Transcript Semileptonic B Decays

Semileptonic B Decays
Masahiro Morii
Harvard University
Determination of |Vub| and |Vcb| with
Inclusive and Exclusive
b  un and b  cn Decays
APS Meeting, April 22-25, 2006
The Unitary Triangle
goal: Over-constrain the apex (  , ) to test the
completeness of the Cabibbo-Kobayashi-Maskawa model
 The
Left side: |Vub /Vcb|
Angles: CP violation

  21.71.3
1.2 degrees  Let’s measure the opposite side precisely!
APS April Meeting 2006
M. Morii, Harvard
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Semileptonic B Decays

Natural probe for |Vub| and |Vcb|
Parton level
W
b


Hadron level
n
b
B
Vub ,Vcb
u, c


Vub
u
XXuu , X c
Gc larger than Gu by a factor ~50


Decay rate Gx G(b  xn)  |Vxb|2
n
Extracting b  un signal challenging
Sensitive to hadronic effects
Must understand them to extract |Vub|, |Vcb|
 Use data to bolster theory

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M. Morii, Harvard
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Inclusive vs. Exclusive
Inclusive B  Xcn
W
B
Exclusive B  D*n
n

W
B
Vcb
D*
B
Exclusive B  pn
n
W

Xu
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n
W
B
Vub

Vcb
Xc
Inclusive B  Xun
n
M. Morii, Harvard
Vub

p
4
Inclusive Measurements
Inclusive B  Xcn
n
W
B
 Operator

GF2 Vub mb5 
 s
1  O 
3
192p
p

Vcb
Xc
Inclusive B  Xun
n
W
B
Product Expansion
predicts total rate Gu as
 1 

 O  2  

 mb 
Perturbative terms
known to O(s2)
Non-perturb. terms
suppressed by 1/mb2

Dominant error from mb5


mb measured to 1%
 2.5% on |Vub|
 Total
Vub
Xu
rate can’t be measured
due to B  Xcnbackground

APS April Meeting 2006



2
M. Morii, Harvard
Must enhance S/B with cuts
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Kinematical Cuts
Three independent kinematic variables in B → Xv
Not to scale!
decay rate

bc
bu
E = lepton energy


bu
bu
q2 = n mass squared
bc
mX = hadron system mass
Measure partial rates in favorable regions of the phase space
Caveat: Spectra more sensitive to non-perturbative effects than
the total rate  O(1/mb) instead of O(1/mb2)


bc
No detector
resolution!
Need to know the Shape Function (= what the b-quark is doing
inside the B meson)
Solution: Measure B  Xcnspectra  Non-perturb. effects
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Inclusive B  Xcn Spectra
 Observables:

E (lepton energy) and mX (hadron system mass)
Measurements by BABAR, Belle, CDF, CLEO, DELPHI
Belle, hep-ex/0508056
E (GeV)
 OPE
Belle, hep-ex/0509013
E (GeV)
mX2 (GeV2/c4)
predicts observables integrated over large phase space
 Moments: E n 
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Gc
E  E

n
d Gc
dE
dE
M. Morii, Harvard
mXn 
1
n d Gc
m
dmX
X

Gc
dmX
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Global OPE Fit
predicts total rate Gc and moments En, mXn as functions
of |Vcb|, mb, mc, and several non-perturb. params
 OPE

 Eg
Each observable has different dependence
 Can determine all parameters from a global fit
spectrum in B  Xsg decays connected directly to the SF
Small rate and high background makes it tough to measure
 Measured by BABAR, Belle, CLEO
hep-ex/0507001
BABAR
APS April Meeting 2006
PRD 72:052004
Eg (GeV)
M. Morii, Harvard
Partial BF (10-4/100 MeV)
Partial BF (10-3/100 MeV)

BABAR
preliminary
Eg (GeV)
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OPE Fit Results
BABAR
PRD69:111103 PRD69:111104
PRD72:052004 hep-ex/0507001
Belle
PRL93:061803 hep-ex/0508005
CLEO
PRD70:031002 PRL87:251807
CDF
PRD71:051103
DELPHI EPJ C45:35
& Flächer (hep-ph/0507253)
fit data from 10 measurements with an OPE calculation by
Gambino & Uraltsev (Eur. Phys. J. C34 (2004) 181)
 Buchmüller

Fit parameters: |Vcb|, mb, mc, mp2, mG2, D3, LS3, BR(B  Xcn
Vcb  (41.96  0.23exp  0.35OPE  0.59Gsl ) 10 3
2%
mb  4.590  0.025exp  0.030OPE GeV
1%
mc  1.142  0.037 exp  0.045OPE GeV
Needed for |Vub|
b  sg
mp2  0.401  0.019exp  0.035OPE GeV 2
BR  10.71  0.10exp  0.08OPE %

Goodness of the fit and the consistency
between Xcn and Xsg add confidence
to the theory
APS April Meeting 2006
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b  cn
combined
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Inclusive B  Xun
 Measure
partial BF DB(B  Xun in a region where ...
the signal/background is good, and
 the partial rate DGu is reliably calculable

possibilities – Review a few recent results
25
20
b  uv
15
10
5
b  cv
0.5
1
1.5
2
b  cv
2.5
mX (GeV)
E (GeV)
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b  uv
mX cut
mX-q2 cut
q2 (GeV2)
E endpoint
q2 (GeV2)
 Many
Large DGu generally
good, but not always
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Lepton Endpoint

BABAR PRD 73:012006
Belle PLB 621:28
CLEO PRL 88:231803
Find leptons with large E
Push below the charm threshold
 Larger signal acceptance
 Smaller theoretical error
 S/B ~ 1/15 (E > 2 GeV)  Accurate
subtraction of background is crucial!
BABAR

BABAR 80fb-1
Belle 27fb-1
E (GeV)
|Vub| (10-3)
2.0–2.6
4.41  0.29exp 
0.31SF+theo
1.9–2.6
4.82  0.45exp 
0.30SF+theo
Data
MC bkgd.
b  cv
Data – bkgd.
MC signal
b  uv
-1
Shape9fb
Function:
determined from
theOPE
CLEO
2.2–2.6
4.09
0.48fitexp 
0.36SF+theo
Theory errors: Lange et al. PRD72:073006
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BABAR hep-ex/0507017
Belle PRL 95:241801
Hadronic B Tag

reconstructed B
Fully reconstruct one B in hadronic decays
Use the recoiling B with known charge and momentum
 Access to all kinematic variables

P  EX  PX
253M BB
v
lepton
Belle 253M BB
Region
|Vub| (10-3)
mX < 1.7 GeV, q2 > 8 GeV2
4.70  0.37exp 
0.31SF+theo
mX < 1.7 GeV
4.09  0.28exp 
0.24SF+theo
P > 0.66 GeV
4.19  0.36

X
Prelim.
|Vub| from Inclusive B  Xun

|Vub| determined to 7.4%


Experimental
4.5%
SF params.
4.1%
Theory
4.2%
Expt. and SF errors will
improve with more data
Theory errors from

World Average 4.45  0.33
Sub-leading SF (3.8%)

c2/dof = 5.5/6

Weak annihilation (1.9%)

APS April Meeting 2006
M. Morii, Harvard
Higher-order nonperturbative corrections
Can be constrained with
future measurements
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BABAR hep-ex/0601046
SF-Free |Vub| Measurement

Possible to combine b  uv and b  sg so that the SF cancels
G( B  X u n ) 
Vub
Vts
2
2
 W ( Eg )
d G( B  X s g )
dEg
dEg
Weight function

BABAR applied Leibovich, Low, Rothstein
(PLB 486:86) to 80 fb-1 data
mX cut
Full
rate
Theory error
|Vub| (10-3)
1.67 GeV 4.43  0.45exp  0.29theo
Expt. error
2.5 GeV 3.84  0.76exp  0.10theo
Trade SF error  Stat. error
1.67
 mX < 2.5 GeV is almost (96%) fully
inclusive  Theory error reduces to 2.6%

APS April Meeting 2006
M. Morii, Harvard
mX cut (GeV)
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Inclusive vs. Exclusive
Inclusive B  Xcn
W
B
Exclusive B  D*n
n

W
B
Vcb
D*
B
Exclusive B  pn
n
W

Xu
APS April Meeting 2006
n
W
B
Vub

Vcb
Xc
Inclusive B  Xun
n
M. Morii, Harvard
Vub

p
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Exclusive Measurements
 Exclusive
rates determined by
|Vxb| and Form Factors

Theoretically calculable at
kinematical limits


D* or
Lattice QCD works if
is ~ at rest relative to B
p
Vcb
Exclusive B  pn
n
W
B
Then use FF normalization
from the theory
APS April Meeting 2006

D*
 Measure

n
W
B
Empirical extrapolation is
necessary to extract |Vxb| from
measurements
differential rates to
constrain the FF shape
Exclusive B  D*n
M. Morii, Harvard
Vub

p
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Exclusive B  D*n
 Decay
rate is
form factor
2
2
d G( B  D ln ) GF Vcb
2
d

F
(
w
)
G(w)
3
dw
48p
D* boost in the B rest frame
*
phase space
F(1) = 1 in the heavy-quark limit; lattice QCD: F (1)  0.9190.030
0.035
Hashimoto et al,
 F(w) shape expressed by 2 (slope at w = 1) and
PRD 66 (2002) 014503
R1, R2 (form factor ratios)


Curvature constrained by analyticity
 Measure

Caprini, Lellouch, Neubert
NPB530 (1998) 153
decay angles q, qV, c
Fit 3-D distribution in bins of w
to extract 2, R1, R2
APS April Meeting 2006
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BABAR hep-ex/0602023
B  D*n Form Factors
 BABAR
measured FF params. with 79
w

R2  0.885  0.040stat  0.026syst
 2  1.145  0.059stat  0.046syst
Using BABAR measurements only
APS April Meeting 2006
Signal MC vs. bkgd.-subtracted
data, 1D projections
cosqV
cosq
R1  1.396  0.060stat  0.044syst
fb-1
c
R1 and R2 improved by a factor 5
over previous CLEO measurement
PRL 76 (1996) 3898

Will improve all measurements of B
 D*n
M. Morii, Harvard
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|Vcb| from B  D*n
 HFAG
average still uses FF from CLEO
Average 37.6  0.8
c2/dof = 30.2/14
New BABAR FF
|Vcb| = (40.9  0.9  1.5F(1))  10-3 c.f. (42.0  0.7)10-3 from inclusive OPE fit
APS April Meeting 2006
M. Morii, Harvard
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Exclusive B  pn


B  pv rate is given by
GF2
d G( B  p n )
2
3
2 2

Vub pp f  (q )
2
3
dq
24p
One FF for B → pv
with massless lepton
Form factor f+(q2) has been calculated using

Lattice QCD



Unquenched calculations by
Fermilab (hep-lat/0409116) and
HPQCD (PRD73:074502)
12% for q2 > 16 GeV2
Light Cone Sum Rules


Ball & Zwicky (PRD71:014015)
13% for q2 < 16 GeV2
Ball-Zwicky
Fermilab
HPQCD
ISGW2
Quark model, PRD52 (1995) 2783
APS April Meeting 2006
M. Morii, Harvard
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BABAR PRD 72:051102
Untagged B  pn

Missing 4-momentum = neutrino

Reconstruct B  pv and calculate mB and DE  EB  s 2
data
MC signal
signal with
wrong p
b  uv
b  cv
other bkg.
BABAR 80fb-1 PRD72:051102
B(B0  p  n )  (1.38  0.10stat  0.18syst ) 104
BABAR

Measured q2 spectrum starts to constrain
the FF shape

APS April Meeting 2006
LQCD/LCSR favored over ISGW2
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BABAR hep-ex/0506064, 0506065
Belle hep-ex/0508018
D(*)n-tagged B  pn

Reconstruct one B in D(*)v and look for B  pv in the recoil


B  D*n BF large; two neutrinos in the event
Event kinematics determined assuming
known mB and mv = 0
pn
253fb-1
Belle
Signal appears in 0 < xB2 < 1
APS April Meeting 2006
p
D

v
n
M. Morii, Harvard
soft p
v

Mode
BF (10-4)
B0  pn 1.38  0.24
B+  p0n 0.77  0.16
0

BABAR B  p n 1.02  0.28
Prelim. B+  p0n 1.86  0.44
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|Vub| from B  pn
 Average
BF measurements and apply FF calculations
DB(q2 < 16) (10-4)
0.94  0.06stat 
0.06syst
Form Factor q2 (GeV2)
Ball-Zwicky
< 16
HPQCD
> 16
FNAL
> 16
DB(q2 > 16) (10-4)
Total B (10-4)
0.39  0.04stat 
0.04syst
|Vub| (10-3)
1.34  0.08stat 
0.08syst
3.36  0.15exp 0.55
0.37 theo
4.20  0.29exp 0.63
0.43theo
3.75  0.26exp 0.65
0.43 theo
LCSR
Unquenched
LQCD
Inclusive: 4.45  0.20exp  0.26SF+theo
Consistent within (large)
FF errors
 Experimental errors already competitive

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Summary


Semileptonic B decays offer exciting physics opportunities
 |Vub /Vcb| complements sin2 to test (in)completeness of the SM
Challenge of hadronic physics met by close collaboration
between theory and experiment
 Inclusive B  Xcn & Xsg fit precisely determines |Vcb|, mb, etc.


Inclusive |Vub| achieved 7.4% accuracy



Dramatic progress in both measurement and interpretation of
inclusive B  Xun in the last 2 years
Room for improvements with additional data statistics
B  D*n form factors have improved by a factor 5
Measurements of B  pnbecoming precise

Improved form factor calculation needed
APS April Meeting 2006
M. Morii, Harvard
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Backup Slides
Weak Annihilation

WA turns B+ into n+ soft hadrons

Size and shape of WA poorly known
Minimize the impact



Measure Xun with v. loose cuts

Cut away large q2 region
Measure WA contribution

Gsl(D+) vs. Gsl(Ds)


Distortion in q2


CLEO-c
CLEO hep-ex/0601027
G(B+  Xun) vs. G(B0  Xun)

Work in progress
APS April Meeting 2006
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