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SM expectations on sin2 b(f 1 ) from b → s penguins. Chun-Khiang Chua Academia Sinica FPCP 2006 9 April 2006, Vancouver. Mixing induced CP Asymmetry. Bigi, Sanda 81. Quantum Interference. Both B 0 and B 0 can decay to f: CP eigenstate . If no CP (weak) phase in A: A= ±A - PowerPoint PPT Presentation
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1
SM expectations on sin2 from b → s penguins
Chun-Khiang ChuaAcademia Sinica
FPCP 2006 9 April 2006, Vancouver
2
Mixing induced CP Asymmetry
)0(0 tB
Both B0 and B0 can decay to f: CP eigenstate.
If no CP (weak) phase in A:
A=±A
Cf=0, Sf=±sin2
0B
LSKJf ,/Oscillation, eim t
(Vtb*Vtd)2
=|Vtb*Vtd|2 e-i 2
)( 0 fBAA
)( 0 fBAA
A
AeSC
mtSmtC
ftBftB
ftBftBa
if
f
ff
f
ff
ff
f
2
22
2
00
00
,||1
Im2 ,
||1
||1
,sincos
))(())((
))(())((
Bigi, Sanda 81
Quantum Interference
Direct CPA Mixing-induced CPA
3
The CKM phase is dominating The CKM picture in the
SM is essentially correct:
WA sin2=0.687±0.032 Thanks to BaBar, Belle and
others…
0
||
||
***
)(
)(
1
3
tdtbcdcbudub
itdtd
iubub
VVVVVV
eVV
eVV
4
New CP-odd phase is expected… New Physics is expected
Neutrino Oscillations are observed Present particles only consist few % of t
he universe density What is Dark matter? Dark energy? Baryogenesis nB/n~10-10 (SM 10-20)
It is unlikely that we have only one
CP phase in Nature
NASA/WMAP
5
The Basic Idea A generic b→sqq decay amplitude:
For pure penguin modes, such as KS, the penguin amplitude does not have weak phase [similar to the J/KS amp.]
Proposed by Grossman, Worah [97]
A good way to search for new CP phase (sensitive to NP).
ttbts
ccbcs
uubus FVVFVVFVVfBA ***0 )(
0// SSsss KJKJKKK SSS
6
The Basic Idea (more penguin modes) In addition to KS, (’KS, 0KS, 0KS, KS, KS) were propose
d by London, Soni [97] (after the CLEO observation of the large ’K rate)
For penguin dominated CP mode with f=fCP=M0M’0, cannot have color allowed tree (W± cannot produce M0 or M’0) In general Fu should not be much larger than Fc or Ft
More modes are added to the list: f0KS, K+K-KS, KSKSKS Gershon, Hazumi [04], …
ttbts
ccbcs
uubus FVVFVVFVVfBA ***0 )(
0// SS KJKJfff SSS
7
sin2eff
To search for NP, it is important to measure the deviation of sin2eff in charmonium and penguin modes
Deviation NP
How robust is the argument?
What is the expected correction?
8
Sources of S:
Three basic sources of S: VtbV*ts = -VcbV*cs-VubV*us
=-A2 +A(1-)4-iA4+O(6) (also applies to pure penguin modes)
u-penguin (radiative correction): VubV*us (also applies to pure penguin modes)
color-suppressed tree Other sources?
LD u-penguin, CA tree?
*usubVV
b u
d d
9
Corrections on S Since VcbV*cs is real, a better expression is to use the unit
ary relation t=-u-c (define Au≡Fu-Ft, Ac≡Fc-Ft;; Au,Ac: same order for a penguin dominated mode):
Corrections can now be expressed as (Gronau 89)
To know Cf and Sf, both rf and f are needed.
ttbts
ccbcs
uubus FVVFVVFVVfBA ***0 )(
)()( 2***0 ib
uccbcs
ccbcs
uubus eRAAVVAVVAVVfBA
)/arg( ,/
,sinsin||2 ,cossin2cos||2cf
uff
cfc
ufuf
ffffff
AAAAr
rCrS
~0.4 2
10
Several approaches for S
SU(3) approach (Grossman, Ligeti, Nir, Quinn; Gronau, Rosner…) Constraining |Au/Ac| through related modes in a model independe
nt way
Factorization approach SD (QCDF, pQCD, SCET)
FSI approach (Cheng, CKC, Soni)
Others
)/arg( ,/
,sinsin||2
,cossin2cos||2
cf
uff
cfc
ufuf
fff
fff
AAAAr
rC
rS
11
SU(3) approach for S Take Grossman, Ligeti, Nir, Quinn [03] as an example
Constrain |rf|=|uAu/cAc| through SU(3) related modes
cfcbcd
ufubud
cfcbcs
ufubus
BVVBVVfBA
AVVAVVfBA
'*
'*0
**0
)'(
)(
)'(
:)3(
0
'
'**
'
)('
')(
fBACAVVAVV
BCASU
f
ff
cfcbcd
ufubud
f
cuf
ff
cuf
f
csudcdusf
ufubus
cfcbcs
cfcbcd
ufubud
ud
usf r
VVVVr
AVVAVV
AVVAVV
V
Vr
1
)/()(ˆ
**
**
b→s
b→d
O(2)
12
S<0.22
An example
|r’Ks|≡
13
More SU(3) bounds (Grossman, Ligeti, Nir, Quinn; Gronau, Grossman, Rosner) Usually if charged modes a
re used (with |C/P|<|T/P|), better bounds can be obtained. (K- first considered by Grossman, Isidori, Worah [98] using -, K*0
K-) In the 3K mode U-spin sym.
is applied. Fit C/P in the topological a
mplitude approach
⇒S
19.0|)(|15.0)(ˆ
18.0|~)(|14.0~)(ˆ
29.0|)(|23.0)(ˆ
10.008.0)'(ˆ
22.0|)'(|17.0)'(ˆ
00
SS
SS
S
SS
KSKr
KKKSKKKr
KSKr
Kr
KSKr
Gronau, Grossman, Rosner (04)
|Sf|<1.26 |rf||Cf|<1.73 |rf|
Gronau, Rosner (Chiang, Luo, Suprun)
14
S from factorization approaches There are three QCD-based factorization app
roaches: QCDF: Beneke, Buchalla, Neurbert, Sachrajda [se
e talk by Alex Williamson] pQCD: Keum, Li, Sanda [se
e talk by Satoshi Mishima] SCET: Bauer, Fleming, Pirjol, Rothstein, Stewart
[see talk by Christian Bauer]
15
S)SD calculated from QCDF,pQCD,SCET
Most |S| are of order 2, except KS, 0KS (opposite sign)
Most theoretical predictions on S are similar, but signs are opposite to data in most cases
Perturbative phase is small S>0
QCDF: Beneke [results consistent with Cheng-CKC-Soni]
pQCD: Mishima-Li SCET: Williamson-Zupan
(two solutions)
16
A closer look on S signs and sizes
0 ][
][][~
)]([
][)]([~)'(
0 ][
][][~
)]([
][)]([~)(
0 ][
][][~
][
][][~)(
0 ][
][][~
][
][][~)(
0 ][
][~
)]([
)]([~)(
0] Re[ ,Re]cos[||
64
264)(
64
2640
46
2460
46
246
64
64
2
2
SP
CP
ara
aaraK
A
A
SP
CP
ara
aaraK
A
A
SP
CP
aar
aaarK
A
A
SP
CP
aar
aaarK
A
A
SP
P
ara
araK
A
A
A
ArS
c
u
cMc
uuMu
Sc
u
c
u
cKc
uuKu
Sc
u
c
u
ccK
uuuK
Sc
u
c
u
ccK
uuuK
Sc
u
c
u
cc
uu
Sc
u
c
u
)(2
1dduu
constructive (destructive)Interference in P of ’Ks (Ks)
)(3
1~ ),2(
6
1~' ssdduussdduu
small
large
small (’Ks)large (Ks)
small
large
Beneke, 05
B→V
17
723 5.6 2437
1.7 6.0 48
517 4.5 211
7.133.13
0
1.02.0
5.111.03.12.07.111.06.11.0
1415
0
7.85.02.21.15.96.05.21.1
0
B
B
KB
Expt(%) QCDF PQCD
Direct CP Violations in Charmless modes
With FSI ⇒ strong phases ⇒ sizable DCPV
FSI is important in B decays What is the impact on S
1314
0
13
0
4711431
211144
)(%)( )(%)( )(%) (
B
KB
ExptAcpFSIAcpFSInoAcp
Cheng, CKC, Soni, 04Different , FF…
18
FSI effects on sin2eff (Cheng, CKC, Soni 05) FSI can bring in additional
weak phase B→K*, K contain tree V
ub Vus*=|Vub Vus|e-i
Long distance u-penguin and color suppressed tree
19
FSI effects in rates
FSIs enhance rates through rescattering of charmful intermediate states [expt. rates are used to fix cutoffs (=m + r QCD, r~1)].
Constructive (destructive) interference in ’K0 (K0).
20
FSI effects on direct CP violation
Large CP violation in the K, K mode.
21
FSI effect on S
Theoretically and experimentally cleanest modes: ’Ks (Ks) Tree pollutions are diluted for non pure penguin modes: KS, 0KS
22
FSI effects in mixing induced CP violation of penguin modes are small The reason for the smallness of the deviations:
The dominant FSI contributions are of charming penguin like. Do not bring in any additional weak phase.
The source amplitudes (K*,K) are small (Br~10-6) compare with Ds*D (Br~10-2,-3)
The sources with the additional weak phase are even smaller (tree small, penguin dominate)
If we somehow enhance K*,Kcontributions ⇒ large direct CP violation (AKs). Not supported by data
23
Results in S for scalar modes (QCDF) (Cheng-CKC-Yang, 05) S are tiny (0.02 or less):
LD effects have not been considered.
Do not expect large deviation.
24
K+K-KS(L) and KSKSKS(L) modes
Penguin-dominated KSKSKS: CP-even eigenstate.
K+K-KS: CP-even dominated,
CP-even fraction: f+=0.91±0.07 Three body modes Most theoretical works are based on flavor symmetr
y. (Gronau et al, …) We (Cheng-CKC-Soni) use a factorization approach
25
K+K-KS and KSKSKS decay rates KS KS KS (total) rat
e is used as an input to fix a NR amp. (sensitive).
Rates (SD) agree with data within errors. Central values sli
ghtly smaller. Still have room fo
r LD contribution.00.004.006.000.008.016.0
expttheory
00.004.006.003.040.116.0
expttheory
02.024.202.603.040.188.0
03.054.098.203.022.040.0excluded
04.083.008.304.046.043.0
05.048.129.506.013.165.0
70.031.238.810.059.108.1
expt6
theory6
92.0
07.091.092.0
74.5
2.12.6
)48.0()(
88.1)(
45.5)(
2.14.1233.7
)10()10(state Final
L
S
LSS
SSS
K
CPS
CPS
S
KKK
ff
KKK
ff
KKK
inputKKK
CP
KKK
KKK
KKK
BB
S
26
It has a color-allowed b→u amp, but…
The first diagram (b→s transition) prefers small m(K+
K-) The second diagram (b→u transition) prefers small m
(K+K0) [large m(K+K-)], not a CP eigenstate Interference between b→u and b→s is suppressed.
b→s b→u
27
CP-odd K+K-KS decay spectrum
Low mKK: KS+NR (Non-Resonance)..
High mKK: (NR) transition contribution..SKKB 0
b→s b→u
28
CP-even K+K-KS decay spectrum
Low mKK: f0(980)KS+NR (Non-Resonance).
High mKK: (NR) transition contribution. SKKB 0
b→s
b→u
29
K+K-KS and KSKSKS CP asymmetries
Could have O(0.1) deviation of sin2 in K+K-KS It originates from c
olor-allowed tree contribution.
Its contributions should be reduced. BaBar 05
S, ACP are small In K+K-Ks: b→u pr
efers large m(K+K-) b→s prefers small m(K+K-), interference reduced small asymmetries
In KsKsKs: no b→u transition.
06.008.012.007.011.028.0
05.000.002.006.001.006.0
01.029.095.002.032.011.0excluded
01.016.073.001.027.000.0
01.029.095.002.032.011.0excluded
007.0000.0001.0018.0000.0001.0
007.0000.0000.0018.0000.0000.0
004.0024.0080.0015.0011.0013.0excluded
002.0040.0113.0013.0023.0031.0
18.017.0
014.0024.0080.0015.0011.0013.0excluded
eff
77.0
214174.0
214116.0)(
09.0)(
10916.0)(
Expt.(%)
024.0
25.065.0024.0
34.009.0025.0)(
0460)(
57.00250)(
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
30
Conclusion The CKM picture is established. However, NP is expected
(m, DM, nB/n). The deviations of sin2eff from sin2 = 0.6870.032 are at
most O(0.1) in
B0 KS, KS, 0KS, ’KS, 0KS, f0KS, a0KS, K*00, KSKSKS. The O(0.1) S in B0→KKKS due to the color-allowed tree co
ntribution should be reduced. A Dalitz plot analysis will be very useful.
The B0→’KS, KS and B0→KSKSKS modes are very clean. The pattern of S is also a SM prediction. A global analysis
is helpful. Measurements of sin2eff in penguin modes are still good pl
aces to look for new phase(s) SuperB →0.1.
31
Back up
32
A closer look on S signs (in QCDF)
M1M2: (B→M1)(0→M2)
,Re
c
u
A
AS
33
Perturbative strong phases:
penguin (BSS) vertex corrections (BBNS) annihilation (pQCD)
Because of endpoint divergences, QCD/mb power corrections in QCDF due to annihilation and twist-3 spectator interactions can only be modelled
with unknown parameters A, H, A, H, can be determined (or constrained) from rates and Acp.
Annihilation amp is calculable in pQCD, but cannot have b→uqq in the annihilation diagram in b→s penguin.
)1(ln ,
,
0
,HAi
HAB
HA em
y
dyX
b
d
sq
q
34
Scalar Modes
The calculation of SP is similar to VP in QCDF All calculations in QCDF start from the following projection:
In particular
All existing (Beneke-Neubert 2001) calculation for VP can be brought to SP with some simple replacements (Cheng-CKC-Yang, 2005).
SVPhxMdxezqzqph hzkzki ,, ),(0|)'()(|)( ||
1
0
)'( 21
35
FSI as rescattering of intermediate two-body state FSIs via resonances are assumed to be suppressed in B decays due to the lack of resonances at energies close to B mass.
FSI is assumed to be dominated by rescattering of two-body intermediate states with one particle exchange in t-channel. Its absorptive part is computed via optical theorem:
i
ifTiBMfBMm )()( 2
• Strong coupling is fixed on shell. For intermediate heavy mesons,
apply HQET+ChPT
• Form factor or cutoff must be introduced as exchanged particle is
off-shell and final states are necessarily hard
Alternative: Regge trajectory, Quasi-elastic rescattering …
(Cheng, CKC, Soni 04)
36
BR
SD
(10-6)
BR
with FSI
(10-6)
BR
Expt
(10-6)
DCPV
SD
DCPV
with FSI
DCPV
Expt
B 16.6 22.9+4.9-3.1 24.11.3 0.01 0.026+0.00
-0.002 -0.020.03
B0 13.7 19.7+4.6-2.9 18.20.8 0.03 -0.15+0.03
-0.01 -0.110.02
B0 9.3 12.1+2.4-1.5 12.10.8 0.17 -0.09+0.06
-0.04 0.040.04
B0 6.0 9.0+2.3-1.5
11.51.0 -0.04 0.022+0.008-0.012 -0.090.14
For simplicity only LD uncertainties are shown here
FSI yields correct sign and magnitude for A(+K-) !
K anomaly: A(0K-) A(+ K-), while experimentally they differ
by 3.4SD effects?Fleischer et al, Nagashima Hou Soddu, H n Li et al.]
Final state interaction is important.
_
_
_
_
37
BR
SD
(10-6)
BR
with FSI
(10-6)
BR
Expt
(10-6)
DCPV
SD
DCPV
with FSI
DCPV
Expt
B0+ 8.3 8.7+0.4-0.2 10.12.0 -0.01 -0.430.11 -0.47+0.13
-0.14
B0+ 18.0 18.4+0.3-0.2 13.92.1 -0.02 -0.250.06 -0.150.09
B000 0.44 1.1+0.4-0.3 1.80.6 -0.005 0.530.01 -0.49+0.70
-0.83
B0 12.3 13.3+0.7-0.5 12.02.0 -0.04 0.370.10 0.010.11
B 6.9 7.6+0.6-0.4
9.11.3 0.06 -0.580.15 -0.07+0.12-0.13
Sign and magnitude for A(+-) are nicely predicted !
DCPVs are sensitive to FSIs, but BRs are not (rD=1.6)
For 00, 1.40.7 BaBar
Br(10-6)= 3.11.1 Belle
1.6+2.2-1.6 CLEO Discrepancy between BaBar and Belle should be clarified.
﹣
__
B B B
_
38
Factorization Approach SD contribution should be studied first. Che
ng, CKC, Soni 05 Some LD effects are included (through BW).
We use a factorization approach (FA) to study the KKK decays.
FA seems to work in three-body (DKK) decays CKC-Hou-Shiau-Tsai, 03.
Color-allowed Color-suppressed
39
K+K-KS and KSKSKS (pure-penguin) decay amplitudes
Tree
Penguin
40
Factorized into transition and creation parts
Tree
Penguin
41
sin2eff in a restricted phase space of the K+K-KS decay
The corresponding sin2eff, with mKK integrated up to mKK
max. Could be useful for experiment.
CP-even
Full, excluding KS