Transcript CP VIOLATION (B-factories)

CP VIOLATION (B-factories)
P. Pakhlov (ITEP)
The major experiments to explore CP
Kaon system:
Indirect CP Violation
Direct CP Violation
K+ → π+νν
Not useful to constrain CKM matrix
parameters (too large hadronic uncertainties)
Rare K decays to πνν
KL → π0νν
Theoretically very clean modes, but a nightmare
for experimentalists: Br ~ 10–11, two neitrinos.
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The major experiments to explore CP
D-meson system?
• Tiny CP violation, due to degenerated unitarity triangle
and GIM/CKM suppression
Rare η decays?
• UL for CP violation in strong interaction
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.
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B-mesons

What are B mesons?
 B0


B+ = u b

JPC = 0 – +

τ = 1.5 × 10-12 s (ct  450 μm)
How are they produced?



=db
bq
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 |bc|2|bu|2  100
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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
Hamiltonian is non-hermitian due to the decay;
Equal from CPT invariance
It is just a numerical
(complex) matrix 2×2:
“Box diagram”
contributes to offdiagonal elements
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Peculiarity of B-meson system
Common CP final states for B0 and B0
Box diagram
Thus, mass (width)-differences are approximated by
where
Contains weak phase
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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
tree diagram (A)
Sanda, Bigi & Carter:
For B(t=0) = B0
×A +
× A
box +
tree diagram
For B(t=0) = B0
× A +
× A
Calculate t-dependent rates:
Remember: |A|=|A|,
|p|=|q|
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B0  J/ KS
b
d
c
J/ψ
c
s
d KS
V*td
b
t
d
d
t
b
+
Vtd
d K
S
s
c J/ψ
c
taking into account
Penguin diagram is difficult to estimate.
But we are lucky: it’s amplitude is
collinear to those of the tree one.
Why?
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B0  π π
Vub
b
d
d π–
u
u +
π
d
A VubVud*
 *
A VubVud
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),
b
d
V*td
t
d
π–
u
u +
π
d
How to take into account this?
Wait for the next lecture.
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(4S) resonance




bb bound state
JPC=1– – (≡ JPC of photon)
(e+e–(4S))  1nb
Good signal/background ~
1:3
e+e–  (4S)  B B



(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!
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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:
A
N ( B1  f CP )( B2  f fl )  N ( B1  f CP )( B2  f fl )
N ( B1  f CP )( B2  f fl )  N ( B1  f CP )(B2  f fl )
0
N = number of events
fCP = 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:
A(t1, t2 ) 
N (t1, t2 )( B1  f CP )(B2  f fl )  N (t1, t2 )( B1  f CP )(B2  f fl )
N (t1, t2 )( B1  f CP )(B2  f fl )  N (t1, t2 )( B1  f CP )(B2  f fl )
 sin 2CP
Need to measure the time dependence of decays to “see” CP violation using the
B’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 Bfactory – 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?)
Asymmetric energies
e
J/
e
t=0
z
KS
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What‘s required to discover CPV?

Produce a
B huge
lot
mesons!
of number
B mesons!
of B mesons!
Need accelerator
Need good
accelerator
with
accelerator
record luminosity

Effectively reconstruct B mesons

Correctly determine the flavor of second B

Precisely reconstruct the decay vertices
Need very good detector with excellent
PID and Vertex
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Two B-factories were approved in 1990
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e+e– Asymmetric B-factories
Mt. Tsukuba
3.5 x 8 GeV
Belle
KEKB
~1 km in diameter
SLAC
3.1 x 9GeV
PEP-II
BaBar
stop Apr-2008
World highest luminosities
L = 2.1 (KEKB) & 1.2 (PEP-II) × 10 34 cm–2 s–1
775(Belle) & 465(BaBar) millions BB-pairs
Also tau- and charm- factories: 109 ττ / cc pairs
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PEP-II at SLAC
KEKB at KEK
9GeV (e–)  3.1GeV (e+)
designed luminosity:
3.5  1033cm-2s-1
achieved
10.2  1033cm-2s-1
(3 times larger!)
13 countries,
57 institutes,
~ 400 persons
Belle
BaBar
11 countries,
80 institutes,
~ 600 persons
8GeV (e–)  3.5GeV (e+)
designed luminosity:
10.0  1033cm-2s-1
achieved
21.2  1033cm-2s-1
(2 times larger!)
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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


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


for example: B  J/ KS
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 BJ/KS


Reconstruct BCP long lived
daughter:
B  J/ KS  ℓℓ 
Check the intermediate masses:
M(ℓℓ) ~ M(J/); M() ~ M(KS)

KS decay
vertex
Check the mass and ENERGY (a
big advantage of B-factories – we
know B energy = Ebeam in the CM
system) of J/KS combination
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BJ/KS
B charmonium KS
Use many other decays B to
charmonium (ηc, χc1, ψ’) + KS
to increase statistics:
• These final states have the
B-candidate CM energy
same (odd) CP eigenvalue
• They are equally theoretically
clean (no penguin uncertainties)
• They can be reconstructed with
the similar high purity
B-candidate CM momentum
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B  J/KL
Important to check if the asymmetry flip the sign for the opposite CP eigen value
Difficult to detect KL: cτ ~ 15m; only nuclear interactions.
Detect nuclear shower in iron: measure
direction but not momentum. Use known
J/KL = Ebeam energy to calculate momentum.
Purity 97 %
CP odd
Purity 59 %
CP even
M bc  E
*2
beam
P
*2
J /Ks
pK L information is poor
→ lower purity
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Step2: Flavor tagging
In ~99% of B0 decays: B0 and B0 are
distinguishable by their decay products
Semileptonic decays
B0
X ℓ+ ν
X ℓ– ν
B0
Hadronic decays
B0
DX
DX
B0
|Δt|
(ps)
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.
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Step 3: Vertex reconstruction
Use tracks from both BCP and Btag to find out z-coordinate of the two Bdecay vertices.
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Take into account detector effects
S = sin 2β = 0.65
A=0
0
B
_ tag
B0 tag
True
0
B
_ tag
B0 tag
Detector
smeared
t
1 
Pq  1, t   e 1  ( S sin mt  A cos mt )  R
4
Need to solve
(1  2w)
inverse problem
R : detector resolution
to get true value
w : 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…
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First Observation: CPV in B
2001
B0 tag
_
B0 tag
Events
1137
events
)
J/ψ K*0
31M BB-pairs
[PRL 87,091802(2001)]
sin 2β = 0.99 ± 0.14 ± 0.06
Asymmetry
Asymmetry
(
32M BB-pairs
[PRL 87,091801(2001)]
sin 2β = 0.59 ± 0.14 ± 0.05
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The recent Belle result
B0 tag
_
B0 tag
J/ψ KS
Nsig= 7482
J/ψ KL
Nsig= 6512
sin 2β = 0.642 ± 0.031 ± 0.017
A = 0.018 ± 0.021 ± 0.014
Phys.Rev.Lett., 98, 031802(2007)
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Compare CP odd and even final states
B0 tag
_
B0 tag
B0 tag
_
B0 tag
Asymmetry= –ξCP sin 2β sin(Δm Δt)
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
sin 2β = 0.687 ± 0.028 ± 0.012
A = 0.024 ± 0.020 ± 0.016
Phys.Rev. D79, 072009 (2009)
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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
b
c
c
d
d
d
J/ψ
π0
A VcbVcd*
 *
A VcbVcd
CP even
c
d
b
c
d
d
D+
D–
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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?
No,
Yes,because
becausewe
thehave
time
not
for yet
thisproved
lecturethat
is
KM
almost
anzatz
over.works
well.
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The CM+KM test
One way to test the Standard Model is to measure the 3 sides & 3 angles
and check if the triangles closes!
How to measure other UT angles?
 
VudV*ub
VcdVcb* 
  Arg 
* 
VudVub 
*
VudVub

 Arg 
* 
 VtdVtb 
α
How to measure UT sides?
VtdV*tb
γ
β
VcdV*cb
VcdVcb* 
  Arg 
* 
 VtdVtb 
experimentally
easy
sin2β:
b  cc s : Bd  J /Ks0 , Bd  J /KL0 , Bd  J /K *0
b  cc d : Bd  DD , Bd  DD * , Bd  D*D , Bd  D*D *
b  sss, dds : Bd   0 Ks0 , Bd  Ks0
sin2α:
b  udd : Bd   0 0 , Bd     , Bd      , Bd   0 0
sin2γ:
b  cs u : B  DK
hard
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