Rare and Semileptonic Decays of B and K Mesons
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Transcript Rare and Semileptonic Decays of B and K Mesons
Radiative and Electroweak Penguin
Decays of B Mesons
Jeffrey D. Richman
University of California, Santa Barbara
BABAR Collaboration
11th International Conference on B Physics at Hadron Machines
Oxford, Sept. 28, 2006
Outline
Overview: a little history, physics goals, and challenges.
B+r+g, B0r0g, B0wg and measurement of |Vtd/Vts|
BK l+l- and BK* l+l-: search for new physics using the
lepton forward-backward asymmetry
Inclusive BXs g: branching fraction measurements and
extraction of heavy-quark expansion parameters from the
Eg spectrum.
Conclusions
My apologies for not covering all results on
radiative/electroweak penguin decays in this talk!
Radiative penguin decays of B mesons
Observation of BK* g
CLEO II (1993): Loops in B decays!
Now it’s a physics program!
PRL 71, 674 (1993): cited >500 times!
B(106 )
B( B K *g )
4 105
Rare, but not all that rare!
M ( K *g )
What can we learn from bs, d transitions?
Flavor-changing neutral currents probe SM at 1-loop level.
g
b u, c, t
d
W
s, d
d
(dominated by t quark)
b
g ,Z
s
u, c, t
d
W
d
(+ W+W- box diagram)
New physics can affect the amplitudes at leading order!
As for bc or bu semileptonic decays, the amplitude in
EM/EW penguins is factorizable (only one hadronic current).
What can we learn from bs,d transitions?
b
d
g
Vtb
W
t
*
td
V
d
d
b Vub
d
W
u
d
Presence of only single hadronic current allows us to isolate
non-perturbative QCD parameters in well-defined way. Can
be related to same parameters for other decays.
Exclusive decays: decay form factors fi(q2). bs transition
is similar to bu (heavy to light)
Inclusive decays: parameters of heavy-quark expansion
(mb, mp2,…)
Can extract information on CKM elements if info on hadronic
parameters is available from data, theory, or both.
Observation of bd g and Measurement of |Vtd/Vts|
b
B
u
g
g
u, c, t
b u, c, t
d
W
u
r
B
0
W
d
d
d
r ,
w
0
+ W annihilation diagram (small)
B( B rg )
Vtd
*
B( B K g ) Vts
2
m m
m m
2
B
2
B
*
2 3
r
2 3
K*
T1K (0)
r
1.17 0.09
T1 (0)
2
T (0)
1 R
T (0)
r
1
K*
1
1/
2
R 0.1 0.1
Ali, Lunghi, Parkhomenko,
PLB 595, 323 (2004)
Ball and Zwicky, JHEP 0604, 046 (2006)
B r g 2 B 0 r 0g
2 B 0 wg
I-spin (r), quark model (w). Expect small I-spin violation: (1.1+/-3.9)%.
Measurement of bd g Decays (Belle)
Belle, PRL 96, 221601 (2006); 386 M BB.
Nsig 8.5
Signal
continuum background
Nsig 20.7
N sig 5.7
Nsig 36.9
BK*g
Good particle ID is critical
in this measurement to
suppress BK* g feeddown.
Measurement of bd g Decays (BABAR)
BABAR, hep-ex/0607099, 347 M BB
projections of 4-D fit
signal +
bkgnd
bkgnd
B+r+g
Nsig 42.414.1
12.6
B+r+g
B0r0g
B0r0g
Nsig 38.710.6
9.8
signal
Comparison of bd g Branching Fractions
CKM fitter includes CDF
Bs mixing result.
Error on CKM Fitter
prediction includes uncert.
on BVg form-factor
ratio.
I-spin consistency?
(106 )
Mode
BABAR (10-6) (6.3 s signif.) Belle (10-6) (5.1s signif.)
preliminary; hep-ex/0607099
PRL 96, 221601 (2006).
B r g
1.060.35
0.31 0.09
B0 r 0g
0.770.21
0.19 0.07
B0 wg
0.84 (90% C.L.)
0.09
1.170.35
0.310.08
0.14
0.580.34
0.310.10
1.01 0.21 0.08
0.10
1.320.34
0.310.09
B ( r , r 0 , w) I -avg g
0.12
0.550.43
0.370.11
Extracting |Vtd /Vts| from bd g Decays
Belle, PRL 96, 221601 (2006).
Vtd
0.018
0.1990.026
0.025 0.015
Vts
courtesy M. Bona (UTfit collab.)
BABAR, hep-ex/0607099
(preliminary)
Vtd
0.017
0.1710.018
0.021 0.014
Vts
CDF, hep-ex/0606027
(preliminary)
Vtd
0.008
0.2080.001
0.002 0.006
Vts
Consistent within errors.
Theoretical uncertainties limiting both approaches.
BKl+l- and BK*l+l- in the SM and Beyond
Photon penguin
g
b
d
Z penguin
u, c, t
W
u, c, t
W
d
d
W+W- box
b
Z
b
s
W
s
d
W
s
u, c, t
d
d
• Dependence on kinematic variables in 3-body decays can be used to
study the different amplitudes and their interference effects.
• The mode BKl+l- is allowed as well as BK*l+l- (BKg forbidden
by conservation of angular momentum).
Amplitude for BK*l+lM (B K
*
GF EM *
)
VtsVtb C9eff K * s g m PLb B
2p
mix of Z-penguin,
W+W-
box
Kruger and Matias; PRD 71, 094009 (2005)
photon penguin
dom. at v. low q2
mb eff
*
2 2 C7 K sis m q PRb B g m
q
C10 K * s g m PLb B
g mg 5
Short-distance physics encoded in Ci’s (Wilson coefficients);
calculated at NNLO in SM:
Ali et al., PRD 61, 074024 (2000)
C7eff 0.3 C9 +4.3 C10 4.7
C9, C10 generate asymm. in lepton angular distribution over most of q2.
Ci’s can be affected by new physics, which enters at same order as SM
Form Factors and Observables
Long distance QCD physics is mainly described in terms of form
factors, which are functions of q2 ( p p )2
• 4 semileptonic form factors: A1, A2, V, A0 (similar to BD*l, Brl
• 3 penguin form factors: T1, T2, T3
Form factor uncertainies 35% uncertainty in rate predictions.
K
K
B
K*
d
d
d
cos
0 d cos
1 d cos d cos
1
AFB
p
0
d
d
d
cos
0 d cos
1 d cos d cos
1
0
( s q2 )
dAFB
mm
C10 Re C9eff VA1 + b B C7eff
ds
s
0.16
2
s0 4.07 0.13
GeV
mK *
VT2 1
mB
mK *
ˆ
(1
m
)
AT
1
1 1
K*
mB
Precise SM prediction due to ff cancellation.
Predictions for AFB in BK*l+l-: SM and beyond
q q
2
q
2
q2 qmax
2
min
s
K*
K* s
q
C7eff C7 (SM)
Standard Model
C9eff C10eff C9 (SM)C10 (SM)
0.16
s0 4.07 0.13
GeV 2
C7eff C7 (SM), C9eff C10eff C9 (SM)C10 (SM)
BKl+l- and BK*l+l- : q2 distributions
B Kmm
B K *m m
J/yK
SUSY models
Pole from K*g, even in m+m-
y(2S)K
SM nonres
SM nonres
q2
q2
constructive interf.
destructive
BKl+l- and BK*l+l-: the J/y veto
The decays BJ/y K and BJ/y K* are huge backgrounds and
must be carefully removed (also By(2S)K, y(2S)K*).
These backgrounds are restricted in q2, but there is a tail due to
bremsstrahlung in the electron modes.
But BJ/y K and BJ/y K* are valuable control samples; use
them to study efficiency of almost any analysis cut.
Ali, Kramer, Zhu: B( B K *
J/y and y(2S) veto: MC BKe+e-
m
7
;1 q2 7 GeV2 ) (2.920.67
)
10
0.61
m(e+e-) projection: MC BKe+e-
BKl+l- Signal from BABAR
BABAR, PRD 73, 092001 (2006)
9.8
Nsig 45.5-8.9
• summed over all K l+l- modes (K+e+e-, K+m+m- KS e+e-, KS m+m-)
• significance 6.6 s; rarest observed B decay
B( B K
) (0.34 0.07 0.02) 106
(averaged)
BK*l+l- Signal from BABAR
BABAR, PRD 73, 092001 (2006)
13.7
Nsig 57.1-12.5
B( B K *
6
) (0.780.19
0.11)
10
0.17
229 M BB
BK(*)l+l- Signals from Belle
Belle, PRL 96, 251801 (2006)
386 M BB
Nsig 96.0 12.0
Nsig 113.6 13.0
(data sample used for study of Wilson coefficients)
BKl+l- and BK*l+l- branching fractions
BABAR (10-6)
Mode
PRD 73, 092001 (2006)
BK
B K*
Belle (10-6)
preliminary
0.340.07
0.07 0.02
0.5500.075
0.070 0.027
0.780.19
0.17 0.11
1.650.23
0.22 0.11
BK*l+l-: BABAR results on K* polarization and AFB
1 d
3
3
FL cos2 K (1 FL )sin 2 K
d cos K 2
4
use in 2 bins
of q2
BABAR, PRD 73, 092001 (2006)
K* polarization
Data
SM
C7 C7 (SM)
Polarization consistent with SM, but doesn’t discriminate
against new physics scenarios with current data sample.
Theory predictions in graphs: Ali et al., PRD 66, 034002 (2002); Ball and Zwicky, PRD 71, 014029 (2005).
BK*l+l-: BABAR results on AFB and L
1 d
3
3
2 *
F
sin
(1 FL )(1 cos2 l* ) AFB cos l*
L
l
*
d cos l 4
8
use in 2 bins
of q2
Data
C7 C7 (SM)
SM
C9eff C10eff C9 (SM)C10 (SM)
C7eff C7 (SM),
C9eff C10eff C9 (SM)C10 (SM)
excluded at 3.6s!
Any AFB<0 excluded at >2.7s
q2 range (GeV2)
0.1 8.41
10.42
AFB B K
AFB
0.19 (95% C.L.)
0.15
0.21
0.23
0.720.28
0.26 0.08
0.08
q
2
FL
0.770.63
0.30 0.07
0.510.22
0.25 0.08
0.1 GeV 2 (AFB=0 in SM and many BSM)
Belle results on AFB for BK(*)l+lB K*
SM: A7 0.33, A9 4.07, A10 4.21
A7 A7 (SM)
Standard Model
A7 0.28, A9 2.22, A10 3.82
A7 0.28, A9 2.42, A10 3.82
AFB B K *
AFB B K
0.50 0.15 0.02
0.10 0.14 0.01
q
Belle, PRL 96, 251801 (2006)
2
Belle results on Wilson coefficients for BK(*)l+l• fix |A7| to SM (BXs g)
• fit for A9/A7 and A10/A7
• data consistent with SM SM
• quadrants II, IV allowed
fit
A10>0
SM
12.3
12.8
1400
A9 A10
26.4
2
A7
95% C.L. A9 A10 < 0 excludes quadrants I,III
at 98.2% C.L.
Inclusive B Xs g
• Canonical process for studying bs transition. Theory uncertainties
currently at 10% level (NLO); pushing toward 5% (NNLO).
• Huge theoretical effort to predict branching fractions & photon
energy spectrum.
• Branching fraction measures |C7|; spectrum is insensitive to new
physics but is sensitive to mb and Fermi motion of b-quark (“shape
function”).
Eg 1.6 GeV
T. Hurth, E. Lunghi, W. Porod, Nucl. Phys. B 704, 56 (2005).
B( B X sg ) 3.61 0.24
0.40
mc / mb
ACP ( B X sg ) (0.42 0.08mc / mb 0.03CKM
0.15
0.08 scale
M. Neubert, Eur. Phys. J. C 40, 165 (2005).
B( B X sg ) 3.47 0.33
0.41
0.02CKM 0.24param 0.14scale 104
0.32
pert 0.29 param
104
)%
Inclusive B Xs g: some history
CLEO, PRL 74, 2885 (1995); 2.01 fb-1 on Y(4S), 0.96 fb-1 below Y(4S)
Backgrounds: B decays, continuum, e+e-qqg (ISR), e+e-qqp0X
“Event-shape analysis”
“B-reconstruction analysis”
total background
(points w/error bars)
scaled off resonance
Eg
B( B X sg ) (2.32 0.57 (stat.) 0.35 (sys.)) 104
Challenges of inclusive B Xs g
• Weak experimental signature: single high-energy photon + eventshape cuts. Lots of background from p0’s and h’s! Fully inclusive
analysis is not able to exploit the kinematic constraints (mB, E).
• Difficult to carry analysis down to Eg < 2.0 GeV.
• Want to push toward 5% precision to match the expected precision
of NNLO calculations. (It’s amazing that you can do this analysis
at all!)
• Two methods have evolved from initial CLEO approaches.
Method
Fully inclusive
don’t reconstruct Xs
Advantages
Closest correspondence to
inclusive B(BXs g).
Sum of exclusive Less background due to
BK n(p g
additional kinematic
constraints. Better Eg
resolution.
Disadvantages
Large background; limited
sensitivity at low Eg .
More model dependence due to
finite set of explicitly
reconstructed BXs g decays.
Fully inclusive B Xs g: pushing down the
energy threshold
CLEO, PRL 87, 215807 (2001), 9.1 fb-1
Belle, PRL 87, 061803 (2004), 140 fb-1
Belle, hep-ex/0508005
4
BF (3.21 0.43 0.270.18
)
10
0.10
0.11
4
BF (3.55 0.320.30
)
10
0.31 0.07
Measure for Eg>2.0; extrap. to Eg>0.25 GeV Measure for Eg>1.8 GeV; extrap. to full
Fully inclusive, lepton-tagged B Xs g (BABAR)
• Want to suppress large continuum background.
• Strengthen signature for signal by using decay of 2nd B in event.
• Require high energy lepton: pe*>1.25 GeV, pm>1.9 GeV in addition
to event-shape cuts.
• Tag does not compromise inclusiveness of Xs selection.
BB
dom.
qq + ττ
1.9 Eg* 2.7 GeV
BB
(blind)
XSγ
contin.
dom.
lepton tag from 2nd B meson
BABAR Fully Inclusive B Xs g, w/lepton tag
hep-ex/0607071 (preliminary, submitted to PRL)
88.5 106 BB events
Spectrum from
best fit to kinetic scheme.
Spectrum from
best fit to shape function
scheme.
not efficiency corrected
B( B X sg ) (3.67 0.29 0.34 0.29) 104 Eg 1.9 GeV (measured)
(extrapolated,
B( B X sg ) (3.94 0.31 0.36 0.21) 104 Eg 1.6 GeV
kinetic scheme)
BABAR B Xs g with Sum of Exclusive Final States
Reconstruct 38 exclusive modes
K ( ,,0)
( 4p )
• |E|<40 MeV
• Fit mES distrib. in bins of
m(Xs)
• Correct for efficiency of
each mode and missing
modes fraction (model
dependence)
summed over all m(Xs):
K ( , ,0)
h
( 2p )
3K ( ,,0)
( 1p )
comb. BB
continuum
peaking bknd
signal
BABAR B Xs g with Sum of Exclusive Final States
BABAR, PRD 72, 052004 (2005)
K*(890)
Energy Range Branching
Fraction (10-4)
0.04
Eg >1.9 GeV 3.27 0.180.55
0.40 0.09
0.04
3.35 0.190.56
0.41 0.09
Eg >1.6 GeV
(extrapolated)
• averages over two shape-function schemes
• errors: stat, sys, variation of shape fcn params
K*(890)
Value (GeV or GeV2)
Eg Moments
2.321 0.0380.017
0.038
Eg
Eg Eg
2
2
0.0253 0.01010.0041
0.0028
• Eg (min) = 1.897 GeV
Summary of B Xs g Branching Fraction Measurements
B( B X sg ) (3.55 0.24
0.09
0.10
4
0.03) 10
HFAG
average
Extraction of heavy-quark expansion
parameters from BXs g
Using heavy-quark expansion (HQE), moments of inclusive B decay
distributions can be expressed in terms of non-perturbative QCD
parameters and quark masses.
• BXs g inclusive Eg spectrum
• BXc l inclusive El spectrum and M(Xc) hadron mass distrib.
• mb now determined to about 1% and |Vcb| is determined to <2%.
Eg
Eg Eg
2
mb
2
2
g (mb , mp2 ,...)
(kinetic energy squared of b-quark)
Fits to moments of inclusive BXc l and BXs g
distributions
Buchmüller and Flächer, PRD 73, 073008 (2006);
Data from BaBar, Belle, CDF, CLEO, & DELPHI
mp
Vcb
2
(GeV 2 )
b sg
all moments
(10 3 )
all moments
bc
bc
mb
mb
kinetic mass scheme
mb (4.590 0.025exp 0.030HQE ) GeV mp2 (0.401 0.019exp 0.035HQE ) GeV2
Vcb (41.96 0.23exp 0.35HQE 0.59sl ) 103 mb used for |Vub| (7.5% error!)
Conclusions
Studies of radiative/electroweak penguins have moved far beyond
BK*g.
Observation of exclusive bd g decays: B(r0, r+, w) g
Use to extract |Vtd/Vts|; consistent with value from Bs mixing.
Precision limited by theoretical uncertainties.
Electroweak penguins decays BK l+ l-, BK* l+ l-, and
BXs l+ l- have been measured. First studies of decay
distributions have been performed and exclude some non-SM
scenarios. Much more data needed to exploit full potential.
Inclusive BXs g measurements provide information on mb
and non-pert. QCD parameters and help improve precision on
|Vcb| and |Vub|. Difficult issues with systematic errors, but goal si
to achieve 5% uncertainty on branching fraction.
Much more to learn about penguins; we will study them for
many years to come at BaBar, Belle, and LHC-b!
Backup slides
BK*l+l-: K* polarization vs. q2
SM
M(l+l-) distributions from BJ/y K+ control
samples: data vs. Monte Carlo
BABAR
points: data
histogram: MC
absolute normalization
Bremsstrahlung tails well described by MC.
Lepton angular distribution in l l rest frame
l
l
sq m
2
2
l
B
s
q
K
*
use l- if B
use l+ if B
dAFB
C10 Re C9eff VA1
ds
mbmB eff
+
C7
s
mK *
VT2 1
mB
mK *
(1 mˆ K * ) AT
1 1 1
mB
T2 ( s0 ) mK *
s0
mb
C7eff
1
2
eff
mB
mB Re C9 s0 A1 ( s0 )
mB
0.16
2
s0 4.07 0.13
GeV
T1 ( s0 ) mK *
1
mB
V ( s0 )
Ali, Kramer, Zhu, hep-ph/0601034
BK*l+l- Dalitz plot
Can see AFB behavior and q2 dependence from the Dalitz plot
q2
AFB >0
effect of g pole
1
cos
1
AFB 0 at q2
4 GeV 2
AFB 0
E
Note: BKl+l- is expected to have very small AFB, even in presence of
new physics; effectively provides a crosscheck.
Extracting AFB and FL in bins of q2
1 d
3
3
2
FL cos K (1 FL )sin 2 K
d cos K 2
4
1 d
3
3
2 *
2 *
*
F
sin
(1
F
)(1
cos
)
A
cos
L
l
L
l
FB
l
*
d cos l 4
8
BABAR, PRD 73, 092001 (2006)
q2 0.1 GeV2
q 0.1 GeV
2
2