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Semileptonic B Decays
Masahiro MoriiHarvard University
Determination of |Vub| and |Vcb| withInclusive and Exclusive
b u and b c Decays
APS Meeting, April 22-25, 2006
APS April Meeting 2006 M. Morii, Harvard 2
The Unitary Triangle The goal: Over-constrain the apex to test the
completeness of the Cabibbo-Kobayashi-Maskawa model
Let’s measure the opposite side precisely!
( , )
Angles: CP violation
Right side: md /m
s
Left side: |Vub /Vcb|
1.31.221.7 degrees
APS April Meeting 2006 M. Morii, Harvard 3
B
uX
b
u
ubVB
, cuX X
Hadron level
Semileptonic B Decays Natural probe for |Vub| and |Vcb|
Decay rate x (b x) |Vxb|2
c larger than u by a factor ~50 Extracting b u signal challenging
Sensitive to hadronic effects Must understand them to extract |Vub|, |Vcb|
Use data to bolster theory
b
,u c
, cub bV V
Parton level
W
APS April Meeting 2006 M. Morii, Harvard 4
Inclusive vs. ExclusiveInclusive B Xc
Inclusive B Xu
B
W
cX
cbV
B
W
uXubV
Exclusive B D*
B
W
*DcbV
Exclusive B
B
W
ubV
APS April Meeting 2006 M. Morii, Harvard 5
Inclusive Measurements Operator Product Expansion
predicts total rate u as
Dominant error from mb5
mb measured to 1% 2.5% on |Vub|
Total rate can’t be measured due to B Xcbackground Must enhance S/B with cuts
5
2
22
31
192
1
b
b sF ubG V
m
m
OO
Perturbative terms known to (s
2)Non-perturb. terms suppressed by 1/mb
2
Inclusive B Xc
Inclusive B Xu
B
W
cX
cbV
B
W
uXubV
APS April Meeting 2006 M. Morii, Harvard 6
Three independent kinematic variables in B → Xv
Measure partial rates in favorable regions of the phase space Caveat: Spectra more sensitive to non-perturbative effects than
the total rate (1/mb) instead of (1/mb2)
Need to know the Shape Function (= what the b-quark is doing inside the B meson)
Solution: Measure B Xcspectra Non-perturb. effects
Kinematical Cuts
q2 = mass squared mX = hadron system massE = lepton energy
b c
b u
b c
b ub c
b u
Not to scale!
No detector resolution!
Not to scale!
No detector resolution!
deca
y ra
te
APS April Meeting 2006 M. Morii, Harvard 7
Inclusive B Xc Spectra
Observables: E (lepton energy) and mX (hadron system mass) Measurements by BABAR, Belle, CDF, CLEO, DELPHI
OPE predicts observables integrated over large phase space
Moments:
Belle, hep-ex/0508056
E (GeV) E (GeV)
1 c
c
n n dE E d
dEE E
1n
Xn cX X
c X
dm dm
dmm
mX2 (GeV2/c4)
Belle, hep-ex/0509013
APS April Meeting 2006 M. Morii, Harvard 8
Global OPE Fit OPE predicts total rate c and moments E
n, mXn as functions
of |Vcb|, mb, mc, and several non-perturb. params Each observable has different dependence
Can determine all parameters from a global fit
E spectrum in B Xs decays connected directly to the SF Small rate and high background makes it tough to measure Measured by BABAR, Belle, CLEO
BABAR
preliminary
E (GeV)
Par
tial
BF
(10
-4/1
00 M
eV)
hep-ex/0507001
Par
tial
BF
(10
-3/1
00 M
eV)
BABAR PRD 72:052004
E (GeV)
APS April Meeting 2006 M. Morii, Harvard 9
OPE Fit Results Buchmüller & Flächer (hep-ph/0507253)
fit data from 10 measurements with an OPE calculation by Gambino & Uraltsev (Eur. Phys. J. C34 (2004) 181)
Fit parameters: |Vcb|, mb, mc, 2, G
2, D3, LS
3, BR(B Xc
Goodness of the fit and the consistencybetween Xc and Xs add confidenceto the theory
Needed for |Vub|3
exp OPE
exp OPE
exp OPE
2 2exp OPE
exp OPE
(41.96 0.23 0.35 0.59 ) 10
4.590 0.025 0.030 GeV
1.142 0.037 0.045 GeV
0.401 0.019 0.035 GeV
10.71 0.10 0.08 %
slcb
b
c
V
m
m
BR
2%
1%
BABARPRD69:111103 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
combined
b s
b c
APS April Meeting 2006 M. Morii, Harvard 10
Inclusive B Xu Measure partial BF (B Xu in a region where ...
the signal/background is good, and the partial rate u is reliably calculable
Many possibilities – Review a few recent results
0.5 1 1.5 2 2.5
5
10
15
20
25
b cv
E (GeV)
q2 (G
eV2 )
b uv
E endpoint
E -q2 cut
q2 (G
eV2 )
mX (GeV)
b cv
b
uv
mX cut
mX-q
2 cut
Large u generally good, but not always
APS April Meeting 2006 M. Morii, Harvard 11
Lepton Endpoint 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!
E (GeV) |Vub| (10-3)
BABAR 80fb-1 2.0–2.6 4.41 0.29exp 0.31SF+theo
Belle 27fb-1 1.9–2.6 4.82 0.45exp 0.30SF+theo
CLEO 9fb-1 2.2–2.6 4.09 0.48exp 0.36SF+theo
BABAR PRD 73:012006Belle PLB 621:28
CLEO PRL 88:231803
BABAR
MC bkgd.b cv
Data
Data – bkgd.
MC signalb uv
Shape Function: determined from the OPE fit
Theory errors: Lange et al. PRD72:073006
Hadronic B Tag Fully reconstruct one B in hadronic decays
Use the recoiling B with known charge and momentum Access to all kinematic variables
BABAR hep-ex/0507017Belle PRL 95:241801
lepton
v
X
253M BB
X XP E P
Region |Vub| (10-3)
Belle 253M BB
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 0.36exp 0.28SF+theo
BABAR 210M BB mX < 1.7 GeV, q2 > 8 GeV2 4.75 0.35exp 0.32SF+theo
reconstructed B
Prelim.
APS April Meeting 2006 M. Morii, Harvard 13
|Vub| from Inclusive B Xu |Vub| determined to 7.4%
Expt. and SF errors will improve with more data
Theory errors from Sub-leading SF (3.8%)
Higher-order non-perturbative corrections
Weak annihilation (1.9%) Can be constrained with
future measurements
Experimental 4.5%
SF params. 4.1%
Theory4.2
%
World Average 4.45 0.33
2/dof = 5.5/6
APS April Meeting 2006 M. Morii, Harvard 14
SF-Free |Vub| Measurement
Possible to combine b uv and b s so that the SF cancels
BABAR applied Leibovich, Low, Rothstein(PLB 486:86) to 80 fb-1 data
Trade SF error Stat. error mX < 2.5 GeV is almost (96%) fully
inclusive Theory error reduces to 2.6%
2
2 ( )( )
( ) ub su
ts
W EV d B X
B X dEdEV
Weight function
BABAR hep-ex/0601046
mX cut (GeV)1.67
Theory error
Expt. errormX cut |Vub| (10-3)
1.67 GeV
4.43 0.45exp 0.29theo
2.5 GeV 3.84 0.76exp 0.10theo
Fullrate
APS April Meeting 2006 M. Morii, Harvard 15
Inclusive vs. ExclusiveInclusive B Xc
Inclusive B Xu
B
W
cX
cbV
B
W
uXubV
Exclusive B D*
B
W
*DcbV
Exclusive B
B
W
ubV
APS April Meeting 2006 M. Morii, Harvard 16
Exclusive Measurements Exclusive rates determined by
|Vxb| and Form Factors Theoretically calculable at
kinematical limits Lattice QCD works if D* or
is ~ at rest relative to B Empirical extrapolation is
necessary to extract |Vxb| from measurements
Measure differential rates to constrain the FF shape Then use FF normalization
from the theory
Exclusive B D*
B
W
*DcbV
Exclusive B
B
W
ubV
APS April Meeting 2006 M. Morii, Harvard 17
Exclusive B D* Decay rate is
(1) = 1 in the heavy-quark limit; lattice QCD: (w) shape expressed by 2 (slope at w = 1) and
R1, R2 (form factor ratios) Curvature constrained by analyticity
Measure decay angles , V, Fit 3-D distribution in bins of w
to extract 2, R1, R2
22*2
3
( )( ) ( )
48F cbG Vd B D l
w wdw
d F G phase space
form factor
D* boost in the B rest frame0.0300.035(1) 0.919
FHashimoto et al,PRD 66 (2002) 014503
Caprini, Lellouch, NeubertNPB530 (1998) 153
APS April Meeting 2006 M. Morii, Harvard 18
B D* Form Factors BABAR measured FF params. with 79 fb-1
R1 and R2 improved by a factor 5 over previous CLEO measurement PRL 76 (1996) 3898
Will improve all measurements of B D*
BABAR hep-ex/0602023
Signal MC vs. bkgd.-subtracteddata, 1D projections
w cos cosV
1 stat syst
2 stat syst
2stat syst
1.396 0.060 0.044
0.885 0.040 0.026
1.145 0.059 0.046
R
R
Using BABAR measurements only
APS April Meeting 2006 M. Morii, Harvard 19
|Vcb| from B D* HFAG average still uses FF from CLEO
New BABAR FF
c.f. (42.0 0.7)10-3 from inclusive OPE fit
Average 37.6 0.8 2/dof = 30.2/14
|Vcb| = (40.9 0.9 1.5(1)) 10-3
APS April Meeting 2006 M. Morii, Harvard 20
Exclusive B B v rate is given by
Form factor f+(q2) has been calculated using Lattice QCD
Unquenched calculations by Fermilab (hep-lat/0409116) andHPQCD (PRD73:074502)
12% for q2 > 16 GeV2
Light Cone Sum Rules Ball & Zwicky (PRD71:014015) 13% for q2 < 16 GeV2
22 223
2 3
( )
24( )F
ub
Gd BV f
dqqp
One FF for B → vwith massless lepton
Ball-ZwickyFermilabHPQCD
ISGW2
Quark model, PRD52 (1995) 2783
APS April Meeting 2006 M. Morii, Harvard 21
Untagged B Missing 4-momentum = neutrino
Reconstruct B v and calculate mB and
BABAR 80fb-1 PRD72:051102
dataMC signalsignal withwrong b uvb cvother bkg.
BABAR PRD 72:051102
Measured q2 spectrum starts to constrain the FF shape LQCD/LCSR favored over ISGW2
BABAR0 4
stat syst( ) (1.38 0.10 0.18 ) 10B B
2BE E s
APS April Meeting 2006 M. Morii, Harvard 22
D(*)-tagged B Reconstruct one B in D(*)v and look for B v in the recoil
B D*BF large; two neutrinos in the event Event kinematics determined assuming
known mB and mv = 0
vv
D
soft
BABAR hep-ex/0506064, 0506065Belle hep-ex/0508018
253fb-1
Signal appears in 0 < xB2 < 1
Mode BF (10-4)
Belle
B0 1.38 0.24
B+ 0.77 0.16
BABARPrelim.
B0 1.02 0.28
B+ 1.86 0.44
APS April Meeting 2006 M. Morii, Harvard 23
|Vub| from B Average BF measurements and apply FF calculations
Consistent within (large)FF errors
Experimental errors already competitive
Form Factor q2 (GeV2) |Vub| (10-3)
Ball-Zwicky < 16
HPQCD > 16
FNAL > 16
exp theo0.550.373.36 0.15
exp theo0.630.434.20 0.29
exp theo0.650.433.75 0.26
LCSR
UnquenchedLQCD
Inclusive: 4.45 0.20exp 0.26SF+theo
(q2 < 16) (10-4) (q2 > 16) (10-4) Total (10-4)
0.94 0.06stat 0.06syst
0.39 0.04stat 0.04syst
1.34 0.08stat 0.08syst
APS April Meeting 2006 M. Morii, Harvard 24
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 & Xs fit precisely determines |Vcb|, mb, etc.
Dramatic progress in both measurement and interpretation of inclusive B Xu in the last 2 years
Inclusive |Vub| achieved 7.4% accuracy Room for improvements with additional data statistics
B D* form factors have improved by a factor 5 Measurements of B becoming precise
Improved form factor calculation needed
Backup Slides
APS April Meeting 2006 M. Morii, Harvard 26
Weak Annihilation WA turns B+ into + soft hadrons Size and shape of WA poorly known Minimize the impact
Measure Xu with v. loose cuts
Cut away large q2 region Measure WA contribution
sl(D+) vs. sl(Ds) CLEO-c
Distortion in q2
CLEO hep-ex/0601027
(B+ Xu) vs. (B0 Xu) Work in progress
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