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WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
Hadronic rare B-decaysSanjay K Swain
Belle collaboration
•B- -> DcpK(*)-
•B- -> D(KS+-)K- Dalitz analysis•B -> •B -> K(*)
•Conclusion
OutlineV ud
V ub
VcdVcb
Vtd V
tb*
*
*
3()
2()
1()
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
Using B-DCPK- mode (GLW method)•B- DCPK- where DCP = (D0 D0 )
•A(B-DCPK-) |A(B-D0K-)|+|A(B-D0K-)|ei ei
•A(B+DCPK+) |A(B+D0K+)|+|A(B+D0K+)|e-i ei
When D0 D0
CP-even states (D1): K+K- , + - CP-odd states (D2): KS 0, KS , KS , KS , KS ’
2
1 ¯
3
3
commonfinal state
¯
¯
PLB 253(1991)483PLB 265(1991)172
}Color-favored
b
uu
cu
K
DB
-
-
--
-
o }uu
c
K
D
B-
--
-
Color-suppressed
Vcb
Vub-
s
}s
o}3=arg(Vub
) u
-
*b
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
GLW method cont…..
3
A(B+ D0K+)A(B- D0K-)
A(B+ D0K+)
A(B- D0K-)
A(B+ DCPK+)
A(B- DCP
K-)
=
Reconstruct the two triangles 3
—
-3
One can measure 3 even if =0( without strong phase)
Non vanishing strong phase ( 0) Direct CP violation
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
GLW method cont…
Solution: One can instead measure
R1,2 = R /RDCP Dnon-CP
= 1 + r2 2r cos()cos(3)
where R DCP B (B- D1,2K-) + C.C
B (B- D1,2-) + C.C=
A1,2 = B (B- D1,2K-) B (B+ D1,2K+)
B (B- D1,2K-)
-
+
2r sin()sin(3)
3 independent measurements 3 unknowns r , , 3 (solve it)
But A1R1 = - A2R2
1 + r2 2r cos()cos(3)B (B+ D1,2K+)
=
Amp(B- D0K-) 0.1 x Amp(B- D0K-)
Also B- D0[K+-]K- has same final state as B- D0[K+-]K- (DCSD)
But
_
_
r = |BKD|/|BKD|_
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
Kinematics to identify signal•Candidates are identified by two kinematic variables
Beam constrained mass (Mbc)= (E2beam-pB
2) Energy difference ( E) = EB - Ebeam
•But @(4S) peak energy: 24% BB 76% Continuum (qq, q =u, d, c or s)
KEKB operates here
–
We use continuum suppression variables -> LR( CosB , Fisher)
-
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
Results (78 fb-1) B D B D K
Flavorspecific
CPeven
CP odd
6052 88
683.432.8
648.331
347.521
47.38.9
52.49
134.414.7
15.66.4
6.35.0
E E
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
Double ratios(R1,2) and asymmetries(A1,2)
R1 = 1.21 0.25 0.14 and R2 = 1.41 0.27 0.15
A0 = 0.04 0.06(stat) 0.03 (sys) ( non-CP mode)
A1 = +0.06 0.19(stat) 0.04 (sys) ( CP + mode)
A2 = - 0.18 0.17 (stat) 0.05(sys) ( CP – mode)
We cannot constrain 3 with these statistics.
25.0 6.5 22.1 6.1
20.5 5.6 29.9 6.5
EE
CPeven
CPodd
( r2 = 0.31 ± 0.21 , just 1.5 away from physical boundary)
r = |BKD|/|BKD|_
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
B-D0K*- mode (90 fb-1 data)
Signal MCdata
Works exactly same way as B- -> DCPK- decayLook for CP asymmetries and double ratios -> constraint 3
169.5±15.4
16
Flavor specific modes
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
B-DCPK*- mode
Can not constraint 3 with this statistics -> need more data
CP asymmetries : A1 = -0.02 ± 0.33(stat) ± 0.07(sys)
A2 = 0.19± 0.50(stat) ± 0.04(sys)
13.1 ± 4.3
4.3
7.2 ± 3.6
2.4
CP-even
CP-odd
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
B±D(KS +-)K± Dalitz analysis(140 fb-1)
In case of B- DCPK- where DCP =(D0 D0 ) both D0 and D0 decays to CP eigenstates ( K+K-..)
One can write the total amplitude for B+ DK+ :
Amp(B+ ->DK+) = f(m+2,m-
2 ) + r. ei(
3 + ) f(m-
2 , m+2 )
(B- decay amplitude can be written similar way : -> ,3 -> -3)
m+2(m-
2) -> squared of invariant mass of KS+
(-)combinations f -> complex amplitude of D0-> KS+- decay
f( m+2,m-
2) = ak. ei Ak(m+2,m-
2) + b ei
-> both 2-body resonances and non-res component
--
D0K0
D0K0 D0KS
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
Suppose all D0K0 decays are via K*
D0K*
KS
D0K*
KS
M(KS )2
M(KS )2 Dalitz plot
interference
Simple example
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
D0KS
K*
KS
KS
KSf2
reality is more complex(& better)
many amplitudes &strong phases(13)lots of interference
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
Fit results for D ->KS +- decay
Resonance Amplitude Phase
K*-(892)+
KS0
K*+(892)-
KS
KSf0(980)
KSf0(1370)
KSf2(1270)
K*0-(1430)+
K*2-(1430)+
K*-(1680)+
KS1(M=535±6 MeV, =460±15
MeV) KS2(M=1063±7 MeV, =101±12
MeV) Non-resonance
1.706 ± 0.0151.0(fixed)0.136 ± 0.0080.032 ± 0.0020.385 ± 0.0110.49 ± 0.041.66 ± 0.052.09 ± 0.051.2 ± 0.051.62 ± 0.0241.66 ± 0.090.31 ± 0.046.51 ± 0.22
138 ± 0.90 (fixed)330 ± 3114 ± 3214.2 ± 2.3311 ± 6341.3 ± 2.3353.6 ± 1.8316.9 ± 2.184 ± 10217.3 ± 1.4257 ± 11149 ± 1.6
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
B B+
B±D(KS +-)K± Dalitz analysis
Fit Dalitz distributions for B+ and B- decay simultaneously-> r , 3 , as free parameters
Use D0KS to make Dalitz-plot model fit 58K events with 13 amplitudes
Select B±K± D0(KS events 107 ± 12 events in 142 fb-1 Belle data
Form Dalitz plots for B+ & B
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
B±D(KS +-)K± Dalitz analysis
Weak phase 3 = 950 ±250(stat) ±130 (sys)±100
strong phase = 1620 ±250(stat) ±120(sys) ±240
(3rd error is model uncertainty) r = 0.33 ± 0.10(stat)
@90% C.L :0.15<r<0.5 ,610<3<1420, 1040<<2140
3
r
3
r = |BKD|/|BKD|_
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
B -> +0 mode(first observation)data used:78 fb-1
B(B+ -> +0) =(31.77.1(stat) 6.4(sys) 2.1(pol))x10-6
ACP(B -> 0) = (0.1 ±22.4(stat)
±2.8(sys))%
First observation of charmless vector-vector mode
0
+
0
+
B+
B+
u
b
d
-
W
--
-
u
u
u
u
u
b
d
u
u
-
-
W
Z/
EWP
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
Helicity analysis
0 momentum requirement
final state is vector-vector system -> give S ,P or D wave
Both longitudinal and transverse polarization are possible
Longitudinal pol. ratio , = (94.810.6(stat) 2.1(sys))%
L
fit result
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
B ->K(*) (78 fb-1) BF’s
- -b
s
u
-
Penguin
Mode BF x 10 -6
K+
K0
K*0
K*+
9.4 ± 1.1 ± 0.79.0 ± 2.2 ± 0.710.0 ± 1.6 ± 0.86.7 ± 2.1 ± 1.0
s
s
u
W
u , c, t---136±15
35.6±8.4
58.5±9.1
8±4.311.3±4.5
Vts
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
B -> K* (78 fb-1) polarizationK+
|A0|2 = 0.43 ± 0.09 ± 0.04|A |2 = 0.41 ± 0.10 ± 0.04 (CP odd and CP even states) andarg(A ) = 0.48 ± 0.32 ± 0.06arg(A ) = -2.57 ± 0.39 ± 0.09
T
T
=
Distribution of decays->A0 , A , A , tr , , tr T =
K*
Ax -> complex amplitudes
Amplitudes are determined byunbinned max likelihood fit:
z tr
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
Summary
•Now we have better measurement on CP asymmetries and ratio of BF’s in B- -> DCPK- mode
• Constrained 3 using Dalitz analysis of B- -> D(KS+-)K- decay
• Measured the branching fractions and different helicity amplitudes in B -> mode.
• Measured the branching fractions and helicity amplitudes in B -> K(*) mode
• Lot more other hadronic rare B-decays……..
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
MC with3 = 70o
B+ / B
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
~2.4σ separation
B
B+
B±D(KS +-)K± Dalitz analysis
Fit Dalitz distributions for B+ and B- decay simultaneously-> r , 3 , as free parameters
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
KEKB Accelerator
Two separate rings
Finite crossing angle
Ldesigned= 1034 cm-2s-1
Achieved:
Lpeak > 1034 cm-2s-1
Integrated Luminosity
~ 158 fb-1
Ee = 3.5 GeV
Ee = 8.0 GeV
+
-
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
Detector Performance
K/ separation is done using:
ACC, TOF, dE/dx( CDC)
PID(K) =
Wide momentum range
L(K)
L(K) + L()
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
Background Suppression•Variables to distinguish signal from continuum events
CosB
•Event Shape variable: (Fisher) BB : SphericalContinuum: back-to-back(jet-like)
–
Be+ e-
B
CONTINUUM
SIGNAL
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
CosB Fisher
Likelihood ratio
Background Suppression
Signal
Continuum
WIN-03, Lake Geneva, Wisconsin Sanjay K SwainHadronic rare B decays
Main question: “Is V unitary” ?
Three generation quark mixing matrix(V)
V =
tbtstd
cbcscd
ubusud
VVV
VVV
VVV
3 = arg(V* )ub
(Also known as )
VudVub+ VcdVcb+ VtdVtb = 0
Orthogonality of 1st and 3rd column gives:
* **a
b
-b
= arg( )a-b
*–3 = arg( )VcdVcb
VudVub*
V udV ub
VcdVcb
Vtd V
tb*
*
*
3()
2()
1()
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