Measurement of CP Violation in B J/ψφ - · PDF fileHow current matter-antimatter...

Measurement of CP Violation in Bs → J/ψφ at CDF

Michal Kreps for the CDF collaboration

(rad) s

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-1CDF Run II Preliminary L = 1.35 fb

95% C.L.68% C.L.SM prediction

⇒

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95% C.L.68% C.L.

SM prediction

New Physics

⇒ ?

www.kit.edu www2.warwick.ac.uk

Discovery of CP violation��

��

��

�� Neutral kaon puzzle in late 1950s

��

��

��

�� Two particles (K1, K2) with same mass, but

different lifetime and different decay mode

��

��

��

�� K2 is CP odd and if CP is conserved can

decay only to 3 π

��

��

��

�� Observation of K2 → π+π− in 1964 by

Cronin and Fitch ⇔ CP is not conserved

2 Michal Kreps – Measurement of CP Violation in Bs→J/ψφ at CDF21 September 2010

Explaining CP violation��

��

��

�� Observation by Cronin and Fitch requires ≈ 10−3 admixture of

wrong CP state in wave function

��

��

��

�� In 1973 Kobayashi and Maskawa concludes that

��

��

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�� No reasonable way to include CP violation in model with 4

quarks��

��

��

�� Introduction of CP violation needs new particles��

��

��

�� One of the suggested ways uses 6 quark model

��

��

��

�� CP violation ⇔ complex phase in quark mixing (CKM) matrix

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

=

1 − λ2/2 λ Aλ3(ρ− iη)−λ 1 − λ2/2 Aλ2

Aλ3(1 − ρ− iη) −Aλ2 1

��

��

��

�� Nobel prize in 2008


Implications��

��

��

�� When Kobayashi and Maskawa proposed their explanations, only

3 quarks were known

��

��

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�� The six quark model had several implications:

��

��

��

�� Existence of another 3 quarks to be seen by experiment��

��

��

�� In 1980/1981 several people predicted large CP violation in B

system

-1

0

1

-1

0

1

-1

0

1

sin2

φ 1 . s

in(∆

md∆

t)

(c) J/ψKL (ξf = +1)

(a) Combined

Asy

mm

etry

(b) (cc)KS (ξf = −1)−

-8 -4 840∆t (ps)

-1

0

1(d) Non-CP sample

-1

-0.5

0

0.5

1 BABAR

-1

-0.5

0

0.5

1

-5 0 5

Asy

mm

etry

∆t (ps)

-4

-3

-2

-1

0

-1 0 1 2sin2β

ln(L

/Lm

ax)

��

��

��

�� Start of dedicated B physics

experiments

��

��

��

�� In 2001 Belle and Babar

experiments observe large CPviolation in B0 decay

��

��

��

�� Since then many measure-

ments performed to check idea


Global status

VCKM =

1 − λ2/2 λ Aλ3(ρ− iη)−λ 1 − λ2/2 Aλ2

Aλ3(1 − ρ− iη) −Aλ2 1

γ

γ

αα

dm∆Kε

Kε

sm∆ & dm∆

SLubV

ν τubV

βsin 2

(excl. at CL > 0.95) < 0βsol. w/ cos 2

excluded at CL > 0.95

α

βγ

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

1.5excluded area has CL > 0.95

ICHEP 10

CKMf i t t e r


Are we done?

��

��

��

�� Does not look to be case

��

��

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�� Many unanswered questions

��

��

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�� SM has many free parameters��

��

��

�� What is the meaning of generation, why we need more than

one?��

��

��

�� What is the origin of dark matter and dark energy?��

��

��

�� How current matter-antimatter asymmetry is generated?

��

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�� No baryon number violation in SM��

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�� CP violation in SM is many order of magnitude too small��

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�� In SM cannot generate needed phase transition

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�� SM is probably just low energy approximation of final big theory of

everything


Role of flavor physics��

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�� Several extensions of SM exists, each postulating new particles

��

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�� Some examples

��

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�� Fourth generation introduces two additional quark, VCKM is

changed to 4 × 4 matrix��

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�� Supersymmetry has partner for each SM particle��

��

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�� In supersymmetry squarks/sleptons mix through 3 × 3 matrix

m211 m2

12 m213

m221 m2

22 m223

m231 m2

32 m233

��

��

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�� Looking for indirect effects of new physics to discover it

��

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�� If new physics is discovered, understand which model is right one


CPV in Bs → J/ψφ

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

=

1 − λ2/2 λ Aλ3(ρ− iη)−λ 1 − λ2/2 Aλ2

Aλ3(1 − ρ− iη) −Aλ2 1

��

��

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�� Vts known from unitarity

��

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�� Need to check also by experiment

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�� Best testing ground is decay Bs → J/ψφ

b

t, c, u

t, c, u

W−W+

b

s

ss

cc

b

s

c

c

s

s

��

��

��

�� New physics in mixing can have large effect on CP violation

��

��

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�� Search for large CP violation in Bs → J/ψφ


Sidenote on phases��

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�� Bs system is described by equation

iddt

(∣

∣B0s (t)⟩

∣

∣B0s (t)⟩

)

=(

M− i2Γ

)

(∣

∣B0s (t)⟩

∣

∣B0s (t)⟩

)

��

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�� Box diagram of mixing give rise to M12 and Γ12

��

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�� Interesting quantities and relation to observables:

��

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��

∆Ms = 2|MSM12,s| · |∆s|

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�� φs = arg(−M12/Γ12) = φSM

s + φ∆s , in SM φs = (4.2 ± 1.4) · 10−3

��

��

��

��

∆Γs = 2|Γ12,s| · cos(

φSMs + φ∆s

)

��

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�� CP Violation in Bs → J/ψφ measures

��

��

��

�� φ

J/Ψφs = −2βs + φ∆s + δSM

Peng. + δNPPeng.

in SM 2βs = 2 arg(−VtsV ∗tb/VcsV ∗

cb) ≈ 0.04

��

��

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�� With current CDF precision we really test presence of large φ∆s


Analysis logic��

��

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�� Principle is to measure time dependent asymmetry of CP

eigenstate

A =N(B, t) − N(B, t)

N(B, t) + N(B, t)

��

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�� We need to find in data

��

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�� Bs → J/ψφ decays��

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�� Measure decay time��

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�� Find out whether it was produced as B or B

K+K−Bs

+µ−µ

K

Bq

K

l


Likelihood anatomy

��

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�� Signal PDF for single tag

Ps(t , ~ρ, ξ|D,σt ) =1 + ξD

2P(t , ~ρ|σt )ε(~ρ)

+1 − ξD

2P(t , ~ρ|σt )ε(~ρ)

��

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�� ξ = −1, 0, 1 is tagging decision

��

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�� D is event-specific dilution

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�� ε(~ρ) - acceptance function in angular space

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�� P(t , ~ρ|σt ) (P(t , ~ρ|σt )) is PDF for Bs (Bs)


Likelihood anatomyd4P(t , ~ρ)

dtd~ρ∝ |A0|2T+f1(~ρ) + |A‖|2T+f2(~ρ) + |A⊥|2T−f3(~ρ)

+ |A‖||A⊥|U±f4(~ρ) + |A0||A‖| cos(δ‖)T+f5(~ρ)

+ |A0||A⊥|V±f6(~ρ)

T± = e−Γt × [cosh(∆Γt/2) ∓ cos(2βs) sinh(∆Γt/2)∓ η sin(2βs) sin(∆mst)] ,

U± = ±e−Γt ×[

sin(δ⊥ − δ‖) cos(∆mst)

− cos(δ⊥ − δ‖) cos(2βs) sin(∆mst)

± cos(δ⊥ − δ‖) sin(2βs) sinh(∆Γt/2)]

,

V± = ±e−Γt × [sin(δ⊥) cos(∆mst)− cos(δ⊥) cos(2βs) sin(∆mst)± cos(δ⊥) sin(2βs) sinh(∆Γt/2)] .


Issue of s-wave��

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�� We reconstruct Bs → J/ψφ with φ→ K +K−

��

��

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�� But wide resonance f0(980) can also decay to K +K− and

Bs → J/ψK +K− is also possible (called s-wave)

��

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�� There are arguments that s-wave can be large

��

��

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�� Stone et al, PRD79, 07024 (2009) predicts

B(Bs → J/ψf0(980))B(f0(980) → ππ)B(Bs → J/ψφ)B(φ→ KK )

' 0.2 − 0.3

��

��

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�� Best upper bound from Belle

B(Bs → J/ψf0(980))B(f0(980) → ππ) < 1.63 · 10−4 at 90% C.L.

��

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�� S-wave can contribute to reconstructed signal

��

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�� It is CP-odd eigenstate with its own angular and time dependence

��

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�� Sizeable contribution which is not accounted for can bias result

⇒ Account for it in the likelihood


Treatment of s-wave��

��

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�� Add amplitude for s-wave ⇔ four angular terms (amplitude2 + 3

interference terms)

��

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�� S-wave amplitude is pure CP-odd eigenstate with its own angular

dependence

��

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�� Strong phases vary over resonance

⇒ Need to start with K +K− mass included��

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�� Relativistic Breit-Wigner propagator for p-wave��

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�� Constant for s-wave

��

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�� Keep K +K− mass as unobserved ⇔ integrate over it

��

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�� Interference between p-wave and s-wave could break last

symmetry

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�� Full math spelled out in arXiv:1008.4283


Previous results

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95% C.L.68% C.L.SM prediction

(rad) s

β-1 0 1

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-1

(ps

Γ∆

-0.6

-0.4

-0.2

0.0

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95% C.L.68% C.L.

SM prediction

New Physics

CDF 1.35 fb−1

p-value = 15%

CDF 2.8 fb−1

p-value = 7%

CDF 2.8 fb−1 + DØ 2.8 fb−1

p-value = 3.4%

What next?


Tevatron and CDF experiment

0

250

500

750

1000

1250

1500

1750

2000

0 50 100 150 200 250 300 350Day

CD

F A

cqui

red

Lum

inos

ity (

pb-1

)

200120022003

2004

2005

2006

20072008

2009

2010

��

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�� pp collisions at

√s = 1.96 TeV

��

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�� Peak luminosity ≈

3.5 − 3.8 · 1032 cm−2s−1

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�� Collected about ≈ 7fb−1


Selection

Network output-1.0 -0.5 0.0 0.5 1.0

Can

dida

tes

per

0.02

310

410

510SignalBackground

CDF Run II Preliminary -1L=5.2 fb

]2) [GeV/cφ ψMass(J/5.28 5.3 5.32 5.34 5.36 5.38 5.4 5.42 5.44 5.46

2C

andi

date

s pe

r 2

MeV

/c

0

100

200

300

400

500

600

700

800

900

-1CDF Run II preliminary L = 5.2 fb

Neural Network Cut-0.5 0.0 0.5 1.0

par

abol

ic e

rror

sβ

0.110

0.115

0.120

0.125

0.130

0.135

0.140

CDF Simulation = 0.02sβInput

��

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�� Latest analysis uses 5.2 fb−1

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�� Events selected using dimuon trigger

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�� Typical event has few dozens tracks ⇒

lot of background

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�� Neural network to select interesting

events

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�� Select ≈ 6500 Bs → J/ψφ decays


Flavor tagging

K−

Bs

SST

OST

a l −

b K+

b

u

u

Bb

s

Κ s

s/d/d

/π+ +/d

��

��

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�� Determination of the flavor at

production time

��

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�� Difficult task due to large number of

tracks

��

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�� Benefits from PID

��

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�� Calibrated with data


OST Calibration

]2

invariant mass [GeV/c+ KψJ/5.20 5.25 5.30 5.35 5.40

)2en

trie

s/(5

MeV

/c

0

2000

4000

6000

8000

10000

12000

14000

-1CDF II Preliminary, 5.2 fb

51,920 +/- 388 Signal Events

OST Predicted Dilution0.0 0.2 0.4 0.6 0.8 1.0

OS

T M

easu

red

Dilu

tion

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0-1

CDF Run II Preliminary L = 5.2 fb

events+B 0.09±Slope = 0.93

OST Predicted Dilution0.0 0.2 0.4 0.6 0.8 1.0

OS

T M

easu

red

Dilu

tion

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0-1


events-B 0.10±Slope = 1.12 B+ B−

��

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�� Flavor tagging algorithm is characterized by

��

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�� Efficiency ε��

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�� Dilution D = 2 · P − 1

��

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�� Quantity εD2 defines effective statistics

��

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�� Opposite side tagging is independent of studied hadron

��

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�� Effective power of OST is εD2 = 1.2%


SSKT Calibration

5.4 5.5 5.6

2C

andi

date

s pe

r 3

MeV

/c

0

50

100

150

200

250

300

350

400 DataFit Function

π s D→ sB Ks D→ sB

Comb. Backgr. Xs D→B

75±S = 5613

33±B = 1070

0.17±S/B = 5.25

0.70± = 68.66 S+BS/

-1CDF Run 2 Preliminary, L = 5.2 fb (+ cc)- K

+ K→ φ,

-π φ → -s, D+π -

s D→ 0sB

2Invariant Mass in GeV/c

5.4 5.5 5.6

data

(dat

a -

fit)

-2

0

2

-1Mixing Frequency in ps

10 20 30

Am

plitu

de-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0Amplitude A

-1Sensitivity: 37.0 ps

-1CDF Run 2 Preliminary, L = 5.2 fb

-1Mixing Frequency in ps

10 20 30

Am

plitu

de-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

��

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�� SSKT depends on the meson we study

��

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�� Only way to calibrate is to use Bs itself

��

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�� Fortunately Bs oscillation is sensitive to

quality of tagging

��

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�� Principle

A = Nmix−NunmixNmix +Nunmix

= A · D cos (∆mt)

��

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�� Use decays:

��

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�� Bs → Dsπ with Ds → φπ, Ds → K ∗K and

Ds → πππ

��

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�� Bs → Dsπππ with Ds → φπ

��

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�� In total ≈ 12900 signal events

��

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�� Total tagging power εD2 = 3.2 ± 1.4%

��

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��

∆ms = 17.79 ± 0.07(stat)


Angular efficiencies

CDF Run II Preliminary, L=5.2 fb−1

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�� Derived from large statistics MC

��

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�� Parameterized in three dimensions

��

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�� CP Violation relatively insensitive to exact details

��

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�� Efficiency compares well with angular distributions of combinato-

rial background


Lifetime and width difference

KK) [cm] ψct (J/-0.2 -0.1 0 0.1 0.2 0.3

mµev

ents

per

50

1

10

210

310

Data - signal regionFitSignalLightHeavyBackground

-4-2024

pull


Distribution for BsH

Distribution for BsL

Signal mass region

Under SM assumption (βs = 0) we measure:cτ = 2

ΓH+ΓL= 1.529 ± 0.025(stat) ± 0.012(syst) ps

∆Γs = 0.075 ± 0.035(stat) ± 0.01(syst) ps−1


Polarization amplitudes

)ψcos(-1.0 -0.5 0.0 0.5

Ent

ries

per

0.12

rad

0

100

200

300

400

500

600

700Data

Fit

)θcos(-1.0 -0.5 0.0 0.5

Ent

ries

per

0.12

rad

0

100

200

300

400

500

600

700Data

Fit

φ0 2 4 6

Ent

ries

per

0.42

rad

0

100

200

300

400

500

600

700Data

Fit

CDF Run II Preliminary, L = 5.2 fb

)ψcos(-1.0 -0.5 0.0 0.5

Ent

ries

per

0.12

rad

0

100

200

300

400

500

600

700

800 Data

Fit

)θcos(-1.0 -0.5 0.0 0.5

Ent

ries

per

0.12

rad

0

100

200

300

400

500

600

700

800 Data

Fit

φ0 2 4 6

Ent

ries

per

0.42

rad

0

100

200

300

400

500

600

700

800 Data

Fit

CDF Run II Preliminary, L = 5.2 fb

|A|||2 = 0.231 ± 0.014(stat) ± 0.015(syst)|A0|2 = 0.524 ± 0.013(stat) ± 0.015(syst)φ⊥ = 2.95 ± 0.64(stat) ± 0.07(syst)

Signal

Background


CP Violation

(rad) sβ-1 0 1

)

-1

(ps

Γ∆

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6


95% CL

68% CL

SM prediction

(rad) sβ-1 0 1

log

(L)

∆2

0

2

4

6

8

10

12

14

16

1895% CL

68% CL

SM prediction


��

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�� SM p-value is 44%

��

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�� Corresponds to 0.8σ

��

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�� Significant improvement

��

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�� Strong phases free

��

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�� SM p-value is 31%

��

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�� Comparable to 2D case ⇔ ∆Γ

consistent with SM

��

��

��

�� βs ∈ [0.02, 0.52] ∪ [1.08, 1.55]

@ 68% C.L.


Comparison to previous result

(rad) sβ-1 0 1

)

-1

(ps

Γ∆

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6


95% CL

68% CL

SM prediction

(rad) s

β-1 0 1

)

-1

(ps

Γ∆-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6


95% C.L.68% C.L.

SM prediction

New Physics

��

��

��

�� Concentrate on size of the allowed region

��

��

��

�� Significant improvement compared to our previous result


Size of the adjustment

) pln(L∆20 5 10 15

1-C

L

-210

-110

1 68% CL

95% CL


rand

omiz

ed n

uisa

nce

para

met

ers

non-

Gau

ssia

n er

rors

idea

l

(rad) sβ-1 0 1

)

-1

(ps

Γ∆

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6


95% CL

68% CL

SM prediction (rad) sβ-1 0 1

)

-1

(ps

Γ∆

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6


5.99

2.30

SM prediction


S-wave check

Prob 0.3225

)2 Mass (GeV/c-

K+ KψJ/5.30 5.35 5.40 5.45

2C

andi

date

s pe

r 4

MeV

/c

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Prob 0.3225

-1CDF Run II Preliminary L = 3.8 fbdatatotal fit

signal0sB

combinatorial bkg0misreconstructed B

)2 Mass (GeV/c-

K+K1.00 1.050

500

1000

1500

2000

2500data

total fit

combinatorial background

0misreconstructed B0f

-1CDF Run II Preliminary 3.8 fb2C

andi

date

s pe

r 2

MeV

/c

S-wave fraction 0.00 0.02 0.04 0.06 0.08 0.10

log

(L)

∆2

0

1

2

3

4

5

6

7

8

9-1


95% CL

68% CL

(rad) sβ-1 0 1

)

-1

(ps

Γ∆

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6 S-wave not included

S-wave included

5.99

2.30

-1CDF Run II Preliminary L = 5.2 fb��

��

��

��

�� Q: Is change since last time due to

previously omitted s-wave?

��

��

��

�� A: No, likelihood almost same with s-wave

fixed to zero

��

��

��

�� Q: Is the K +K− mass consistent with our

fit model?

��

��

��

�� A: Yes it is


Effect of flavor tagging��

��

��

�� With tagging of εD2 ≈ 5% we

don’t gain lot in precision

��

��

��

�� Main effect in reducing

ambiguities

��

��

��

�� Untagged case symmetric under

each��

��

��

�� 2βs → −2βsδ⊥ → δ⊥ + π

��

��

��

��

∆Γ → −∆Γ

2βs → 2βs − π

��

��

��

�� Tagged symmetry

��

��

��

�� 2βs → π − 2βs

∆Γ → −∆Γ

δ|| → 2π − δ||δ⊥ → π − δ⊥


Different parts of data


Different parts of data

(rad) sβ-1 0 1

)

-1

(ps

Γ∆

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6


S-wave not included

-1Data 0-1.35 fb

5.99

2.30

SM prediction

(rad) sβ-1 0 1

)

-1

(ps

Γ∆

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6


S-wave not included

-1Data 1.35-2.8 fb

5.99

2.30

SM prediction

(rad) sβ-1 0 1

)

-1

(ps

Γ∆

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

S-wave not included

-1Data 2.8-5.2 fb

5.99

2.30

SM prediction


Conclusions��

��

��

�� Significantly improved measurement of the CPV in Bs → J/ψφβs ∈ [0.02, 0.52] ∪ [1.08, 1.55] @ 68% C.L.

��

��

��

�� CDF data now agree on the ≈ 1σ level with SM

��

��

��

�� Best measurement of

��

��

��

�� Mean lifetime��

��

��

�� Width difference between mass eigenstates��

��

��

�� Polarization amplitudes

(rad) sβ-1 0 1

)

-1

(ps

Γ∆

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6


95% CL

68% CL

SM prediction


Prospects��

��

��

�� Couple of improvements possible beyond collecting data

��

��

��

�� Include other triggers gives ≈ 25% more statistics��

��

��

�� Add Bs → ψ(2S)φ��

��

��

�� Look for Bs → J/ψf0(980) with f0(980) → π+π−

��

��

��

�� Add K +K− mass as fit variable - helps in ambiguity resolution

��

��

��

�� Still collecting data, expect to have ≈ 2 times more by the end of

2011

��

��

��

�� Extension of running by 3 years under discussion

store number1000 2000 3000 4000 5000 6000 7000 80000

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01/1001/0901/0801/0701/0601/0501/0401/03

Delivered

Acquired

)-1Luminosity (pb

0

250

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1000

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2000

0 50 100 150 200 250 300 350Day

CD

F A

cqui

red

Lum

inos

ity (

pb-1

)

200120022003

2004

2005

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20072008

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2010


Measurement of CP Violation in B J/ψφ - · PDF fileHow current matter-antimatter...

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