CP violation in B → ππ, ρπ
Hiro Sagawa (KEK)
FLAVOR PHYSICS & CP VIOLATION,
Ecole Polytechnique, Paris, France
on June 3-6, 2003
1
Outline
• CP asymmetries in B0 → π+π− decay
– CP violating parameters : Sππ and Aππ(= − Cππ)
Belle
BaBar
• Belle : hep-ex/0301032 ( to be appeared in PRD )
• BaBar : Phys. Rev. Lett. 281802
– Bound on Penguin Pollution from isospin
relation ( B→π+π−, π−π0 , and π0π0 decays )
• CP asymmetries in B0 → ρπ decay (π+π−π0)
– Quasi-two-body analysis
• BaBar : update at Recontres de Moriond 2003
2
Introduction
3
Introduction
Quark mixing is described by the 3x3 Cabibbo-Kobayashi-Maskawa
(CKM) matrix.
(Wolfenstein parametrization)
Vud
V =  Vcd

V
 td
Vus
Vcs
Vts
 1− 1 λ 2
Vub  
2
Vcb  = 
−λ
 
Vtb   Aλ 3 (1− ρ − iη )

λ
1
1− λ 2
2
− Aλ 2
Aλ 3 ( ρ − iη ) 
Aλ 2
1

 + O (λ 4 )



One irreducible complex phase
derives CP violation .
Unitarity triangle
φ2(α)
B → ππ, ρπ
b → uud
VudVub* + VcdVcb* + VtdVtb* = 0
φ3 (γ)
φ1 (β)
4
CP violation in mixing and decay
B
0
Af
mixing
B
0
decay
Af
CP
B
CP
fCP
0
Af
≠ mixing
B
0
decay
Af
CP
CP
fCP
λf
CP
q Af
= ⋅
p Af
CP
CP
CP violation in neutral B meson results from
the interference between decays with and without mixing.
5
Time evolution in B0 → π+π–
Pππ (∆t ) =
q
e
−|∆t |/ τ B0
4τ Β
[1 + q ⋅ {Sππ sin(∆md ∆t )
0
+ Aππ cos(∆md ∆t )}]
Sππ
q= +1 for B0 tag
−1 for B0 tag
2 Im λππ
=
,
2
1+ | λππ |
∆t=∆z/(βγc)
| λππ |2 −1
Aππ =
= −Cππ
2
| λππ | +1
(Belle)
6
CP violation in B0 → π+π–
mixing
λππ
*
tb
b
B0
d
*
ud
V Vtd V Vub
=
*
*
VtbVtd VudVub
d
t B0
t
b
Tree(T) decay
W+
b
B0
bd
Aππ = 0
b
B0
t B0
g
d
Tree + Penguin
Tree only
λππ = e 2 iφ
u +
π
d
u π−
d
Penguin(P)
2
1+ | P / T | e iδ e iγ
,
( φ2 = α )
λππ = e
iδ − iγ
1+ | P / T | e e
Aππ ∝ sin(δ ) → direct CP violation, ( Aππ = −Cππ )
d π+
u
u π−
d
2 iφ 2
7
Sππ = sin(2φ 2 ) Sππ = 1 − Cππ sin(2φ2eff ) → related to φ2 thru. isospin analysis
2
Analysis Procedure
8
Data sample
Event
Selection
Flavor
tagging
Continuum
suppression
Vertex
and ∆t
π+π−, ρπ(π+π−π0 ) : charmless B decays
BR ~ 10-5-10-6 : rare decays
world average BR(π +π − ) = 4.8 ± 0.5
(10-6)
BR( ρ +π − ) = 25.4 ± 4.2
BR( ρ 0π 0 ) < 5.3
(HFAG table)
Need a lot of data
Data sample
π+π−
Belle 85 million BB pairs
BaBar 88 million BB pairs
ρπ
BaBar 89 million BB pairs
9
Kinematics: Reconstruction of CP side
Event
Selection
Flavor
tagging
Continuum
suppression
Beam − constrained mass
*2
− p*B2
M bc ≡ Ebeam
Energy difference
*
∆E ≡ E B* − Ebeam
Kinematics
Signal MC
*
Ebe
am : cms beam energy
E B* : cms energy of B candidate
p*B : cms momentum of B candidate
Signal MC
K +π − π +π −
Vertex
and ∆t
qq background
Mbc(GeV/c2)
qq background
∆E(GeV)
10
Good K/π separation
Event
Selection
Belle
ACC(Aerogel Cherenkov Counter)
+ CDC dE/dx
Threshold type
Flavor
tagging
Continuum
suppression
Vertex
and ∆t
For the tracks in the momentum
range that covers
the B0 → π+π− signal,
π effciency = 91%
10.3% of kaons are misidentified as pions.
10.0 ±0.2% from K−
10.6 ±0.2% from K+
The effect of asymmetry of this misidentification
is negligible for the measurement of Aππ and Sππ.
11
Good K/π separation
Event
Selection
Flavor
tagging
Continuum
suppression
Vertex
and ∆t
BaBar
DIRC
(Detector of Internally Reflected Cherenkov light)
π/K separation
8σ θ at 2 GeV / c
C
2.5σ θ at 4 GeV / c
C
Cherenkov angle (θ C+ , θ C−):
is used separately as PDF for maximum likelihood fit.
θ C+ , θ C− : Cherenkov angle for positively
and negatively charged tracks
12
Flavor tagging
Event
Selection
Flavor
tagging
Use flavor specific
properties and correlations
Continuum
suppression
Vertex
and ∆t
13
Continuum background
Event
Selection
use kinematics and topology to separate
spherical B decays from jetty qq events
Flavor
tagging
Continuum
suppression
Vertex
and ∆t
14
Continuum suppression
B0 → π+π− for the case of Belle
Cut on a likelihood ratio (LR) that combines
an event topology variable (SFW) and
B flight direction (cosθB )
SFW: Super Fox Wolfram
Fisher discriminant using modified Fox-Wolfram moments
qq
Signal
Signal
qq
Signal
qq
SFW
cosθB
LR
15
Vertex reconstruction
Event
Selection
Flavor
tagging
Continuum
suppression
Vertex
and ∆t
Example vertices
• The same algorithm as
that used for sin2φ1
meas.
• Resolution mostly
determined by the tagside vtx.
B0 lifetime of
control sample
1.551±0.018(stat) ps
(PDG02: 1.542±0.016 ps)
Time resolution (rms)
1.43ps
16
CP asymmetries in B0 → π+π−
17
Event reconstruction (Belle)
Beam-constrained mass (Mbc)
(in ∆E signal region)
energy difference (∆E)
(in Mbc signal region)
B-candidate energy – beam energy
(CMS)
π+ π−
Kπ
Kπ
π+ π−
qq continuum
other rare B decays
18
(a) q = +1
40
B0 tag
Large CP Violation is seen !
Total
π+–π−
qq + Kπ
Events/(1.25ps)
60
20
0
0
-5
π+π− yield
40
60
40
20
5
∆t (ps)
0
(b) q = −1
B0 tag
0
-5
∆t (ps)
q = +1
q = −1
(c)
30
Total
+ −
π –π
qq + Kπ
5
LR>0.825
sin term
20
10
0
Asymmetry
Events/(1.25ps)
Fit results
(Belle)
1
+ −
∆t (ps)
B→π π
cos term
0
5
0
-1
sin term
(d)
-5
∆t (ps)
Aππ = +0.77 ± 0.27( stat ) ± 0.08( syst
) = −Cππ
Sππ = −1.23 ± 0.41( stat )
+0.08
−0.07
( syst )
hep-ex/0301032
accepted for
Phys. Rev. D
19
Confidence Regions (Belle)
Feldman-Cousins frequentist approach
CL for CP conservation
3.4σ
1) Evidence for CP violation
in B0 → π+π–
2) “Indication” of direct CP Violation (Aππ>0)
20
Constraints on the CKM angle φ2(α)
Sππ = [sin 2φ 2 + 2 | P / T | sin(φ1 − φ 2 ) cos δ − | P / T |2 sin 2φ1 ]/ Rππ ,
Aππ = −[2 | P / T | sin(φ1 + φ 2 )sin δ ]/ Rππ ,
Rππ = 1 − 2 | P / T | cos(φ1 + φ 2 ) cos δ + | P / T |2
|P/T| 0.15-0.45 (representative)
φ1
φ2
δ
Theory ~0.3
23.5deg
φ2
(=β)
(Belle & BaBar combined)
(=α)
|P/T|=0.45
strong phase difference
78o<φ2<152o
(95.5%C.L.)
δ ≡ δ P − δT
δ<0 favored
21
Constraint on ρ-η
PDG2002 + ( Belle φ1 & φ2 )
φ2=78o
φ2=118o
φ3
φ2
φ1
φ2=152o
Belle’s results
of φ1 and φ2
are consistent
with other
measurements.
22
mES and ∆E (BaBar)
Phys Rev Lett 89, 281802 (2002)
mES
∆E
ππ-enhanced events
q q + K π background
mES
∆E
Kπ-enhanced events
q q + ππ background
23
CP asymmetry result (BaBar)
0
Asym (∆t ) =
0
N ( Btag
) − N ( B tag )
0
tag
N (B ) + N (B )
0
tag
= Sππ sin(∆md ∆t ) − Cππ cos(∆md ∆t )
(Cππ = − Aππ )
Sππ = 0.02 ± 0.34 ± 0.05
Cππ = −0.30 ± 0.25 ± 0.04
Asymmetry
Events/1ps
Aππ / 2 ps
Events
/ 1 ps
Phys Rev Lett 89, 281802 (2002)
Projection in signal ππ-enhanced events
20
(a)
0
20
(b)
B00 tags
B tags
B 0tags
qq + K π
0
B tag
0
0.5
(c)
-0.5
-5
(Aππ=+0.30)
-2.5
0
2.5
5
(ps))
∆t ∆t
( ps
24
Fit results (Belle&BaBar)
The difference is at
2.2σ level.
It’s early to say
conclusively for
the difference.
&
25
Comparison with predictions
Rc lines = 0.18( pink ),
0.23( purple ),
PQCD
0.30(blue ),
0.45( green).
Purple regions : PQCD favored
Region for each φ2 (60o, 100o,
150o)
Aππ Belle
hep-ex/0301032
(%)
77 ± 27 ± 8
BaBar
PQCD
PRL,281802 PRD67,054009
(2002)
(2003)
30 ± 25 ± 4
16 ~ 30
QCDF
NPB606,245
(2001)
−6 ± 12
26
A bound on θ=|φ2eff-φ2|
with an upper limit on π0π0
BRs : π +π − ,π +π 0 ,π 0π 0 (limit)
2
CP asymmetries : Aππ , Sππ ( = 1 − Aππ
sin 2(φ 2 + θ ))
(φ 2 = −α , Aππ = −Cππ )
can constrain on φ2 using isospin relation.
1 +−
A
2
1 +−
A
2
A (A )
A00
A =A
+−
+−
2θ
+0
Amplitude for
−0
A
00
B 0 ( B ) → π 0π 0
−0
B + ( B − ) → π +π 0 (π −π 0 )
A (A )
ij
B ( B ) → π +π −
00
A00 ( A )
+0
0
0
A =e
0
2φ3
A
ij
27
A bound on θ=|φ2eff-φ2|
• Gronau/London/Sinha/Sinha bound (PL B514, 315 (2001))
B
+−
+0
+B −B
)
00 2
− B +− B +0
2
B +− B +0 1 − Aππ
Average branching ratios
for π +π − , π +π 0 , π 0π 0
B + − = (4.8 ± 0.5) × 10−6 ,
| θ |< 48o @90%C .L.
θ(deg)
(
cos 2θ ≥
1
2
B 00 (limit) = 3.6 × 10−6
B +0 = (5.6 ± 0.9) × 10−6 ,
B 00 =< 3.6 × 10−6 , HFAV table
Aππ = 0.48 ± 0.19.
00
B /B
+−
28
CP asymmetries in B0 → ρπ
29
CP-Violating Asymmetries in
B0 → ρ+π−, ρ+Κ−
• Principle: measure α directly, even with penguins using
full Dalitz-plot analysis
– difficulty
• Combinatorics and lower efficiency in three-body topology with π0
• Large backgrounds from misreconstructed signal events and other B
decays
Need large statistics to extract α cleanly
• “quasi-two-body” analysis:
– Select the ρ-dominated region of the π+π−π0 /K+π−π0 Dalitz
plane (Rejected when 0.4 < m (π +π 0 ), m (π −π 0 ) < 1.3GeV / c 2 .)
– Suppression of qq backgrounds
– Simultaneous fit for ρ+π− and ρ+Κ−
30
CP Violation Study in B0 →ρπ
decay
Final
state π+π−π0: not a CP eigenstate
Basically there are0 four tree amplitudes:
B → ρ π +B → ρ π
0
+
0
−
−
B →ρ π
+
−
B 0 → ρ −π +
+
and B → ρ π
0
−
+
0
+ B → ρ +π
B 0 → ρ +π −
≠
0
B → ρ −π +
≠
31
−
B0 →ρπ Time-dependence
Decay rate distribution
( ± for ρ charge )
32
Time-integrated
asymmetry:
+ −
− +
ρh
ACP
=
N (ρ h ) − N (ρ h )
N (ρ +h− ) + N (ρ −h+ )
Time evolution includes:
( S ρh + Q∆S ρh ) sin( ∆md ∆t )
(C ρh + Q∆C ρh ) cos(∆md ∆t )
Q is the ρ charge
direct CP violation → ACP and C = 0
indirect CP violation → S = 0
∆C and ∆S are insensitive to CP violation
ρK is selfC ρK = 0, ∆ C ρK
tagging:
Fit for:
ρπ
= − 1, S ρ K = 0 , ∆ S ρ K = 0
ρK
ACP , ACP , C ρπ , ∆C ρπ , S ρπ , ∆S ρπ
33
B0 →ρπ/ρK (BaBar)
Yields and Charge Asymmetries
The results with 89 million BB
pairs @2003 Moriond EW
Preliminary
BR of ρπ and ρK
B0 →ρπ
B0 →ρK
B ( B → ρ ±π m ) = (22.6 ± 1.8 ± 2.2) × 10−6
−6
B ( B → ρ ± K m ) = (7.3+−1.3
±
1.3)
×
10
1.2
Charge asymmetry of ρπ and ρK
Aρ K = +0.28 ± 0.17 ± 0.08
Aρπ = −0.18 ± 0.08 ± 0.03
qq
qq + B − related
34
B0 →ρπ/ρK (BaBar) : ∆t
distributions
B+continuum
background
B-related background
2σ (or more)
from zero
35
Direct CP violation in
0
A+ − ≡
0
N ( B ρπ → ρ +π − ) − N ( Bρπ
→ ρ −π + )
0
N ( B ρπ → ρ π ) + N ( Bρπ → ρ π )
+
−
0
−
+
=
0
A−+ ≡
0
→ ρ +π − )
N ( B ρπ → ρ −π + ) − N ( Bρπ
0
N ( B ρπ → ρ π ) + N ( Bρπ → ρ π )
−
+
A+ − = −0.62+−0.24
0.28 ± 0.06
+0.16
−0.17
A−+ = −0.11
0
+
−
=
0
B
→ ρπ
ρπ
ρπ
− C ρπ − ACP
ACP
⋅ ∆C ρπ
ρπ
⋅ C ρπ
1 − ∆C ρπ − ACP
ρπ
ρπ
⋅ ∆C ρπ
+ C ρπ + ACP
ACP
ρπ
⋅ C ρπ
1 + ∆C ρπ + ACP
A−+
(0,0)
± 0.04
A+−
36
Comparison with predictions
BaBar:
Aρπ = -0.18 ± 0.08 ± 0.03
Cρπ = +0.36 ± 0.15 ± 0.04
∆Cρπ = +0.28 ± 0.19 ± 0.04
QCDF:
w/ Charming
Penguin(CP):
Aρπ = -0.015 Sρπ = -0.015
Cρπ = 0.019 Cρπ = 0.092
∆Cρπ = 0.250 ∆Cρπ = 0.228
Phys. Rev. D67,094019,
2003
37
Prospect (B0 →π+π-)
Sππ = −1.23 ± 0.42 ( Belle )
Aππ = +0.30 ± 0.25 ( BaBar )
Sππ = +0.02 ± 0.34 ( BaBar )
δSππ
δAππ
Aππ = +0.77 ± 0.28 ( Belle )
L(fb−1)
L(fb−1)
38
Prospect (B0 →ρπ)
C ρπ = +0.36 ± 0.18
δCρπ
δAρπ
Aρπ = −0.18 ± 0.08
L(fb-1)
L(fb-1)
δSρπ
S ρπ = +0.19 ± 0.24
L(fb-1)
39
Summary
• Measurement of CP asymmetries in B0 → π+π−
2σ lines
Cππ (= − Aππ )
Sππ
Belle − 0.77 ± 0.27 ± 0.08 − 1.23 ± 0.41+−0.08
0.07
BaBar − 0.30 ± 0.25 ± 0.04 + 0.02 ± 0.34 ± 0.05
• Still early to say conclusively for the difference.
• Measurement of CP asymmetries in B0 → ρπ
– Quasi-two-body analysis was performed by BaBar.
– Hint of Direct CPV ?
A−+ = −0.62−+0.24
0.28 ± 0.06
A+− = −0.11−+0.16
0.17 ± 0.04
(0,0)
40
end
41