theoretical review on sin2 b(f 1 ) from b → s penguins
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1
Theoretical review on sin2 from b → s penguins
Chun-Khiang ChuaChung Yuan Christian University
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:
Cf=0, Sf=fsin2
0B
LSKJf ,/Oscillation, eim t
(Vtb*Vtd)2
=|Vtb*Vtd|2 e-i 2
)( 0 fBAA
)( 0 fBAA
fi
ff
ff
f
ff
ff
f
eAA
pqSC
mtSmtCftBftBftBftBa
2
22
2
00
00
,||1
Im2 ,
||1||1
,sincos ))(())(())(())((
Bigi, Sanda 81
Quantum Interference
Direct CPA Mixing-induced CPAf = 1
3
The CKM phase is dominating The CKM picture in the
SM is essentially correct:
WA sin2=0.681±0.025 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 on
e 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 proposed b
y 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 Most data: S<0
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, LD CS tree, 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 effects (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
csudcdusfufubus
cfcbcs
cfcbcd
ufubud
ud
usf r
VVVVrAVVAVVAVVAVV
VVr
1
)/()(ˆ
**
**
b→s
b→d
intrinsic un.: O(2)
12
S<0.22
An example
|r’Ks|≡
icA ic|A|: conservative, less modes better bound
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)(ˆ39.0|)(|
|)(|31.0)(ˆ02.1)(ˆ
29.0|)(|23.0)(ˆ10.008.0)'(ˆ
22.0|)'(|17.0)'(ˆ
00
SS
SSS
S
SSS
S
S
SS
KSKrKKKSKKKS
KKKrKKKr
KSKrKr
KSKr
Gronau, Grossman,Rosner (04)Engelhard, (Nir), Raz (05,05)
|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 Martin Beneke] pQCD: Keum, Li, Sanda [se
e talk by Cai-Dai Lu] SCET: Bauer, Fleming, Pirjol, Rothstein, Stewart
[see talk by Ira Z. Rothstein]
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
Signs and sizes of S?
QCDF: Beneke [results consistent with Cheng-CKC-Soni]
pQCD: Mishima-Li SCET: Williamson-Zupan
(two solutions)
Some “hints” of deviations, e.g. 0KS
16
Dominant Penguin Contributions (PP,PV)
Dominant contributions: (similar sizes, common origin) (V-A)(V-A): a4, (S+P)(S-P): rM2 a6 (: M1=V) Constructive Interference: a4+rM2a6 M2M1=PP,VP Destructive Interference: a4rPa6, M2M1=PV Interferences between q=s and q=d amp. (in KS’, KS)
V=(V-A)/2+(V+A)/2
17
KS
No CS tree, unsuppressed P S small (~0.03) and positive
Beneke, 05
18
KS, KS
KS: C(a2) + suppressed P S large Opposite signs come from signs in wave functions.
KS: C(a2) + unsuppressed P S small, signs different from (KS), due to a6 terms
)(2
1 dduu
Ratio of F.F. fM not shown
00 ,
,
00 ,
,
19
KS, ’KS
Contructive interference in P(’KS) both in a4,6 and in q=d,s S>0 and small Destructive interference in P(KS) in q=d,s S>0, large (unstable)
)( '
)( '
)( '
)(3
1~
),2(6
1~'
ssdduu
ssdduu
Ps>PdP flip sign
)2/1(tan3.39 1
20
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
21
FSI effect on S
SmallS for ’Ks, Ks. Tree pollutions are diluted for non pure penguin
modes: KS, 0KS
FSIs enhance rates through rescattering of charmful intermediate states [expt. rates are used to fix cutoffs (L=m + r LQCD, r~1)].
22
FSI effects in mixing induced CP violation of penguin modes are small The reason for the smallness of the deviations:
Use rates to fix FSI parameters: F.F. FSI contributions dominated by DsDbar final states The dominant FSI contributions are of charming penguin like.
Do not bring in any additional weak phase.
Other sources of LD contributions? A(K) and 00 rate may hint at larger and complex CS tree
… SU(3): Chiang, Gronau, Rosner, Luo, Suprun Zhou; Charng, Li, … Implications on S?
See Cheng Wei’s talk
23
S from RGI parametrizations aaa
Ciuchini et al.; taken from 0801.1833
at UL=0.5S are still small:
A(K-0)
24
A(K)S?
C from exchange-type rescattering of T (enhance A, B(00)) Similar results for S:
CKC,Hou,Yang 2003; CKC 2007
QE FSI:TC
25
Results in S for scalar modes (QCDF) (Cheng-CKC-Yang, 05) S are tiny (0.02 or less):
LD effects have not been considered.
26
K+K-KS(L) and KSKSKS(L) modes
Penguin-dominated KSKSKS: CP-even eigenstate. K+K-KS: CP-even dominated,
CP-even fraction: f+0.9 Three body modes Most theoretical works are based on flavor symmetr
y. (Gronau et al, …) We (Cheng-CKC-Soni) use a factorization approach
See Hai-Yang’s talk for more details
27
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
K
K
28
CP-odd K+K-KS decay spectrum
Low mKK: KS+NR (Non-Resonance).. High mKK: bu transition contribution. Experimental data: KS only bu is highly constrained.
b→s b→u
See Hai-Yang’s talk
29
CP-even K+K-KS decay spectrum
Low mKK: f0(980)KS+NR (Non-Resonance). High mKK: bu transition contribution. b s and bu do not interfere
b→s
b→u
peak at mKK 1.5 GeV due to X0(1550) See Hai-Yang’s talk
30
S for K+K-KS, KSKSKS and others S are small.
For KsKsKs: - no b→u transition.
For K+K-KS: - b→u prefers large m
(K+K-), not seen - b→s prefers small m
(K+K-), - interference reduced small S
sin2=0.6810.025 (all charmonium), 0.695+0.018-0.016 (CKM fit)
theory expt
S(K+K-KS) =0.040+0.028-0.033
0.05±0.11
S(KSKSKS) =0.038+0.027-0.032 -0.10±0.20
S(KS00) =0.048+0.027-0.032 -1.200.41
S(KS+-) =0.037+0.031-0.032
Stheory < O(0.1)Cheng,CKC,Soni, 2007
See Hai-Yang’s talk
31
Conclusion The CKM picture is established. However, NP is expected (m, DM, nB/n). In most calculations: the deviations of sin2eff from sin2 = 0.6810.025 are
At most O(0.1) in B0 KS, ’KS, 0KS, f0KS, a0KS, K*00, KSKSKS…
Larger |S|: B0 KS, 0KS, KS… The color-allowed tree contribution to S in B0→KKKS is constrained by d
ata to be small. In existing theoretical claculations:
S in B0→’KS, KS and B0→KSKSKS modes are tiny. Not affected by LD effects explored so far. Need more works to handle hadronic effects. More measurements [SU(3)].
The pattern of S is also a SM prediction. Most S>0. A global analysis is helpful. Measurements of sin2eff in penguin modes are still good places to look fo
r new phase(s) SuperB →0.1.
32
Back up
33
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
4711431211144)(%)( )(%)( )(%) (
BKB
ExptAcpFSIAcpFSInoAcp
Cheng, CKC, Soni, 04Different , FF…
34
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).
35
FSI effects on direct CP violation
Large CP violation in the K, K mode.
36
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
74.52.12.6
)48.0()(88.1)(45.5)(
2.14.1233.7)10()10(state Final
L
S
LSS
SSS
K
CPS
CPS
S
KKKff
KKKff
KKKinputKKK
CPKKKKKKKKK
BB
S
37
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.
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
009.0001.0020.0001.0excluded
008.0007.0019.0004.0
009.0001.0020.0001.0excluded
eff
77.0 1514 69.0 8763.4)(
86.4)(8763.4)(
Expt.(%)(%)718.0
20.058.0719.010.073.0728.0)(
726.0)(10.073.0721.0)(
Expt.2sinState Final
LSS
SSS
KL
CPS
KS
f
LSS
SSS
KL
CPS
KS
KKKKKK
KKKKKK
KKKA
KKKKKK
KKKKKK
KKK
L
S
L
S
sin2=0.6800.025 (all charmonium), 0.695+0.018-0.016 (CKM fit)
38
b→sqq tCPV measurements
2-body: HYC,Chua,Soni;Beneke
3-body: CCS
Naïve b→s penguin average: 0.68±0.04, 0.56±0.05 (if f0K0 excluded), 0.0.12.2, 2.6 deviation from b→ccs average
Sf= ± sin2efffrom b→ccs
39
A closer look on S signs and sizes
)(2
1 dduu
constructive (destructive)Interference in P of ’Ks (Ks)
small
large
small (’Ks)large (Ks)
small
large
Beneke, 05
0 ][
][][~)]([
][)]([~)'(
0 ][
][][~)]([
][)]([~)(
0 ][
][][~][
][][~)(
0 ][
][][~][
][][~)(
0 ][][~
)]([)]([
~)(
0] Re[ ,Re]cos[||
64
264)(
64
2640
46
2460
46
246
64
64
2
2
SPCP
araaara
KAA
SPCP
araaara
KAA
SPCP
aaraaar
KAA
SPCP
aaraaar
KAA
SPP
araara
KAA
AArS
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
)(3
1~ ),2(6
1~' ssdduussdduu
B→V
40
A closer look on S signs (in QCDF)
M1M2: (B→M1)(0→M2)
,Re
c
u
AAS
41
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,
HAiHA
BHA em
ydyX
b
d
sq
q
42
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
43
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)
44
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.
_
_
_
_
45
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
_
46
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
47
K+K-KS and KSKSKS (pure-penguin) decay amplitudes
Tree
Penguin
48
Factorized into transition and creation parts
Tree
Penguin
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