11
Final state interactions in hadronic B decays
Hai-Yang Cheng
Academia Sinica
FSIs
BRs & CPV in B decays
Polarization anomaly in BK*
QCD & Hadronic Physics, Beijing, June 16-20, 2005
2
Importance of FSI in charm decays has long been recognized
some nearby resonances exist at energies mD
charm is not very heavy
General folklore for B decays:
FSI plays a minor role due to large energy release in B decays
and the absence of nearby resonances
There are growing hints at some possible soft final-state
rescattering effects in B physics
3
sinsin )()(
)()(
fBfB
fBfBACP B f
One needs at least two different B f paths with distinct weak & strong phases
strong phase weak phase
ei(+)
BaBar Belle Average
B0→K-+ -0.130.03
-0.100.25
-0.110.02
B0→+- -0.470.16
-0.530.30
-0.470.14
B0→+- 0.090.16
0.560.13
0.370.10
600
00
10)6.05.5()()(
)()(
KK
KKACP
first confirmed DCPV (5.7) in B decays (2004)
1. Direct CP violation
_
__
Recall in kaon decays
4
1037
47
211
(%) Expt
0
1314
0
0
B
B
KB
723
7.1
517
pQCD
1.02.0
6.5
0.6
4.5
QCDF
2.131.00.31.28.123.08.21.2
5.111.03.12.07.111.06.11.0
7.85.02.21.15.96.05.21.1
10.3
9.12
4.1
QCDF(S4)
pQCD (Keum, Li, Sanda): A sizable strong phase from penguin-induced annihilation by introducing parton’s transverse momentum
QCD factorization (Beneke, Buchalla, Neubert, Sachrajda):Because of endpoint divergences, QCD/mb power corrections due to annihilation and twist-3 spectator interactions can only be modelled
QCDF (S4 scenario): large annihilation with phase chosen so that a correct sign of A(K-+) is produced (A=1, A= -55 for PP, A=-20 for PV and A=-70 for VP)
Comparison with theory: pQCD & QCDF
1 with )1(ln HA,,
0
,,
HAiHA
BHA e
m
y
dyX
input
5
SD perturbative strong phases:
penguin (BSS) vertex corrections (BBNS)
weak
strong
Nonperturbative LD strong phases induced from power corrections especially from final-state rescattering
annihilation (pQCD)
Need sizable strong phases to explain the observed direct CPV
If intermediate states are CKM more favored than final states, e.g. BDDsK
large phases
large corrections to rate
6
2. Some color-suppressed or factorization-forbidden or penguin-dominated modes cannot be accommodated in the naïve factorization approach
Some decay modes do not receive factorizable contributions
e.g. B Kc0 with sizable BR though c0|c(1-5)c|0=0.
Color-suppressed modes e.g. B0 D0 h0 (h0=0,,0,,’), 00, 00 have the measured rates larger than theoretical expectations.
Penguin-dominated modes such as BK*, K, K, K* predicted by QCDF are consistently lower than experiment by a factor of 2 3
importance of power corrections (inverse powers of mb) e.g. FSI, annihilation, EW penguin, New Physics, …
7
Our goal is to study FSI effect on BRs and CPV (direct & indirect) in B decays (Polarization anomaly in BK* will be briefly mentioned)
LD rescattering can be incorporated in any SD approach but it requires modelling of 1/mb power corrections
We would provide a specific model for FSI to compute strong phases so that we can predict (rather than accommodate) the sign and magnitude of direct CP asymmetries
8
Regge approach [Donoghue,Golowich,Petrov,Soares]
FSI phase is dominated by inelastic scattering and doesn’t vanish even
in mb limit
QCDF [Beneke,Buchalla,Neubert,Sachrajda]
strong phase is O(s, /mb): systematic cancellation of FSIs in mb
Charming penguin [Ciuchini et al.] [Colangelo et al.] [Isola et al.]
long distance in nature, sources of strong phases, supported by SCET
One-particle-exchange model for LD rescattering has been applied to charm and B decays [Du et al.][Lu,Zou,..]
Quasi elastic scattering model [Chua,Hou,Yang]
Consider MMMM (M: octet meson) rescattering in BPP decays
Diagrammatic approach [Chiang, Gronau, Rosner et al.] …
Approaches for FSIs in charmless B decays
9
All two-body hadronic decays of heavy mesons can be expressed interms of six distinct quark diagrams [Chau, HYC(86)]
All quark graphs are topological and meant to have all stronginteractions included and hence they are not Feynmangraphs. And SU(3) flavor symmetry is assumed.
Diagrammatic Approach
(penguin) (vertical W loop)
(tree)
(color-suppressed) (exchange)
(annihilation)
10
Global fit to B, K data (BRs & DCPV) based on topological diagrammatic approach yields [Chiang et al.]
naively) 25.0( )]94(exp[)46.0( 43
52
43.0
30.0
eff
eff
iT
C
PPB
]59[exp)05.044.0()(
)(2 0
0
000
iET
EC
DBA
DBA
DB
consistent with that determined from B D decays
11
quark exchange
quark annihilation
meson annihilation
possible FSIs
W exchange
Color suppressed C
At hadron level, FSIs manifest as resonant s-channel & OPE t-channel graphs
B0D00
relevant for e.g. B0
12
FSI as rescattering of intermediate two-body states
[HYC, Chua, Soni]
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 [Nardulli,Pham][Falk et al.] [Du et al.] …
13
Dispersive part is obtained from the absorptive amplitude via dispersion relation
''
)'( )(
0
22 ds
ms
sMmPmMe
s BB
= mexc + rQCD (r: of order unity)
or r is determined by a fit to the measured rates
r is process dependent
n=1 (monopole behavior), consistent with QCD sum rules
Once cutoff is fixed direct CPV can be predicted
subject to large uncertainties and will be ignored in the present work
Form factor is introduced to render perturbative calculation meaningful
n
QCD
n
t
m
t
mtF
2
22
)(
LD amp. vanishes in HQ limit
14
Inputs
Form factors:covariant light-front approach: relativistic QM for s-wave to s-wave and p-wave transitions (HYC,Chua,Hwang 2004)
CLF Ball & Zwicky Beneke & Neubert
F0B(0) 0.250.03 0.2580.031 0.280.05
A0B(0) 0.280.03 0.3030.028 0.370.06
SD approach: QCD factorization (default scenario) with A=H=0 in
)1(ln ,
,
0
,HAi
HAB
HA em
y
dyX
double counting problem is circumvented
15
Theoretical uncertainties (SD)
1. variation of CKM parameters
=(6315)
2. quark masses: ms(2 GeV)= 9020 MeV
3. renormalization scale: from =2mb to mb/2
4. heavy-to-light form factors: e.g. FB(0)=0.250.03
5. meson distribution amplitudes
16
Theoretical uncertainties (LD)
1. Model assumption
multi-body contributions
form-factor cutoff:
i). n=1
ii). = mexc + rQCD (15% error assigned for QCD)
rD=2.1, 1.6, 0.73, 0.67, respectively, for D, , K modes
varies for penguin-dominated PV modes dispersive contribution
2. Input parameters
strong couplings of heavy mesons and their SU(3) breaking
g(D*D)=17.90.31.9 (CLEO)
heavy-to-heavy form factors
n
t
mtF
2
22
)(
17
SD SD+LD Expt
K0 5.6+1.9-1.8 8.6+1.2+2.9
-1.2-1.8 8.3+1.2-1.0
K0 2.0+3.5-1.3 5.6+2.9+3.7
-1.2-2.1 5.60.9
0K0 2.8+3.2-1.6 5.2+3.2+2.6
-1.5-1.2 5.11.6
’K0 42.1+45.6-19.4 69.4+51.3+50.4
-21.4-19.2 68.64.2
K0 1.8+1.2-0.9 1.8+1.2+0.1
-0.8-0.0 <2.0
0K0 5.8+5.5-3.1 9.6+5.5+8.4
-2.9-3.0 11.51.0
f0K0 8.1+3.1-2.6 8.1+3.1+?
-2.7-? 11.33.6
Br (10-6)
first error: SD, second error: LD
LD uncertainties are comparable to SD ones & SD errors are affected only slightly by FSIs.
No reliable estimate of LD rescattering effects for f0KS
18
All rescattering diagrams contribute to penguin topology,
dominated by charm intermediate states
fit to rates rD = rD* 0.67
predict direct CPV
B B
19
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 3.4See Fleischer’s talk]
_
_
_
_
20
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 --
B0 12.3 13.3+0.7-0.5 12.02.0 -0.04 0.370.10 0.160.13
B 6.9 7.6+0.6-0.4
9.11.3 0.06 -0.580.15 -0.190.11
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)= 5.11.8 Belle
1.6+2.2-1.6 CLEO
Discrepancy between BaBar and Belle should be clarified.
﹣
__
B B B
_
21
BR
SD
(10-6)
BR
with FSI
(10-6)
BR
Expt
(10-6)
DCPV
SD
DCPV
with FSI
DCPV
Expt
BK*0 4.4 9.9+3.6-2.7 9.76+1.16
-1.22 0.01 0.0260.003 -0.14+0.09-0.11
B0+K* 3.8 9.9+3.7-2.8 12.7+1.8
-1.7 0.15 -0.44 -0.250.17
BK* 2.8 5.6+1.8-1.4 ? 0.17 -0.390.01 0.040.29
B0*0 1.3 4.4+1.8-1.4
1.70.8 -0.08 0.066+0.005-0.001 -0.01+0.27
-0.26
B B * B *
_
_
BaBar, hep-ex/0504009 Br(B-0K*-)=(6.92.4)10-6
For 0K*0, Br(10-6)= 3.01.0 BaBar
0.4+1.9-1.7
Belle
_
_
K.F. Chen (CKM2005): BaBar
6.92.4
22
Comparison with other approaches
All known existing models fit the data of BRs and DCPV and then make predictions for mixing (indirect) CPV.
e.g. 1. charming penguin (Ciuchini et al. and many others)
Consider charmless B decay BK with BDDsK
charming penguin is CKM doubly enhanced & gives
dominant LD corrections
S(0K0)=0.770.04
CKM2005
a fit result
23
2. Fit QCDF to data fix unknown power correction
parameters A, H, A, H
Aleksan et al. (hep-ph/0301165)
S4 scenario of Beneke & Neubert (hep-ph/0308092)
Leitner, Guo, Thomas (hep-ph/0411392)
Cottingham et al. (hep-ph/0501040)
24
Mixing-induced CP violation [HYC,Chua,Soni]
It is expected in SM that -fSf sin2 0.726 0.037 with deviation at most O(0.1) in B0 KS, KS, 0KS, ’KS, 0KS, f0KS, K+K-KS, KSKSKS
[London,Soni; Grossman, Gronau, Ligeti, Nir, Rosner, Quinn,…
25
G. Kane (and others): The 2.7-3.7 anomaly seen in b→s penguin modes is the strongest hint of New Physics that has been searched in past many many years…
It is extremely important to examine how much of the deviation is allowed in the SM and estimate the theoretical uncertainties as best as we can.
A current hot topic
26
In general, Sf sin2eff sin(2+W). For bsqq modes,
cuib
ccscb
uusub
aAaeRA
aVVaVVfBA24
**0
)(
Since au is larger than ac, it is possible that S will be subject to significant “tree pollution”. However, au here is color-suppressed.
Penguin contributions to KS and 0KS are suppressed due to cancellation between two penguin terms (a4 & a6)
relative importance of tree contribution
large deviation of S from sin2
mtAmtSftBftB
ftBftBff
cossin))(())((
))(())((
Time-dependent CP asymmetries:
27
SD Expt SD Expt
KS 0.747+0.002-0.039 0.350.20 1.4+0.3
-0.5 417
KS 0.850+0.052-0.055 0.550.31 -7.3+3.5
--2.6 4825
0KS 0.635+0.028-0.067 -- 9.0+2.2
-4.6 --
‘KS 0.737+0.002-0.038 0.430.11 1.80.4 48
KS 0.793+0.017-0.044 -- -6.1+5.1
-2.0 --
0KS 0.787+0.018-0.044 0.340.28 -3.4+2.1
-1.1 814
f0KS 0.749+0.002-0.039 0.390.26 7.70.1 1422
S(KS)>sin2, S(0KS)<sin2
FSI can bring in additional weak phase via K*,K intermediate states (even when tree is absent at SD)
-nfSf Af(%)
(see also Beneke)
28
FSI effect is tiny due to small source (K*,K) amplitudes (Br~10-6) com
pared to Ds*D (Br~10-2,-3). It tends to alleviate the deviation from sin2
For 0KS, S=S-sin2<0 at SD but it becomes positive after including FS
I.
Sf is positive and less than 0.1 in SM, while experimentally Sf is al
ways negative
SD SD+LD Expt SD SD+LD Expt
KS 0.747 0.759+0.009-0.041 0.350.20 1.4 -2.6+1.9
-1.3 417
KS 0.850 0.736+0.033-0.38 0.550.31 -7.3 -13.2+4.4
-3.8 4825
0KS 0.635 0.761+0.102-0.127 -- 9.0 46.6+12.9
-15.8 --
‘KS 0.737 0.734+0.004-0.037 0.430.11 1.8 2.1+0.5
-0.3 48
KS 0.793 0.802+0.025--0.046 -- -6.1 -3.7+4.6
-3.0 --
0KS 0.787 0.770+0.016--0.046 0.340.28 -3.4 3.7+2.7
-2.0 - 814
f0KS 0.749 0.749+0.002-0.039
0.390.26 0.8 0.80.1 -1422
-nfSf Af(%)
29
Effective sin2 in K+K-KS & KSKSKS
For K+K-KS, S= -(2f+-1)sin2eff
(f+: CP-even fraction)
For KSKSKS, S= -sin2eff
theory expt theory expt
K+K-KS 0.830+0.063-0.086 0.60+0.22
-0.20 0.74+1.79-1.18 -
910
KSKSKS 0.749+0.003-0.039 0.260.34 0.75+0.09
-0.13 4121
K+K-KS is subject to large tree pollution from color-allowed tree diagrams
KSKSKS is very clean for testing SM
sin2eff
Af(%)
30
Short-distance induced transverse polarization in B V1V2 (V: light vector meson) is expected to be suppressed
)/(1/ ),/(1 ||22
|| BVBVLT mmOffmmOffff
Get large transverse polarization from B Ds*D* and then convey it to
K* via FSI
B B
*sD *
sD
*D
*K*K
D
(*)
sD(*)
sD
Polarization anomaly in B K* Polarization anomaly in B K*
fL(Ds*D*) 0.51 contributes to f only
f|| 0.41, f 0.08
[HYC, Chua, Soni]
Confirmed for B with fL 0.97
but for BK* fL 0.50, f|| 0.25, f 0.25
31
B BsD *
sD
*D
*K *KD
very small perpendicular polarization, f 2%, in sharp contrast to f 15% obtained by Colangelo, De FArzio, Pham
(*)
sD (*)
sD+ 0 !
Large cancellation occurs in B{Ds*D,DsD*}K* processes. Thi
s can be understood as CP & SU(3) symmetry
While fT 0.50 is achieved, why is f not so small ?
Cancellation in B{VP,PV}K* can be circumvented inB{SA,AS}K*. For S,A=D**,Ds** f 0.22
It is very easy to explain why fL 0.50 by FSI, but it takes some efforts to understand why f f||
3232
Conclusions
DCPV in charmless B decays is significantly affected by
LD rescattering. Correct sign and right magnitude of
DCPV in K-+ and +- are obtained after including FSI.
For penguin-dominated MKS modes, FSI tends to alleviate
the deviation from sin2.
Large transverse polarization fT 0.50 can be obtained
from final-state rescattering of B Ds*D* K*
33
The subleading amplitudes in QCDF develop end-point singularities
)1()(,)(
210 xxx
x
xdx
in twist-3 nonspectator and in annihilation
An end-point singularity means breakdown of simple collinear factorization Use more conservative kT factorizationInclude parton kT to smear the singularity
)(
),(22
210
BT
TT mkxx
kxkddx
Perturbative QCD approach [Keum, Li, Sanda; Lu, Yang, Ukai]
Collinear vs. kT factorization
34
kT factorization
Sudakov factors Sdescribe the parton distribution in kT
KT accumulates after infinitely many gluon exchangesSimilar to the DGLAP evolution up to kT~Q
Parton-level diagrams
Bound-state distributionamplitude
35
Scales and penguin enhancement
b
)( BmO In PQCD this gluon is off-shell by
Slow parton Fast parton
PQCD QCDF 25.1~ 2
For penguin-dominated modes, the branching ratiosWilson coefficients
36
Recent progress on PQCD• Nonfactorizable contributions are important for color-suppresse
d modes---explained B! D00, (J/ c0,c1,c ) K (*) branching ratios, helicity amplitudes (Keum, Kurimoto et al.; Chen, Li).
• Annihilation lowers longitudinal polarization in B! VV. Also predicted pure-annihilation modes, which cannot be done in FA (Lu et al.).
• Predicted CP asymmetry, isospin breaking of B! K*(Matsumori et al.).
• NLO PQCD enhances C, and resolves B! K puzzle (Li, Mishima, Sanda):
LO NLO Data Acp(K+-) -0.13 -0.11 -0.1090.019 Acp(K+0) -0.09 +0.03 0.040.04 Annihilation generates large strong phase, which explains direct CP asymmetries.
37
Baryonic B decays
3-body baryonic B deacys were found to have larger BRs than 2-body decays
There are extensive studies of baryonic B decays in Taiwan both experimentally and theoretically
B-→ppK- : first evidence of charmless baryonic B decay
B→pp(K,K*,)
→p(,K)
→K
B→pp, , pstringent limits)
B→p: first evidence of b→s penguin in baryonic B decays
Expt.
Theory
Chua, Geng, Hou, Hsiao, Tsai, Yang, HYC,…
Publication after 2001: (hep-ph)
0008079, 0107110, 0108068, 0110263, 0112245, 0112294, 0204185, 0204186, 0208185, 0210275, 0211240, 0302110, 0303079, 0306092, 0307307, 0311035, 0503264
0201015, 0405283
Belle group at NTU
first paper on radiative baryonic B decays
C.Q. Geng, this afternoon
39
Regge approach
In evaluating absorptive part via
replace Feynman-diagram strong scattering amplitude T by Regge
amplitude R(s,t):
i
ifTiBMfBMm )()( 2
)()()( 2/)(cos
)(),(1
02
)(
0
2/)( 0
iBMs
ssfBMm
s
s
t
ettsR
tti
(t): residual function, linear Regge trajectory t)=0+’t,
intercept 0=0.45 for , K*,…, -1.8 for D, D*
suppression of FSI with increasing energy s
suppression of charming penguin relative to the light Regge exchanges
''
)'( 1)(
0
22 ds
ms
sMmmM
s BB
uncertainties: t-dep. of (t), BR sensitive to unknown ’
R(s,t) is valid at large s and t 0
41
without FSI with FSI expt
C/T 0.20 0.30exp(-i50)
E/T 0(by hand) 0.14exp(-i84)
(C-E)/(T+E) 0.20 0.43exp(-i69) (0.460.05)exp(-i61)
Br(B0→D+-) 3.210-3 3.110-3 (2.760.25)10-3
Br(B0→D00) 0.610-4 (2.7+2.31.310-4 (2.90.2)10-4
Br(B-→D0-) 4.910-3 (5.0+0.2-0.110-3 (4.980.29)10-3
Even if short-distance W-exchange vanishes (i.e. ESD=0), final-state rescattering does contribute to weak annihilation
B0Ds+K- proceeds via W-exchange
(expt) 0.0050.014 vs019.0)(
)(2
0
0
ET
E
DB
KDB s
42
)(
)(
)(
edcbaiAbsPP
baiAbsEE
baiAbsCC
SD
CD
SD
Cutoff scale is fixed by B K via SU(3) symmetry
too large +- ( 910-6) and too small 00 (0.410-6)
An additional rescattering contribution unique to but not available to K is needed to suppress +- and enhance 00
D+(+)
D-
(-)
+
-
B
B0DD() has the same topology as vertical W-loop diagram V
_
43
BR
SD
(10-6)
BR
with FSI
(10-6)
BR
Expt
(10-6)
DCPV
SD
DCPV
with FSI
DCPV
Expt
B0+ 7.6 4.6+0.9-0.7 4.60.4 -0.05 0.370.10
(input)
0.560.13(Belle)
0.090.16(BaBar)
B000 0.3 1.5+0.3-0.2 1.50.3 0.56 -0.45+0.08
-0.06 0.280.39
B0 5.1 5.30.0 5.50.6 5x10-5 -0.0030.001
-0.020.07
Need to fit to rates and CPV of +- simultaneously
Charming penguin alone doesn’t suffice to explain 00 rate (rD=0.67)
Sign of A(00) can be used to discriminate between different models
W-exchange can receive LD contributions from FSI
Define Teff=T+E+V, Ceff=C-E-V Ceff/Teff=(0.900.02) exp[-i(882)]
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