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Charmless Three-body Decays of B Mesons. Chun-Khiang Chua Chung Yuan Christian University HEP2007, 20 July 2007, Manchester. Introduction. Many three-body B decay modes are observed with rates~10 -5 . These modes usually have non-negligible (sizable) nonresonant (NR) contributions. - PowerPoint PPT Presentation
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1
Charmless Three-body Decays of B Mesons
Chun-Khiang ChuaChung Yuan Christian University
HEP2007, 20 July 2007, Manchester
2
Introduction Many three-body B decay modes are observed with rate
s~10-5.
These modes usually have non-negligible (sizable) nonresonant (NR) contributions.
Some modes, KSKSKS, K+K-KS, are useful for the extraction of sin2eff
Most theoretical works are based on flavor symmetry. (Gronau et al, …)
We (Cheng-CKC-Soni) use a factorization approach to study these modes (FA seems to work for DKK decay) A global analysis
SSS
SS
KKKKKKKKB
KKKKKKKB
,,,
,,,0000
3
Different topological decay amplitudes
Treebu
Penguinbs, d
4
Factorized into creation and transition parts
Creation
Transition
Annihilation
Penguinbs, d
Treebu
5
b→s b→u
A brief look at a typical three-body amp.
The creation part <0→K+K-> is related to the kaon’s e.m. form factors, fitted from
data Non-resonant part is constrained by KSKSKS rate and K+K- mass s
pectrum
The transiton part <B0→K-K0> Use HMChPT amplitude with exponential form momentum depen
dence (NR fixed from rate)
0|| jKK
1232 ).( ipppHMChPT eeAA BNR
6
B0 to K+K-K0 rate:
Final state Expt (10-6) Theory
K0 2.98±0.45 2.6+0.5-0.4
f0(980)K0 9.57±2.51 5.8+0.1-0.5
X0(1550)K0 0.98±0.44 0.93+0.16-0.15
NR 26.7±4.6 18.1+5.1-3.9
total 23.8±2.6 19.8+0.6-0.6
NR rates: 88% from b→s (via <K+K-|ss|0>)
and 3% from b→u transitions
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b→s
b→u
The b→s transition prefers a small m(K+K-)
Low mKK peak due mainly to KS
The b→u transition prefers a small m(K+K0) and hence large m(K+K-) ⇒ tiny interference between b→s & b→u transitions
b→s
b→u
CP-odd K+K-KS decay spectrum
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low mKK peak: f0(980)KS + NR
peak at mKK 1.5 GeV due to X0(1550)
b→s
b→u
CP-even K+K-KS decay spectrum CP-even+CP-odd
9
K+K-KS(L) & KSKSKS(L) rates KS KS KS rate is used as
an input to fix the NR amplitude in 0→KK creation (denoted the parameter)
SD rates agree with data within errors c quark not considere
d yet a small room for LD c
ontribution
1st error: ms, B→K form factors,
2rd error: NR
01.001.001.002.0
theory
01.001.001.002.0
expttheory
03.037.103.019.1
06.014.006.006.0excluded
09.046.010.032.0
11.082.114.049.1
20.028.223.081 .1
expt6
theory6
98.0
07.091.098.0
1463.7
9.02.6input
)14.0( )(
57.1 )(
33.8 )(
2.14.1289.9
)10()10(state Final
L
S
LSS
SSS
K
CPS
CPS
S
KKK
f
KKK
ff
KKK
KKK
CP
KKK
KKK
KKK
BB
S
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B-→K+K-K- decay
The predicted NR rate agrees with Belle The nature of broad X0(1550) (or fX(1500) by Belle) i
s not clear. The large fraction of X0(1550), 121% by BaBar and 63% by Belle, is entirely unexpected, recalling that it is only 4% in K+K-K0
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B→K decays
The predicted NR rate agrees with Belle
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B0→K-+0 decay
1st theory error: NR 2nd theory error: ms, NR, form factors 3rd theory error: Calculations for K-KSKS, KS-0, KS00, KS+- modes
are also available
13
B→KK and Sdecays
KK rate agrees with BaBar and Belle rate is sensitive to B → transition (can be used to fix the NR
parameter)
B0→+-0 is predicted to have a rate (Br=26.310-6) larger than +-
- as it receives +, - and 0 resonant contributions
B-→K+K--
B-→+--
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sin2 is naively expected in K+
K-KS due to color-allo
wed tree contribution, tied to NR amplitude
S, ACP are small in
KSKSKS: no b→u tree
diagram
05.000.007.003.0
04.001.005.001.0
40.153.010.154.0excluded
47.152.001.155.0
40.153.010.154.0excluded
008.0000.0019.0000.0
008.0000.0019.0000.0
12.009.0
009.0001.0020.0001.0excluded
008.0007.0019.0004.0
12.009.0
009.0001.0020.0001.0excluded
eff
77.0
1514 69.0
91563.4)(
86.4)(
91563.4)(
Expt.(%)(%)
718.0
20.058.0719.0
13.058.0728.0)(
726.0)(
13.058.0721.0)(
Expt.2sinState Final
LSS
SSS
KL
CPS
KS
f
LSS
SSS
KL
CPS
KS
KKK
KKK
KKK
KKK
KKK
A
KKK
KKK
KKK
KKK
KKK
L
S
L
S
CP asymmetries in K+K-KS, KSKSKS
sin2=0.6780.025 (all charmonium), 0.695+0.018-0.016 (CKM fit)
15
sin2eff=sin2eff-sin2charmonium
theory expt
sin2(K+K-KS) =0.050+0.028-0.033
-0.098+018-0.16
sin2(KSKSKS) =0.041+0.027-0.032 -0.098±0.20
sin2(KS00) =0.051+0.027-0.032 -1.3980.71
sin2(KS+-) =0.040+0.031-0.032
16
Conclusions It is important to understand the NR amplitudes in 3-body de
cays. We have identified two NR sources. We found large NR signal (35%~40%) in K modes, in favor
of Belle measurements Contribution of X0(1550) to K+K+K- should be clarified Intermediate vector & scalar meson contributions to 3-body
decays are identified. The total rates of 3-body B decays are calculated for the first time
Final-state rescattering known to be important for penguin-induced two-body mode
s some FSI effects for 3-body modes are incorporated in the propagator of resonances LD c-penguin, u-penguin
Full Dalitz plot analysis will be very helpful