision (dilution D)

= tag efficiencyD = 1-2ww = mistag rate

D2 = effective tagging efficiency

Performance of the flavor tag in CDF

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The quality of thePrediction of dilutionCan be checked againstthe data:

We reconstruct a sampleOf B± decays in which one knows the sign of the Bmeson.

We then “predict” the sign of the meson andplot the predicted dilutionvs the actual dilution.

Separately for B+

and B-

Scale (from lepton SVTthis sample; take thedifference B+/B- as anuncertainty). 29

Flavor Tagging Performance and Validation

SST +OST: D2 = 4.68 ± 0.54%

Each tag decision comes with an error estimatevalidated:

1. Using B± (OST) 2. In the B0s mixing (SST)

SST: D2 3.6%OST: D2 1.2%

30

ˆ (sin cos ,sin sin ,cos )n

29ˆ( , , , ) | ( , ) |

16P t A t n

||0

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

2 2

A t A tA t A t i

An analysis of an oscillating polarization.

The measurement is a flavor-tagged analysis of time-dependent angulardistributions

31

The analysis of B0s→J/ can extract these physics parameters:

The exact symmetry..

… is an experimentalheadache.

The measurement of s and are correlated; from theory one has the relation = 2|12|cos(2s) with |12| = 0.048 ± 0.018 and A. Lenz and U. Nierste, J. High Energy Phys. 0706, 072 (2007).

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CDF, 2506 ± 51 events .. And in D0, 1967 ± 65total.. … but 2019 ± 73 tagged events, all tagged. …[and 3150 in 2.8 fb-1]

Next, we’ll run through the CDF analysis, show what you get from flavor tagging, then show the D0 results.

33

Results from 1.7 fb-1 of untagged decays.

34

Phys.Rev.Lett.98:121801,2007

35

Results untagged analysis

StandardModel Fit(no CP violation)

HQET: c(B0s)= (1.00±0.01) c(B0) PDG: c(B0) = 459 ±0.027 m

Phys.Rev.Lett.100:121803,2008

36

More results, untagged analysis

Applying the HQET lifetime constraint:

37

An angular analysis can also be applied to the decay B0-> J/K*

to extract amplitudes ~ CP even / Odd fractions in the final state:

38

Angular fit projections B0 J/ K0*

Angular fit projections B0 J/

39

CDF B0 Angular Analysis

53%

23%

24%

Longitudinal

Transverse Parallel

Transverse Perpendicular

A consistent picture of the CP Odd/Even fraction in B0→J/ K*,B0

s→J/ in CDF, Babar, and Belle experiments:

B0s

57%21%

22%

CDF B0 Angular Analysis

Longitudinal

Transverse Parallel

Transverse Perpendicular

Belle B0 Angular Analysis

57%23%

20%

Transverse Longitudinal

Transverse Parallel

Transverse Perpendicular

Babar B0

56%

21%

23%

Longitudinal

Transverse Parallel

Transverse Perpendicular

B0

B0 B0

R. Itoh et al. Phys Rev. Lett. 98, 121801, 2007 (Belle) B. Aubert et al. PRD 76 (2007) 031102 (Babar)

40

This plot is Feldman-Cousins confidence region in the space of the parameters2s and

The likelihood for the untagged analysis has a higher degree of symmetry(+ with s - s ) than the tagged analysis. As you will soon see

41

Results from 1.35 fb-1 of tagged decays.

42

Tagged analysis: likelihood contour in the space of the parameters s and

One ambiguity is gone, now this one remains

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Constrain strong phases || and to BaBar Values (for B0J/ K* !!)

Constrain s to PDG Value for B0 Apply both constraints.

B. Aubert et al. (BABAR Collaboration), Phys. Rev. D 71, 032005 (2005).

using values reported in:

44

The standard model predictions of s and data consistent with theCDF data at the 15% confidence level, corresponding to 1.5 Gaussian standard deviations.

One dimensional Feldman-Cousins confidence intervals on 2s ( treated as a nuisance parameter):

2s [0.32, 2.82] at the 68% CL.

Assuming |12| = 0.048 ± 0.018 and the assumption of mixing-induced CP violation:

2s [0.24,1.36] U [1.78, 2.90] at the 68% CL.

If we additionally constrain the strong phases || and to the results from B0 J/ K*0 decays and the Bs mean width to the world average Bd width, we find

2s [0.40, 1.20] at 68% CL

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A Feldman-Cousins confidence region in the s- plane is the main result.This interval is based on p-values obtained from Toy Monte Carlo and represents regions that contain the true value of the parameters 68% (95%)of the time.

The standard model agrees with the data at the 15% CL

arXiv:0712.2397v1

46

D0 Strategy (quite different from CDF).

• Strong phases vary around the world average values ( for B0J/ K* !!)

Uncertainty taken to be ± /5 Is this justified? Theory now estimates the difference between the strong phases in the two decays to be < 10 o.

J. Rosner and M. Gronau, Phys.Lett.B669:321-326,2008 )

Obtain “point estimates” in these all of these fits.

Note, D0 has a different name for the CP violation parameter: sJ/ = -2s

CP = CP fit, s

J/floating

SM = Standard model fit, s

J/floating

NP = New Physics fit,s

J/and constrained by the assumption of mixing-induced CP violation.

47

Comparison of |Amplitude|2 (CDF and D0)

48

D0 Result: arXiv:0802.2255v1

49

Likelihood contours for just and for just s=-2s

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Outlook

Note s = -2s

• Fluctuation or something more, it does go in the same direction.• CDF estimates confidence level at 15% using p-values to obtain Ln(L/L0) • D0 estimates confidence level a 6.6% using the probability to extract a lower value than seen in the data, from toy. 51

UTFit group has made an “external” combination.

• “re-introduces” the ambiguity into the D0 result.• does so by symmetrizing; cannot fully undo the strong phase constraint.

arXiv:hep-ph/0803.0659

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Combined by HFAG:

D0 then performed a fitw/o strong phase constraints

53

Summer ‘08

Interim result:

CDF adds the secondhalf of its data, butwithout calibration ofPID and TOF, afterfirst 1.35 fb-1 only OSTtagging is used, and noPID used in selection.

D2 = 1.8% for 2nd half of data

SM p-value is 7%. Fluctuation did not go away

D0 produces a confidence region withoutthe strong phase constraints. 54

ff

fluctuation?

discrepancy?

p-value = 0.0342.12 from SM

p-value 0.022.33 from SM

55

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4th Generation? Outline of arXiv:0803.1234v3 George W.S. Hou

WMap measures:

The SM has all of the ingredients (Sakharov conditions) to generate the 100%Baryon Asymmetry of the Universe, but the quantity:

falls short by ten orders of magnitude. A possible solution is a 4th generation

where J is the Jarlskog Invariant

Assuming mt’ > mb’ > mt and taking,mt’ = 300 GeV, the author predicts large negativevalues of s : -0.7 < sin(2s) < -0.5

CDF Direct Search Limit: mt’ > 256 GeV/c2 ; mb’ > 268 GeV/c2

can provide an enhancement of 1013 or more

What’s expected next?

• Analysis of full5.2 fb-1 dataset.

• dE/dx calibratedand performing in selection + tagging.

• D0 analyzing 6.0fb-1

•Same side kaon tagging beingapplied to the full sample (notjust 1.35 fb-1 as in ‘08 interimupdate.

57

S-WAVE CONTAMINATION?

58

ˆ (sin cos ,sin sin ,cos )n

29ˆ( , , , ) | ( , ) |

16P t A t n

||0

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

2 2

A t A tA t A t i

•When B0s J/ K+K-; m(K+K-)~ 1020 MeV/c2 and L(K+K-) = 1 we

call that B0s J/

•When L=0 we call that the S-wave; it is CP-even and nonresonant.

•Additional terms in the probability density are easy to handle; instead of just this:

23ˆ( , , , ) | ( ) |

16Q t B t n

( ) ( ( ),0,0)B t B t

• Don’t forget the mass dependence.• Or P-wave S-wave interference.• Or the proper detector re-normalization after the detector sculpting.

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Those terms have been included in the likelihood function sowe plan to (finally) respond to the question about S-wave contaminationby not neglecting it, this time.

Plots show tests of the new fitter.

60

CONCLUSIONS B0

s J/ is an important and precise test of the origin of CP violation in the standard model.

D0 has performed a flavor-tagged analysis of 2.8 fb-1.

CDF has used 1.35 fb-1 of data in a first analysis then added another 1.45 fb-1 of data (but with OST only).

There were hints of new physics, at the 2.33 level.

Updates to 5 fb-1 are in progress at CDF, to 6 fb-1 at D0

Look forward to the definitive statement from the Tevatron before too long.

And then we all look forward to very high statistics analyses from the

LHCB61

62

Vub*Vud = O(3) Vtb

*Vtd= O(3)

Vcb*Vcd = O(3)

Vub*Vus= O(4)

Vtb*Vts= O(2)

Vcb*Vcs= O(2)

’

With = 0.2272± 0.0010 A = 0.818 (+0.007 -0.017) = 0.221 (+0.064-0.028) = 0.340 (+0.017-0.045)

One easily obtains a predictionfor s :

2s = 0.037±0.002 63

The A “anomaly” may also have to do with bs

•Direct CP in B+K+ 0 and B0 K+- are generated by the b s transition. These should have the same magnitude.

•But Belle measures (4.4 )

•Including BaBar measurements: > 5

•The electroweak penguin can break the isospin symmetry•But then extra sources of CP violating phase would be required in the penguin

Lin, S.-W. et al. (The Belle collaboration) Nature 452,332–335 (2008).

64

Example of new physics: a fourth generation quarkthat contributes to the Electroweak Penguin

Would have other measureable consequences: e.g. an impact onmixing induced CP violation in B0

s mesons.

Wei-Shu Hou, arXiv:hep-ph/0803.1234

65

66

where i = 0, para, perp and

B

B

An analysis of the decay canbe done with either a mix ofB and B mesons (untagged) or with a partially separated sample (flavor tagged). Latter is moredifficult and more powerful.

ˆ (sin cos ,sin sin ,cos )n ||

0

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

2 2

A t A tA t A t i

29ˆ( , , , ) | ( ) |

16P t A t n

/ 22( ) ( ) ( )

cos2 ( )

imt tii

i

H L s L H

a e eA t E t e E t

/ 22( ) ( ) ( )

cos2 ( )s

imt tii

i

H L s L H

a e eA t E t e E t

( ) ( )

4 2 4 21

( )2

m mi t i t

E t e e

These expressions are:

* used directly to generate simulated events.

* expanded, smeared, and used in a Likelihood function.

* summed over B and ̅B (untagged analysis only)

reference material

67

Proper decay time: distance between production & decay…..

Beam profile~ 30 microns.

Lxy

c = Lxy/sin

= LxyMB/PT

… transformed into the rest frame of the B meson:

Resolution is about 76 fs for the J/ decay mode

68

Semileptonic asymmetry

• We have assumed so far that:

and thus || = 1 .. To a very good approximation. In higher order however |q| ≠ |p| and ||≠1 (at the level of 1-|| < 2.5 x 10-3)

2 siq Ae

p A

•AsSL= 0.020 ± 0.028 (CDF)

http://www-cdf.fnal.gov/physics/new/bottom/070816.blessed-acp-

bsemil/

•AsSL= 0.0001 ± 0.0090 (stat) (D0, dimuon)

•AsSL= 0.0024 ± 0.0117(stat) +0.0015

-0.0024 (syst) (D0, semileptonic B0

s decays)

Phys. Rev. D 76, 057101 (2007)

HQET/Ms12 =(49.7 ±9.4) ±10−4

Semileptonic asymmetry:

12

12

sin( )s

sl ssA

M

tan( )sl sAM

For mixing-induced CP violation

D0 Conf Note 5730

70

combined CDF/D0CDF/D0 + As

sl + assumption of mixing induced CP violation.

Under these assumptions Assl constrains

and s.

Green is 69% CL allowed region.

… with the following effect on the contours: