CP VIOLATION (B-factories)

P. Pakhlov (ITEP)

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The major experiments to explore CPKaon system:

Indirect CP Violation

Direct CP Violation

Not useful to constrain CKM matrix parameters (too large hadronic uncertainties)

Rare K decays to πνν

Theoretically very clean modes, but a nightmare for experimentalists: Br ~ 10–11, two neitrinos.

K+ → π+νν

KL → π0νν

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The major experiments to explore CPD-meson system?

• Tiny CP violation, due to degenerated unitarity triangle and GIM/CKM suppression

EDM of n, p, nuclei? • The present ULs are much higher than the SM predictions (however, they are close to many models beyond SM)

B-meson system? • Large CP violation, • Many independent measurements,• Simple hadron dynamics, because of heavy b-quark• Hadronic uncertainties can be estimated or cancel in appropriate observables.

Rare η decays? • UL for CP violation in strong interaction

Dif

ficu

lt t

o ob

serv

e th

e SM

eff

ect,

test

phy

sics

bey

ond

the

SM

4

B-mesons What are B mesons?

B0 = d b B+ = u b JPC = 0 – +

τ = 1.5 × 10-12 s (ct 450 μm)

How are they produced? e+e– (4S) B B is the cleanest process (large BB/other

cross section; no extra particles) Also at hadron machines: pp B + B + anything

How are they decay? Usually to charm b c, e.g. B D Much rarely to light quarks |bc|2|bu|2 100

b q

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ARGUS and CLEO – pioneers in B-physics Large mixing is observed by ARGUS in 1987

Measurements of |Vcb|, |Vub|, |Vtd| and |Vts|: the UT has

comparable sides and therefore angles are not 0 or 180º.

Large Br(B J/KS) ~ 10–3 – very attractive final state

All these were good news for physicists: Large mixing – easy to measure CP violation, as interference occurs

before B decays CP violation in B can be large Convenient final state

The Nature is more favorable to us than we could expect

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Neutral meson mixing from CKM matrix

Equal from CPT invariance

Hamiltonian is non-hermitian due to the decay;

“Box diagram”

It is just a numerical (complex) matrix 2×2:

contributes to off-diagonal elements

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Peculiarity of B-meson system

Box diagram

Thus, mass (width)-differences are approximated by

where

Contains weak phase

Common CP final states for B0 and B0

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CP violation in B mesons No “KL” methods applicable!

Lifetime difference is tiny ((BH)- (BL)/(B) ~1%): no way to work with a beam of long lived B’s.

Semileptonic asymmetry also vanishes. New ideas required!

Sanda & Carter (1980): consider a final state f common for both B0 and B0:

We arrive at decay rate asymmetry for the B0(t=0) and B0(t=0) because of interference of two amplitudes with different weak phases

The effect is large! Sanda & Carter estimated the asymmetry ~ 0.1 (compare with 0.002 CP violating effects in KL)

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Interfere B fCP with B B fCP Sanda, Bigi & Carter:

× A + × A

× A + × A

For B(t=0) = B0

For B(t=0) = B0

tree diagram (A)

box + tree diagram

Calculate t-dependent rates:

Remember: |A|=|A|,|p|=|q|

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B0 J/ KS

taking into account

Penguin diagram is difficult to estimate. But we are lucky: it’s amplitude is collinear to those of the tree one.

Vtd

V*td

d ds

b cc

J/ψ

KS b cc

d ds

J/ψ

KS

d

b

t

t

+

Why?

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B0 π π

In this case the penguin diagram is not small and has different weak phase:• The indirect CP violation ~ S sin(Δm t), where S≠ sin 2α, but sin(2α + some not-negligible phase).• There will be direct CP asymmetry ~ A cos(Δm t),

udub

udub

VV

VV

A

A*

*

Vub

d dub

du

π+

π–

V*td

du

du

d

bt π–

π+

How to take into account this?Wait for the next lecture.

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(4S) resonance

(4S) B0B0 / B+B– ~ 50:50 + no extra particles! Coherent BB production in P-wave B-energy is known (B momentum is very low ~ 340MeV

A very convenient process to study CP violation in B!

bb bound state JPC=1– – (≡ JPC of photon) (e+e–(4S)) 1nb Good signal/background ~

1:3

e+e– (4S) B B

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How to measure CPV at e+e– collider? The source of B mesons is the (4S), which has JPC = 1– –.The (4S) decays to two bosons with JP = 0–.Quantum Mechanics (application of the Einstein-Rosen-Podosky Effect) tells us that for a C = –1 initial state (Υ(4S)) the rate asymmetry:

0))(())((

))(())((

2121

2121

flCPflCP

flCPflCP

fBfBfBfB

fBfBfBfB

NN

NNA

N = number of eventsfCP = CP eigenstate (e.g. B0→J/ψKS)ffl = flavor state (particle or anti-particle) (e.g. B0→e+X)

However, if we measure the time dependence of A we find:

CPfBfBfBfB

fBfBfBfB

flCPflCP

flCPflCP

ttNttN

ttNttNttA 2sin

),(),(

),(),(),(

))((21))((21

))((21))((21

21

2121

2121

Need to measure the time dependence of decays to “see” CP violation using theB’s produced at the (4S).

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Asymmetric e+e– collaider CP violation asymmetry vanishes if integrated over Δt from

– to + kills good idea? No! but requires new idea:

Need to reconstruct B-decay vertex: Impossible at symmetric B-factory – we don’t know B’s production point!

But possible if (4S) has a sizeable boost in lab frame

We can measure t-dependent asymmetry!

Flavor-tag decay (B0 or B0?)

J/

KS

e

e

zt=0

Asymmetric energies

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What‘s required to discover CPV? Produce B mesons! Need accelerator

Effectively reconstruct B mesons

Correctly determine the flavor of second B

Precisely reconstruct the decay vertices

Produce a lot of B mesons! Need good accelerator

Produce a huge number of B mesons! Need accelerator with record luminosity

Need good detector with excellent PID and Vertex

very

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Two B-factories were approved in 1990

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e+e– Asymmetric B-factories

PEP-II

BaBar~1 km in diameter

Mt. Tsukuba

KEKBBelle

SLAC 3.1 x 9GeV

3.5 x 8 GeV

stop Apr-2008

Also tau- and charm- factories: 109 ττ / cc pairs

World highest luminositiesL = 2.1 (KEKB) & 1.2 (PEP-II) × 10 34 cm–2 s–1

775(Belle) & 465(BaBar) millions BB-pairs

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PEP-II at SLAC KEKB at KEK

Belle

BaBar

9GeV (e–) 3.1GeV (e+)designed luminosity: 3.5 1033cm-2s-1

achieved 10.2 1033cm-2s-1

(3 times larger!)

8GeV (e–) 3.5GeV (e+) designed luminosity: 10.0 1033cm-2s-1

achieved 21.2 1033cm-2s-1

(2 times larger!)

11 countries, 80 institutes, ~ 600 persons

13 countries, 57 institutes, ~ 400 persons

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History of 10 years running

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How to measure CPV at B-factories? Reconstruct the decay of one of the B-mesons’s into a CP

eigenstate for example: B J/ KS

Reconstruct the decay of the other B-meson to determine its flavor (“tag”)

Partial reconstruction is sufficient

Measure the distance (L) between the two B meson decays and convert to proper time

need to reconstruct the positions of both B decay vertices t = L/(c)

Correct for the wrong tag and not perfect vertex resolution Extract CP asymmetry from the dN /d t distribution:

dN/d t ~ e -|t| [1 ± cp sin2 sin(m t)]

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Step 1: Select BJ/KS

Reconstruct BCP long lived daughter:

B J/ KS ℓℓ Check the intermediate masses:

M(ℓℓ) ~ M(J/); M() ~ M(KS)

Check the mass and ENERGY (a big advantage of B-factories – we know B energy = Ebeam in the CM system) of J/KS combination

KS decay vertex

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B-candidate CM energy

B-candidate CM momentum

Use many other decays B to charmonium (ηc, χc1, ψ’) + KS to increase statistics:

• These final states have the same (odd) CP eigenvalue• They are equally theoretically clean (no penguin uncertainties)• They can be reconstructed with the similar high purity

B charmonium KSBJ/KS

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2*/

2*KsJbeambc PEM

Purity 97 %CP odd

Purity 59 %CP even

B J/KLImportant to check if the asymmetry flip the sign for the opposite CP eigen value

Difficult to detect KL: cτ ~ 15m; only nuclear interactions.

pK L information is poor

→ lower purity

Detect nuclear shower in iron: measure direction but not momentum. Use known J/KL = Ebeam energy to calculate momentum.

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Step2: Flavor tagging

B0 B0

D X

D XB0 B0

Semileptonic decays

Hadronic decays

X ℓ+ ν

X ℓ– ν

In ~99% of B0 decays: B0 and B0 are distinguishable by their decay products

All charged tracks (not associated with the reconstructed BCP) are from the second Btag in the event: ℓ, K and even charge provides the information of Btag flavor.

|Δt| (ps)

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Step 3: Vertex reconstructionUse tracks from both BCP and Btag to find out z-coordinate of the two B-decay vertices.

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B0 tag_B

0 tagB0 tag_B

0 tagS = sin 2β = 0.65A=0

Take into account detector effects

)cossin(141

,1 tmAtmSetqPt

)21( w

R

R : detector resolutionw : wrong tag fraction (misidentification of flavor) (1-2w) quality of flavor tagging They are well determined by using control sample D*lν, D(*)π etc…

TrueDetector smeared

Need to solve inverse problem to get true value

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First Observation: CPV in B

1137events

Asy

mm

etry

2001

[PRL 87,091802(2001)] [PRL 87,091801(2001)]

J/ψ K*0

( )

Asy

mm

etry

Eve

nts

sin 2β = 0.99 ± 0.14 ± 0.06 sin 2β = 0.59 ± 0.14 ± 0.05

32M BB-pairs

31M BB-pairs

B0 tag_B0 tag

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The recent Belle result

Nsig= 7482

J/ψ KS

J/ψ KL

Phys.Rev.Lett., 98, 031802(2007)

sin 2β = 0.642 ± 0.031 ± 0.017 A = 0.018 ± 0.021 ± 0.014

B0 tag_B0 tag

Nsig= 6512

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B0 tag_B0 tag

Compare CP odd and even final states

Asymmetry= –ξCP sin 2β sin(Δm Δt)

B0 tag_B0 tag

sin 2β = + 0.643 ± 0.038 A = – 0.001 ± 0.028

sin 2β = + 0.641 ± 0.057 A = – 0.045 ± 0.033

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The recent BaBar result

Phys.Rev. D79, 072009 (2009)

sin 2β = 0.687 ± 0.028 ± 0.012 A = 0.024 ± 0.020 ± 0.016

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There are two solutions for β

How to avoid ambiguity?

In some B decays the asymmetry is related to cos2β. It is difficult to achieve good accuracy, but even rough measurement allows to exclude the second solution.

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Other modes that measure sin2β

d d

d

b c

cD+

D–

d d

d

b c

cJ/ψ

π0

cdcb

cdcb

VV

VV

A

A*

*

CP even

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We have done a great job:• CPV violation is observed in the system different from the neutral kaon system. The CPV large (~70%) compared to 0.2% in K0 decays.• The parameter of CPV is measured with great precision (~ 3%) and related to KM parameters without theoretical uncertainties.• The angle of UT triangle is measured (without ambiguity) with the precision better than 1º.

Can we relax now?

Yes, because the time for this lecture is almost over.

No, because we have not yet proved that KM anzatz works well.

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The CM+KM test

VudV*ub

VcdV*cb

VtdV*tb

β

α

γ

How to measure other UT angles?

*

*

tbtd

cbcd

VV

VVArg

*

*

tbtd

ubud

VV

VVArg

*

*

ubud

cbcd

VV

VVArg

sin2β:

**** ,,,: DDBDDBDDBDDBdccb dddd 000 ,:, sdsd KBKBsddsssb

sin2α:0000 ,,,:

dddd BBBBdudb

sin2γ:

DKBuscb : hard

experimentallyeasy

One way to test the Standard Model is to measure the 3 sides & 3 angles and check if the triangles closes!

0*00 /,/,/: KJBKJBKJBsccb dLdsd

How to measure UT sides?