cp violation in b meson and belle
DESCRIPTION
A sack lunch talk at UIUC Mar. 9th, 2009.TRANSCRIPT
2009/03/09 Sack Lunch Talk @ UIUC 1
CP-violation in B mesons and Belle
Pinghan Chu
University of Illinois at Urbana-Champaign
Sack Lunch Talk @ UIUC
• CP-violation and B decays
• The Belle experiment and analysis
• Recent results of CP-violation in B decays
2009/03/09 Sack Lunch Talk @ UIUC 2
Matter and Antimatter Asymmetry
•Baryon asymmetry of universe
•The Sakharov conditions: three necessary
conditions that a baryon-generating interaction must satisfy to produce matter and antimatter at different rates.(JETP Lett. 5, 24-27, 1967)
•Baryon number B violation -> No experimental evidence
•Interactions out of thermal equilibrium -> The rate of a
reaction which generates baryon-asymmetry must be less than the
rate of expansion of the universe. The particles and antiparticles do
not achieve thermal equilibrium due to rapid expansion decreasing the occurrence of pair-annihilation.
••CPCP-- symmetry violationsymmetry violation -> Discovered in 1964
2009/03/09 Sack Lunch Talk @ UIUC 3
CP-Violation in K meson
•Discovery in neutral
Kaon decays by Cronin and Fitch (PRL 13, 138 ,1967)
•The observation of BR(KL����pp) ~ 2e-3
• KL and KS are the mass eigenstates.
•KL normally decays to ppp, with CP=-1. But pp is CP=+1
•Mass eigenstatesCP eigenstates.
2009/03/09 Sack Lunch Talk @ UIUC 4
CP-Violation in Standard Model - KM model
•Kobayashi and
Maskawa proposed three generations of quarks to produce one irreducible phase accounting for the CP
violation(Prog. Theor. Phys.
49, 652 ,1973)
•CKM matrix uses three mixing angles (q12, q23, q13) and one CP-violating phase
(d13)
2009/03/09 Sack Lunch Talk @ UIUC 5
CKM Matrix
13
13 13
13 13
-iδ
ud us ub 12 13 12 13 13
-iδ -iδ
CKM cd cs cb 12 13 12 23 13 12 23 12 23 13 23 13
iδ iδ
td ts tb 12 23 12 23 13 12 23 12 23 13 23 13
23
22
V V V c c s c s e
V V V V -s c -c s c e c c -s s c e s c
V V V s c -c c s e -c c -s c s e c c
λ1- λ Aλ (ρ-iη)
2
λ-λ 1- Aλ
2
≡ =
≈ , CKM
3 2
d' d
where s' =V s
b' bAλ (1-ρ-iη) -Aλ 1
Wolfenstein parameterization (PRL 51, 1945, 1983)
Cabibbo angle
•S12=sinq12
•c12=cosq12
•CP symmetry is broken by the complex phase appearing in the quark mixing matrix.
13
2
12 C
23
iδ 3
13
s =λ=sinθ 0.22
s Aλ
s e =Aλ (ρ iη)
≈
=
+
o o
12
o o
13
o o
23
13
θ =13.04 ±0.05
θ =0.201 ±0.011
θ =2.38 ±0.06
δ =68.8 ±4.6� �� �� �� �
2009/03/09 Sack Lunch Talk @ UIUC 6
The Unitary Triangle
, ,ππ ρπ ρρ→
⇓
B
2 ( )φ α
*
ij iki
* * *
ud ub cd cb td tb
The unitarity of the CKM matrix leads to:
We can have six relations.
The interesting relation
for B
V V =0, (j k)
V V +V V +V
decays i
V =0
s
≠∑
V udV
* ub V
td V*tb
VcdV*cb
→ ⇒0B D K ⇐ → sB J/ψK1( )φ β3( )φ γ
*
1 *
*
2 2*
* 2
3 *
1arg( ) arg( ) 22.0
1
1arg( ) arg( ) 89.2
(1 )( )2
arg( ) arg(( )(1 )) 68.92
cd cb
td tb
td tb
ud ub
ud ub
cd cb
V V
V V i
V V i
V Vi
V Vi
V V
φρ η
ρ ηφ
λρ η
λφ ρ η
= − = =− −
− −= − = − =
− +
= − = + − =
����
����
����
See later!
0.0009
0.0010
0.021
0.022
0.031
0.016
0.015
0.017
0.2257
0.814
0.135
0.349
A
λ
ρ
η
+
−
+
−
+
−
+
−
=
=
=
=
2009/03/09 Sack Lunch Talk @ UIUC 7
1. Direct CP-Violation
Bf
•CP violation arises from the difference between the magnitudes of a decay amplitude and its CP conjugate amplitude.
•The measurement is to compare the decay rate of B meson and its CP conjugate.
•Only possible source of CP asymmetry in charged meson
decays (for example B+zK+p0, discussed later).
( ) - ( )1,
( ) ( )
,
CP
A B
A B A B
B A =
A B B
f
f
f
f
f
fΓ → Γ →≠
Γ → + Γ
≡ ≡
→
H H
≠ Bf
2009/03/09 Sack Lunch Talk @ UIUC 8
02. B flavor sensitive mode(B )l Dν+ −→ →
•Apply to neutral B0
•Decays have to be flavor sensitive. For example,
•The CP violation is due to mixing of through box-diagrams
0Bl
l Dν− +→
0 0 0 0,
1
2
,
0 0
L H
0
L
L
HB =p B +q B B =p B -q
(
Considering the neutral meson B
If p=q= , B is CP odd and
and B ,
two mass eigenstates are B and B (Light and Heavy)
If the initial
B is CP even s
state i
ta
s B , th
te.)
B
e amp
H
0 0 0( ) ( ) ,
( ) , ( )
H LL H H L
Γ
0 0
Γ- t - t
-imt -imt2 2
m +
litude for B and B at
mqB (t) B B Γ Γ =Γ, m= and m=m -m
p 2
∆m ∆me e co
time t:
s( t) e e sin( t)2 2
g t g t
g t g t i
+ −
+ −
= − ≈ ∆
= =
0 0B -B
2009/03/09 Sack Lunch Talk @ UIUC 9
02. B flavor sensitive mode(B )l Dν+ −→ →0 0
0
0
0 0
0
,
( ) ( ) ( ) ,
( )
( ) - (
2 2
CP
2 2 -Γt
A B B B
q q B p BB A B λ and µ
p p A q A
1+ λ 1- λB (t) B (t) A e + cos(∆mt)-Im(λ)sin(∆
The decay ratio should
B
b
(t) B (A
mt)2
=
2
e
l l
l
l l
l
l D H l D H
l D H t g t g t
l D l D
l D
ν ν
ν
ν ν
ν
+ − + −
+ −
+ −
+ − + −
− +
≡ ≡
= − ≡ ≡
→ = =
Γ → Γ
Γ H
0 0
)( )
( ) ( )
2 2t) 1--(
B (t) B (
cos(∆mt)µ λ Im(µ)-Im(λ))sin(∆mt
t)
) 2l
l l
l D
l D l D
ν
ν ν
+ −
− + + −
→∝ −
Γ → + Γ →
However, since B<<A, the Acp is much suppressed by the second order box diagram
Decay through box diagram
Flavor sensitive
b b c→ →
b c→
2009/03/09 Sack Lunch Talk @ UIUC 10
0 0 0 0
.
, , ,
(
, 0 0
L H cp cp
CP violation comes from the interference between a decay B and another
decay with mixing B B The fin
qAB =p B +q B B =p B -q B
al st
A
ate must be a CP
qA
B
eigenstate.
Im
A BpA
CP
CP CP
f
f
f
f
f λ
λ
≡ ≡
→
→ →
≡
=
H H
( ) - ( )) 0,
( ) ( )
CP CP
CP CP
CP CPCP
CP CP
2
2 2
B(t) B(t) A =
pA B(t) B(t)
λ -1 2Im(λ )cos(∆mt)+ sin(
( and denote the parameters for direct and mixing-induced CP vio
∆mt)= cos(∆mt) sin(∆mt)λ +1 λ +1
lation.)
f f
f f
A S
f f
f f
A S
Γ → Γ →≠
Γ → + Γ →
= +
Bf
Bf
B B
Bf
≠
Bf
+ +
A A and q p≈ ≠In contrast to B<<A
0 0/3. B CP eigenstate(B )SJ Kψ→ →
2009/03/09 Sack Lunch Talk @ UIUC 11
0 0/An example, CP violation in B SJ Kψ→
0
0
0
0
0 0
/
/
1
/
/
/
.2 2
The decay B is the golden mode used for extraction. The direct CP asymmetry
of this decay is expected to be very small. A A and q p
ANow consider calculating
AS
S S
S
S
J J
K
K
K
J
J
K
J K
q
p
ψ
ψ
ψ ψ
ψ φ
λ =
→
= ≃≃≃≃
0
*/* * *
/ / / / *, /
*
/
,
/
*
*
/
( ) ( ) ( ) ,
,d
A
A
For mixing in the B and K
A
-K mixing,
AA
S
J Kq cb csJ K cb cs J K qb qs J K cb cs J K
q u c t J K cb cs
J K
J KKJ
tb td cs cd
tb td K
K
V VV V T V V P V V T
V V
V V V Vq
q
q
p V
q
p
V
p
p
ψ
ψ ψ ψ ψ
ψ
ψ
ψψ
=
=
= + ≈ =
= =
∑
0 0
*
* * *
1 1* * */ 1/sexp( 2 ) Im in(2 )sin(( ) sin( ) )2 , A
S S
cs cd
tb td cs cd cb cs
J K J K
tb td cs cd cb cs
CP
V V
V V V V V Vi
V V V V Vmt
Vψ ψλ φφ λ φ
⇒ = = − − ⇒ =
= ∆
Box diagram
Amplitude ratio from Tree diagram
•Use similar argument to get other angles.Penguin diagram is very small here. No direct CP contribution!
0 0(involves K -K mixing)
2009/03/09 Sack Lunch Talk @ UIUC 12
B factories – Belle and BaBar
2009/03/09 Sack Lunch Talk @ UIUC 13
Analysis Technique (Belle)
•B candidates are identified by
•Beam-constrained mass
•Energy difference
•Dominated background:
•Other background from B decays are examined by Monte Carlo simulations.
2 * 2
bc beam BM = E -(P )
*
B beam∆E=E -E**
BE and P are the reconstructed B
energy and momentum in the CM frame.
B
+ -continuum e e qq processes,
and suppressed by event shapes.
→
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-0.2 -0.1 0 0.1 0.2
∆ E
0
0.2
0.4
0.6
0.8
1
1.2
1.4
5.2 5.25 5.3
Mbc
Argus
function 5.279
GeV/c2
Continuum background
2009/03/09 Sack Lunch Talk @ UIUC 14
Background Suppression
Spherical BB events
Jet-like qq events
+ -
The B decays signal events are
nearly at rest in the (4S)
frame. The daughter particles are
distribu
The dominant background
is from e e qq (q=u,d,s,c
The conti
ted sp
nuum e
)
v
herica
ents a
l
re
of i
l .
y
h
•
ϒ
→
•
•
gh momentum jet-like
and distributing near the
axis of the e e (beam
Event shape variables are used
to reject most of ba
pi
ckg
pe)
ro d.
.
un
+ −
•
2009/03/09 Sack Lunch Talk @ UIUC 15
Event Shape VariablesModified Fox-Wolfram moments•Event shape variables are
correlated with each other.
•Project these variables to 1-dimension by a Fisher Discriminator. (Ann. Eugen. 7
179, 1936)
so oo oo so oo
1 2 2 2 3 3 4 4 5 4
6 thrust 7
F=α R +α R +α R +α R +α R
+α cosθ +α S⊥
⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅
2009/03/09 Sack Lunch Talk @ UIUC 16
Likelihood Ratio Fit
•Use a likelihood ratio to combine
all the information
•2-D likelihood fit for signal determination
+ =
sig
B
sig bkg
ff=Fisher×Cosθ , LR=
f +f
Apply a cut to suppress background
0
0.2
0.4
0.6
0.8
1
1.2
1.4
5.2 5.25 5.3
Mbc
0
0.2
0.4
0.6
0.8 1
1.2
1.4
-0.2
-0.1
0 0
.1 0
.2
∆ E
independent
2009/03/09 Sack Lunch Talk @ UIUC 17
(4 ) .B mesons are produced via the decay chain of e e BB
Only one B meson and one B meson at the same time.
One of the B mesons is tagged as a B by a semileptonic decay B X at
1.
time t ,
anoth
2.
3. l
S
l
+ −
+
→ ϒ →
→
22 2 2( )0 0 1 1[ [ ]( ) ( )] [ (1 ) (1 )cos(
2 2
CPer should be a B at time t and its final state is .
The time difference between these two B is t=t and the decay 4 rate.
l fP t t
l CP f SL f CP
l
l
CP
f
f
t
B B l X t f t e A A m tλ λ− ++Γ → ∝ + −
∆
− ∆ ∆
−
) Im( )sin( )]CP
m tλ+ ∆ ∆
Measurement of Time dependent CP asymmetry
2009/03/09 Sack Lunch Talk @ UIUC 18
Measurement of sin2f1 of J/yK0S
( ) - ( )
( ) ( )
CP CPCP
CP CP
B(t) B(t)A = = cos(∆mt) sin(∆mt)
B(t) B(t)
f fA S
f f
Γ → Γ →+
Γ → + Γ →
0/1 CP
indicates direct CP violation
=0, =sin2 i
,
f S
A
A S f J Kφ ψ=
Belle PRL 98, 031802 2007
•CP violation in B system is well
established within the Standard Model.
CPA
2009/03/09 Sack Lunch Talk @ UIUC 19
Average of sin2f1 from all experiments
sin(2β) ≡ sin(2φ1)
-2 -1 0 1 2 3
BaBararXiv:0808.1903
0.69 ± 0.03 ± 0.01
Belle J/ψ K0
PRL 98 (2007) 0318020.64 ± 0.03 ± 0.02
Belle ψ(2S) KSPRD 77 (2008) 091103(R)
0.72 ± 0.09 ± 0.03
ALEPHPLB 492, 259 (2000)
0.84 +-01..8024 ± 0.16
OPALEPJ C5, 379 (1998)
3.20 +-12..8000 ± 0.50
CDFPRD 61, 072005 (2000)
0.79 +-00..4414
AverageHFAG
0.67 ± 0.02
H F A GH F A GICHEP 2008
PRELIMINARY
ccs
ccs
S =0.672 ±
HFA
0.024
A =0.005
G
±
(b ccs)
0.
:
019
→
Consists of direct CPV
oSin(44 )=0.69SM prediction:
consistent
2009/03/09 Sack Lunch Talk @ UIUC 20
Evident of direct CP:B Kπ Decays→
±
± 0
0 - + 0 + -
0 - + 0 + -K π
- - 0 + + 0
- - 0 + + 0K π
N(B K π )-N(B K π )A =
N(B K π )+N(B K π )
=-0.094±0.018±0.008
N(B K π )-N(B K π )A =
N(B K π )+N(B K π )
=0.07±0.03±0.01
→ →
→ →
→ →
→ →
∓∓∓∓
(Belle, Nature 452, 06827, 2008)
•A simple analysis. Just count the number of B mesons.
•The number difference shows the direct CP violation. The time dependent term (indirect CP-violation) will be time-integrated.
•Good agreement with other experiments. (BaBar, CDF. etc)
0B0B
-B +B
2009/03/09 Sack Lunch Talk @ UIUC 21
B Kπ Decays→
Penguin:suppressed
by the loop(2nd order)
b s→
ub
Tree:suppressed
by small V
b u→
•Sizeable direct CP asymmetry could be generated by the interference (next slide) between tree and penguin amplitudes.
•Sensitive to the f3 angle
0
0
Similar direct CP violation expected for B and
B decays.
K
K
π
π
± ±
±
→
→ ∓∓∓∓
iiii
3( )CPA T P sinδ sinB Kπ φ→ ∝
(since they have similar diagrams.)
2009/03/09 Sack Lunch Talk @ UIUC 22
Direct CP Violation•Direct CP violation may arise from the interference between two amplitudes, like tree diagram and penguin diagram.
•Assume A is tree diagram and B is penguin diagram.
iδ i
A= A
B= B e e φ iδ -i
A= A
B= B e e φ
CP transformation:
weak phase: -
strong phase:
φ φ
δ δ
→
→
CP
A=A
A+B
A+B
δ•Amplitude sum:
δ-φδ+φ
CP
A+B A+B
A A B sinδsinφ
≠
∝
•Two interfered amplitudes with similar order of magnitude.
•Non-vanished strong and weak phase
The difference phase between A+B and A+B induces direct CP violation.
2009/03/09 Sack Lunch Talk @ UIUC 23
± 0
±
± 0
±
0 - + 0 + -
0 - + 0 + -K π
- - 0 + + 0
- - 0 + + 0
K K π
π
π
K
N(B K π )-N(B K π )A =
N(B K π )+N(B K π )
=-0.094±0.018±0.008
N(B K π )-N(B K π )A =
N(B K π )+N(B K π )
=0.07±0.0
∆A=A -A =+0.164±0.03
3± 0
7
0. 1
→ →
→ →
→ →
→ →
∓∓∓∓
∓∓∓∓
•The large deviation in direct CP violation between charged and neutral B meson decays could be an indication of new sources of CP violation?
Hint of New Physics
0 + - + + 0
cp
Both B K and B K have similar diagrams,
but have different A sign and amplitude.
π π→ →iiii
Similar diagram
2009/03/09 Sack Lunch Talk @ UIUC 24
Summary
•The mechanism of CP violation is well established within the framework of Standard Model. But it is still too small to account for the matter-dominated universe.
•A large difference in direct CP violation for
is firmly established at Belle.
•The large deviation could be an indication of new sources of CP violation in b to s penguin loops.
•More data are needed in other modes (e.g. ). The precise measurement of mixing-induced and direct CP violation asymmetries is a promising approach to search for new physics.
0 0 0B K π→
0 + -B K π→
and B K π± ±→ ∓∓∓∓
2009/03/09 Sack Lunch Talk @ UIUC 25
CP-Violation in B meson
0 0 0 0,L H
L,H L,
0
L
H
0
H
B =p B +q B B =p B -q B
Considering the neutral meson B and B , two mass eigenstates are B and B (Light and Heavy)
The
p pi i( - )( )=(m - Γ )( )
±q ±
eigenvalue equation is
( is mass matrix and
q2 2
is deM Γ
M Γ
0 0 0
H LH,L H,L H,L L H H L
Γ- t
-imt2
H
L L H H
L
m +mA (t)=A (0)exp(-(Γ/2+im )t), where
cay matrix.)
The
Γ Γ =Γ, m= and m=m -m2
∆m q ∆mB (t) (A (
amplitude for the states B and B
t) B +A (t) B )=e e cos( t) B i sin( t) B2 p
at time t
h
2
:
T
≈ ∆
= +
0 0
,
( )
0 0 0
cp cp c
2 22
Γ
p
2 - t
qAe decays of neutral B into a CP eigenstate and A B A B
1+ λ 1- λB (t) B (t) A e + cos(∆mt)-Im(λ)sin(∆mt
and p
2 2
A
)CP CP
f f f
f f
λ≡ ≡ ≡
→ = =
H
H H
Γ
It is related to sin2f1 and indirect CP-violation (showed later) due to CP phase.
2009/03/09 Sack Lunch Talk @ UIUC 26
Proposal of B factory
•A. I. Sanda proposed a specific experiments on
B mesons. (PRL 45, 952, 1980, Nucl. Phys. B 193, 85 1981)
•The idea, proposed by Pier Oddone, that these
experiments could be performed by colliding two beams of different energies, one of electrons and one of positrons.
•The construction of new accelerators at KEK and SLAC. In 2002, both Belle (PR D 66, 071102, 2002)
and BaBar (PRL 89, 201802, 2002) reported the first observation of a KM asymmetry in a B-meson
decay.
2009/03/09 Sack Lunch Talk @ UIUC 27
Appendix
•Argus function: ARGUS Collaboration, H. Albrecht et al., Phys. Lett. B 241,
278(1990). The ARGUS function is presented as
(a and b are constants that are determined from the data)• Thrust Angle CosqT (S. Brandt, Ch. Peyrou, R. Sosnowski and A. Wroblewski,
Phys. Lett. 12 (1964) 57 )
•Separate the particles tracks into two groups. One group is a B meson candidate and the other is the other B meson or jet background.•Angle between two groups is the thrust angle.•Random distribution for a real B•Close to +-1 for jet events.
2 2
beam beamax 1-(x/E ) exp(b(1-(x/E ) ))
1max
ii
ii
n P
T=P
n vector is the maximum of all vectors in the group.
n =
⋅∑
∑
��������
����
����
2009/03/09 Sack Lunch Talk @ UIUC 28
Appendix
•Sphericity (J.D. Bjorken and S.J. Brodsky, PR . D1 (1970) 1416)•Define a specific direction of the signal particle’s daughter in the CM frame. •Sum over the transverse momentum with respect to the specified direction and divided it with overall momentum
•Fox-Wolfram moments (G.C. Fox and S. Wolfram, Nucl. Phys. B149 (1979) 413 )
,2,
(cos )
: Legendre polynomials functions
E is the total visible energy of the event.
i j
l l i j
i j tot
l
tot
p pH P
E
P
θ=∑� �� �� �� �
ii
ii
Pt
S=P
∑
∑
����
����
2009/03/09 Sack Lunch Talk @ UIUC 29
Appendix
•Super Fox-Wolfram moments (R. Enomoto, Belle lectures 1999 )•Extension of Fox-Wolfram moments
SO
l i j l i,ji,j
OO
l j k l j,ki,j
SO OOSO OOl ll lSO OO
0
i
j
0
k
p : the momentum of candidate B daughters
p and p : the momentum of other
par
H = p p P(cosθ )
H = p p P(cosθ
ticles except the can
)
H HR =
dida
,R =
te B meson.
H H
∑
∑
� �� �� �� �
� �� �� �� �
2009/03/09 Sack Lunch Talk @ UIUC 30
Appendix
•Cos qB
•The angle between the B meson flight direction and beam direction in the rest frame.•Not correlated with previous parameters.•Due to quantum mechanics, the distribution for B is peak around zero. •The background is randomly distributed.
2009/03/09 Sack Lunch Talk @ UIUC 31
The three categories of CP violation:B-B mixing
Bf ≠ B
f
0 (*)
0 0
CP violation appear in neutral meson mixing.
An example is given in semileptonic neutral
meson decays, such as B decays.
The B B mixing is through the second order
box diagrams and its effec
ll Dν− +→
0 0
0
0 0 0
0
0
( ) - ( )1,
( )
,
( )
L H
CP
q B B
t is very sm
B =p B +q B B =
all.
A =
q
B
p
B
B - B
p
l X l X
l X l X
− +
− +
Γ → Γ →≠
Γ → + Γ →
B B