Transcript Document

Measuring the apex:
|Vub|, |Vcb| and their
relative phase γ (φ3)
γ
VudVub*
VcdVcb*
ICHEP '06
Р. Ковалевски
R. Kowalewski
U. of Victoria
Canada
|Vub|
|Vcb|
Kowalewski
1
Motivation



Vub is a key element of the CKM matrix
1 graduate student lifetime (~20 years)
ago, we didn’t know that Vub ≠ 0:
Was the KM mechanism for CP viable?
Now the precise determination of
Vub / Vcb provides a benchmark for
testing new physics in other processes
 Vud

 Vcd
 V e  i
 td
Vub e  i 

Vcb


Vtb

Vus
Vcs
Vts
UTFit
FPCP 2006
η
Vub
Vcb
β
ρ
ICHEP '06
Kowalewski
2
Big trees dominate!
The decay channels used to study |Vub|, |Vcb| and their
relative phase are all dominated by tree diagrams
Bb
B
q
Vqb
Vcb
ℓ
KD0
ν
“f”
c, u
q
Vub
D0
B-
Lifetime + semileptonic
decay determine |Vqb|
KInterference allows
phase measurement
ICHEP '06
Kowalewski
3
 Vud

 Vcd
 V e  i
 td
Vus
Vcs
Vts
Vub e  i 

Vcb


Vtb

The magnitudes
|Vcb| and |Vub|
ICHEP '06
Kowalewski
4
|Vcb| and |Vub| from semileptonic B decays
Semileptonic B decay theory

Large BF, only one hadronic current

Inclusive decays b  qℓν:


Vqb
Weak quark decay + QCD
corrections  OPE in as and 1/mb
Exclusive decays B  Xℓν:

Form factors: need Lattice QCD
These inclusive and exclusive determinations
of Vqb are complementary
ICHEP '06
Kowalewski
5
|Vcb| and |Vub| from semileptonic B decays
Semileptonic B decay experiment

Inclusive decays b  qℓν:




Measure lepton
Measure pmiss or associated hadrons
Exclusive decays B  Xqℓν:


Vqb
Measure lepton and specified hadrons
Measurements come from Y(4S)BB
BB
Determine non-B contribution using
data below BB threshold
qq
ICHEP '06
Kowalewski
6
See talk of Urquijo, S10
 Vud

 Vcd
 V e  i
 td
Vus
Vcs
Vts
Vub e  i 

Vcb


Vtb

Inclusive |Vcb|
ICHEP '06
Kowalewski
7
|Vcb| from inclusive decays
Inclusive decay width
Total decay width for b  cℓν:

Γ  Vcb
2
3


 μ 2π μ G2 
 ρ 3D ρ LS

G F2 m b5
0
pert
1  A ew A r, μ  z 0 r    z 2  r, 2 , 2   z 3  r, 3 , 3   ...
192π 3
mb
 mb mb 
 mb mb 


free quark ~1.014 ~0.908
decay
Perturbative
corrections


r = mc / mb
Non-perturbative
power corrections
Similar expressions for b  uℓν, b  sγ
Comparison with data relies on quark-hadron duality
 integrate over “broad” regions of phase space
Low-order moments can be calculated reliably
ICHEP '06
Kowalewski
8
|Vcb| from inclusive decays
Global fit for |Vcb|, mb…
Fit predicted moments of inclusive processes bcℓν and bsγ for
various cuts on kinematic variables:

M xn
El  E0
3
  B  M Xn d  f nx ( E0 , mb , mc , G2 , 2 ,  D3 ,  LS
)
E0
e or γ
energy cut
b-quark
mass
c-quark
mass
Matrix elements
appearing at order
1/mb2 and 1/mb3
Calculations available in “kinetic” and “1S” renormalization schemes

Benson, Bigi, Gambino, Mannel, Uraltsev
(several papers)

ICHEP '06
Bauer, Ligeti, Luke, Manohar, Trott
PRD 70:094017 (2004)
47 measured moments used from DELPHI, CLEO, BABAR, BELLE, CDF
(and, of course, the B lifetime)
Kowalewski
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|Vcb|
(10-3)
41.96 ± 0.23exp± 0.35HQE± 0.59ΓSL
mb [kin](GeV)
4.59 ± 0.025exp± 0.030HQE
μπ2[kin](GeV2)
0.401 ± 0.019exp± 0.035HQE
|Vcb| determined to <2%
Only sinθc known better!
kinetic scheme
bsγ
bcℓν
μπ2 (GeV2)
|Vcb| from inclusive decays
Global fit: results
combined
1S scheme
χ2 / Ndof = 19.3/44
New!
χ2 / N'06
ICHEP
dof = 5.7/17
|Vcb|
(10-3)
42.0±0.7fit±0.5αs ±0.6th
|Vcb|
(10-3)
41.5 ± 0.5fit ± 0.2τB
mb[1S](GeV)
4.73 ± 0.05fit
λ1[1S](GeV2)
-0.30 ± 0.04fit
Kowalewski
mb (GeV)
Buchmüller and Flächer,
PRD 73: 073008 (2006)
mb to 1%;
crucial for |Vub|
[kin]/[1S] values agree after
scheme translation
10
See talks of Dubitzky,
Schwanda, S10
 Vud

 Vcd
 V e  i
 td
Vus
Vcs
Vts
Vub e  i 

Vcb


Vtb

Inclusive |Vub|
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Kowalewski
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

Background bcℓν rate is 50 times signal
Restrict kinematics to suppress background: challenge for theory
 OPE convergence is compromised:



Need light-cone distribution (shape) function of b quark
Relate buℓν directly to bsγ (e.g. Lange, Neubert, Paz, JHEP 0510:084, 2005)
Measure bu rate in regions
dominated by bc
 Theory fine; must fight large
uncertainties from background
In all cases sensitivity
to mbN, N»5
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q2 (GeV2)
|Vub| from inclusive decays
Strategies for isolating
buℓν decays
Points are
buℓν
simulation
bc allowed
Kowalewski
Ee (GeV)
12
|Vub| from inclusive decays
Shape function

bsγ spectrum measured by CLEO, Belle, BaBar

SF moments related to HQE parameters
Eγ
m
 b , E 2γ  E γ
2
2
 μ 2π
hep-ex/0607071
preliminary

Subleading shape functions
differ in bsγ, buℓν
Spectrum in lepton
tagged events
ICHEP '06
Kowalewski
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|Vub| from inclusive decays
New measurements
BaBar result:


PRL 96:221801 (2006)
Fully reconstruct 1 B meson; study
semileptonic decay of other B
Relate
mmax
0
mB / 2 dbs
dbu
dmX to 
W E , Emin dE
Emin
dmX
dE
|Vub|=(4.43 ±0.38 ±0.25 ±0.29) 10-3

Measure up to mX < 2.5 GeV
|Vub|=(3.84 ±0.70 ±0.30 ±0.10) 10-3
CLEO limit Weak Annihilation contributions:
ΓWA / Γbu < 7.4% (90% CL) PRL 96:121801 (2006)
ICHEP '06
Kowalewski
Theory errors are small
Will improve – only
88×106 BB used so far
e+
b
u
ν
Isoscalar
hadron
14
|Vub| from inclusive decays
Theory calculations

Two sets of calculations in use for b  sγ and b  uℓν


Bosch, Lange, Neubert, Paz (BLNP): 3-scale OPE
based on HQET, SCET
PRD 72:073006 (2005)
Andersen, Gardi (DGE): parton-level calculation,
only mb and ΛQCD input
JHEP 0601:097 (2006)

Both provide good description of data; give similar results

Bauer, Ligeti, Luke (BLL): |Vub| using mX-q2 cuts
ICHEP '06
Kowalewski
PRD 64:113004 (2001)
15
|Vub| from inclusive decays
Determination of |Vub|
|Vub| = (4.49±0.19±0.27)×10-3
(BLNP)
Major progress since last ICHEP





ICHEP '06
Good C.L. = 41%
Error budget (in %; total 7.3) :
±2.2stat ±2.8exp ±1.9WA
~ exp
±1.9b2c model ±1.6b2u model
±4.2HQ param ±3.8sub SF
~ theory
DGE: (4.46±0.20±0.20)×10-3
C.L. = 12%
BLL mX-q2: (5.02±0.26±0.37)×103
C.L. = 77%
Many measurements use small
fraction of current data samples.
Aggressive target for 2008 is 5%
Kowalewski
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See talk of
Lopes Pegna, S10
 Vud

 Vcd
 V e  i
 td
Vus
Vcs
Vts
Vub e  i 

Vcb


Vtb

Exclusive |Vcb|
ICHEP '06
Kowalewski
17
|Vcb| from exclusive decays
Exclusive bcℓν
decays

Heavy-to-heavy transition; HQ symmetry applies  unique,
universal FF, unit normalization at zero recoil
Light d.o.f.
unchanged!
before
after
ν
b

e
c
form factors

GF2 Vcb
d B  D*

dw
48 3
2
Fw2 Gw
phase space
D* boost in the B rest frame
mB2  mD2 *  q 2
w
; 1  w  1.504
2mB mD*
ICHEP '06
Kowalewski
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|Vcb| from exclusive decays
BD*ℓν form factor


3 non-trivial form factors; 4 observables:
w and 3 angles
HQET-params:
ρ2 = -dF/dw |w=1 ,
R1 ~ V/A1 and
R2 ~ A2/A1
Two measurements from BaBar; averaged
values:
ρ2 = 1.179 ± 0.048 ± 0.028
R1 = 1.417 ± 0.061 ± 0.044
R2 = 0.836 ± 0.037 ± 0.022
pℓ (GeV)
BaBar
hep-ex/0607076
preliminary
F(1)|Vcb| = (34.68 ± 0.32 ± 1.15)×10-3
BF(B0D*+ℓ-ν) = 4.84 ± 0.39%
ICHEP '06
BaBar
hep-ex/0602023
Kowalewski
w
19
|Vcb| from exclusive decays
|Vcb| from BD(*)ℓν


New HFAG average including updated form-factors
F(1)|Vcb| = (36.2 ± 0.8)×10-3
Using F 1  0.91900..030
035
(Quenched LQCD, PRD 66:014503 (2002))


3
Vcb  39.4 0.871.56

10
1.24
(inclusive: |Vcb|=(42.0±0.7)×10-3


ICHEP '06
Work needed on both experiment
and theory to reach the precision
of the inclusive determination
Similar measurements on BDℓ-ν
are harder; in progress
Kowalewski
20
See talks of Dubitzky,
Schwanda, S10
 Vud

 Vcd
 V e  i
 td
Vus
Vcs
Vts
Vub e  i 

Vcb


Vtb

Exclusive |Vub|
ICHEP '06
Kowalewski
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|Vub| from exclusive decays
BFB  πν   1.44 0.08 0.10 104

B  πℓν

α BK  0.53 0.05 0.04
New BaBar B0  π -ℓ+ν




CLEO

ΔBF q 2  16 Ge V2  0.37 0.04 0.03 104
hep-ex/0607060
High statistics ν-reco method
Significantly improved precision
ISGW2 model: C.L. = 0.07%
Data consistent with Lattice
QCD and Becirevic-Kaidalov
preliminary
q2

New CLEO B0  π -/ρ- ℓ+ν

All q2 combined
preliminary
Good quality ν-reco
BFB  πν   1.37 0.16 0.13 104


ΔBF q 2  16 Ge V2  0.40 0.08 0.05 104
mπℓν BFB  ν   2.91 0.38 0.38 104
ICHEP '06
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|Vub| from exclusive decays
B  πℓν with low
background


Reconstruct (tag) one B in hadronic
or semileptonic decay
Compare what’s left with signal
ICHEP '06
π0ℓν
Belle hep-ex/0604024 BaBar hep-ex/0607089
1.38 ± 0.19 ± 0.14
1.12 ± 0.25 ± 0.10
π0ℓν (s.l. tag) x2τ0/τ+
1.43 ± 0.26 ± 0.16
1.35 ± 0.33 ± 0.19
π+ℓν (had tag)
1.49 ± 0.26 ± 0.06
1.07 ± 0.27 ± 0.19
π0ℓν (had tag) x2τ0/τ+
1.60 ± 0.32 ± 0.11
1.52 ± 0.41 ± 0.20
ρ0ℓν / ηℓν
1.33 ± 0.23 ± 0.18
0.84±0.27±0.21
ρ+ℓν / η’ℓν
2.17 ± 0.54 ± 0.32
<1.3
π+ℓν
π+ℓν
π+ℓν
 Belle
253 fb-1
BF (10-4)
ρ+ℓν
Preliminary
BaBar 
211 fb-1
Semileptonic
tag
π0ℓν
ρ0ℓν
Hadronic
tag
(s.l. tag)
Kowalewski
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|Vub| from exclusive decays
New
|Vub| from B  πℓν
New
New
Averages of tagged and untagged
methods are comparable

New
New
New
For |Vub|:


New
Lattice QCD: q2>16 GeV2
Light-cone sum rules: q2<16 GeV2
New
FF normalization errors dominate;
task for theory, CLEO-c

New
(inclusive: |Vub|=(4.49±0.34)×10-3
FF calc
FF norm (ps-1)
Ref
0.56
Ball-Zwicky 3.38  0.12 -0.37
5.44 ± 1.43
PRD 71:014015 (2005)
HPQCD
0.59
3.93 0.26 -0.41
1.46 ± 0.35
PRD 73:074502 (2006)
FNAL
0.61
3.51 0.23 -0.40
1.83 ± 0.50
hep-lat/0409116
1.36
3.54 0.23 -0.63
1.80 ± 0.86
APE '06
ICHEP
Vub [10-3]
6% uncertainty
Nucl. Phys. B619:565 (2000)
Kowalewski
Experimental
error on |Vub|
~ 6%
24
See talks of Marchiori,
Krokovny, S8
 Vud

 Vcd
 V e  i
 td
Vus
Vcs
Vts
Vub e  i 

Vcb


Vtb

The phase: γ (φ3)
ICHEP '06
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The relative phase γ (φ3)
Interference between tree-level decays; theoretically clean
Favored: Vcb Vus*
B-
s
b
u
u
c
u

A B
A B D 0 K 

D0 K 
K(*)D(*)0
Common
final state
f
  r ei e i
 B
K(*)D(*)0
u
Vcs* Vub: suppressed
s
c
u
b
B-
u
Parameters: γ,
(rB, δB) per mode
B
Three methods for exploiting interference (choice of D0 decay modes):
• Gronau, London, Wyler (GLW): Use CP eigenstates of D(*)0 decay,
e.g. D0  Ksπ0, D0  π+ π • Atwood, Dunietz, Soni (ADS): Use doubly Cabibbo-suppressed decays,
e.g. D0  K+π • Giri, Grossman, Soffer, Zupan (GGSZ) / Belle: Use Dalitz plot analysis
of 3-body D0 decays, e.g. Ks π+ πICHEP '06
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The angle γ (φ3)
GLW-based analyses
Measure asymmetry between B+/B- for CP even/odd D decays
B   D K    B   D K  
 2rB sin  B sin 
 CP  

8-fold ambiguity on γ
B   D K    B   D K   1  rB2  2rB cos B cos
and the fractional decay rates to CP eigenstates:

CP 


 
 


 B   D K    B   D K 
2


1

r
 2rB cos B cos
B

0


0

 B  D K  B  D K
Hard to disentangle rB
from γ and δB
Recent results: Belle (PRD 73:051106, 2006), BaBar (PRD 73: 051105, 2006)
Belle 275 106 BB
B+DCP+K
+
Signals seen in CP-even and CP-odd D decays
CP-even
D0 modes
B+DCP-K+
B+DCP+π+
CP-odd
D0 modes
ICHEP '06
BaBar 232 106 BB
B+DCP-π+
Similar measurements
exist in B+  D*0 K+
Kowalewski
27
DCP K* D*CP K
DCP K
The angle γ (φ3)
GLW averages
Implications for rB and γ discussed later
ICHEP '06
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28
The angle γ (φ3)
ADS-based analyses
Use DCS decays to reach same final state, e.g.

favored
suppressed
B   D 0 K   D 0  K  (n π)
B   D 0 K   D 0  K  (n π)
suppressed

ADS
ADS


B

B
favored


 K 
 K 


K
K
 
 
 B
 B
Small product BF but
comparable amplitudes 
large potential asymmetry

AB
    r eiδ e iγ  r e iδ
B
D
 D K π K 
A B  D K π  K 


 K 
 K 

Additional
parameters
rD and δD
 


K
K


r


B
D
 B   K   K    B   K   K 
2rB rD sin  B   D sin 


 B   K   K    B   K   K 
ADS








Modes D*K and DK* also used








2
B
Direct
dependence
 rD2  2rB rD cos B   D  cos
DCSD charm;
rD (Kπ)= 0.0603 ± 0.0025
D*0  D0π and D*0  D0γ have opposite CP
ICHEP '06
Kowalewski
29
The angle γ (φ3)
ADS results
New BaBar result in [K+π-π0]DKBaBar preliminary
hep-ex/0607065
226 106 BB
No signal yet in
suppressed modes
mES
DK  0.039 (95%c.l.)
Belle result in [K+π-]DKBelle hep-ex/0508048 386 106 BB
[K+π-]D K-
DK  0.014 (90%c.l.)
ICHEP '06
[K-π+]D K-
ΔE
Implications for rB and γ discussed later
Kowalewski
30
The angle γ (φ3)
Dalitz analyses

Measure B+/B- asymmetry across Dalitz plot

decay

B   K s    D K 

amplitude


A  f m2 , m2  rB ei ei B f m2 , m2
m2  m2 Ks  
Sensitivity to γ in interference term

Mirror symmetry
between D0 and D0
Dalitz plots
Determine f in flavor-tagged D*+D0π+ decays

Includes GLW (D0  Ks ρ0, CP eigenstate)
and ADS (D0  K*+π-, DCS 2-body decay) regions
2-fold ambiguity on γ: (γ, δ) → (γ+π, δ+π)
ICHEP '06
Kowalewski
31


Select D*+[Ksπ+π-]π+ from e+e-  cc; ~4 105 events
Fit to coherent sum of 15-16 Breit-Wigner
amplitudes plus a non-resonant term
BaBar 270 fb1
preliminary
Excellent fits obtained
m2- (GeV2)
The angle γ (φ3)
Dalitz model for Ksπ+πBelle 357 fb-1
preliminary
hep-ex/0604054
Main contributors:
• K*-(892) π+
• Ks ρ0
• K*0(1430) π -
m2+ (GeV2)
• K*-(892) π+
m2(π+π-) GeV2
• non/broad resonant
Model-independent approach (GGSZ)
using CP-tagged D0 studied by
Bondar, Poluektov in hep-ph/0510246
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Kowalewski
Improved modeling (e.g.
K-matrix formulation)
under study
32
The angle γ (φ3)
Dalitz plots

Plots shown are representative; both experiments have
analyzed DK, D*K and DK* decays
DK+
347 106 BB
ICHEP '06
BaBar preliminary
DK-
D*K+
386 106 BB
Kowalewski
D*K-
Belle hep-ex/0604054
33
The angle γ (φ3)
Results on γ



HFAG averages for x± = rB cos( δB ± γ ) , y± = rB sin( δB ± γ )
UTfit find γ = 78±30° based on B-  D(*) K(*)- decays
Note: σγ depends significantly on the value of rB
Contours do not include
Dalitz model errors
Contours do not include
Dalitz model errors
2γ
ICHEP '06
Kowalewski
34
The angle γ (φ3)
sin(2β+γ)
2 common
final states via
BB mixing
really favored: Vcb Vud*
d
B0
b
u
d
c
d
Asuppressed
Afavored
π-
π+
D(*)+
 rB ei B e i 2   
D(*)-
Time-dependent effect
(due to B0-B0 mixing)
Vcd* Vub: really suppressed
c
d
u
b
d
B0
d
Parameters: γ, 2β
(r, δB) per mode
Large BF but small rB (<2%)
 small CP asymmetry
rB must be estimated from
B0Ds+π – using SU(3)
ICHEP '06
Kowalewski
35
The angle γ (φ3)
B0  D0 K0 feasibility
study
BaBar hep-ex/0604016, soon in PRD
Vub
B0
D0
Vcb
D0
B0
K*0
B0  D0 K*0
K*0
• Interference of B0  D0 K0 with
B0  B0  D0 K0 (K0 and K0 mix)
ΔE
• Determine rDK* in related decay B0  D0 K*0
• BaBar find no signal: rDK* < 0.4 @90% c.l.
• This mode may be harder to use for sin(2β+γ) than predicted;
implications for LHC-b
ICHEP '06
Kowalewski
36
The angle γ (φ3)
Related measurements
Nice ideas, nice work, but
not much impact yet for γ
rDπ from B0Ds(*)π -, SU(3)
B0  Ds a0,2
BaBar hep-ex/0604012, 226 106 BB




BaBar PRD D73 \:071103 (2006)








BF B  D   1.3  0.3  0.2 

BF B  D    2.8  0.6  0.5 
5
 10

BF B  D K  2.5  0.4  0.4 
BF B  D K   2.0  0.5  0.4
rD  1.3  0.2  0.1 
2

 10
rD*  1.9  0.2  0.2 preliminary

s
*
s

s
*
s

BD*D*
BaBar PRD 73:112004 (2006)
BF and charge asymmetries
measured for all B  D(*)D(*)
modes; provides input for
sin(2β+γ) from B0  D(*)+D(*)time-dependent asymmetries
B0  D0 K+ π BaBar PRL 96:011803 (2006)
BaBar show that B  D0 K+πnot promising for measuring γ
ICHEP '06




BF B  Ds a0  1.9 

BF B  Ds* a0  3.6
5
 10 , 90% c.l.
 
BF B  Ds a2  19 
BF B  Ds* a2  20  226 106 BB
Kowalewski
37
The angle γ (φ3)
See talks of Vagnoni, T’Jampens, S8
Current status of UT
Tree-level determination: information
on phase γ (φ3) not yet constraining
All constraints: compatible with SM,
but tension exists between sin2β and
|Vub/Vcb|
“2-σ”
bands
ICHEP '06
Kowalewski
38
Summary

Today:
Vcb  42.0  0.23  0.69103
Vub  4.49  0.19  0.27103
γ(φ 3 )  78  30

What to look for in 2008:





ICHEP '06
“2-σ”
bands
2 ab-1 from the B factories
(>doubling of data sample)
error on |Vub/Vcb| of ~5%
error on γ: ~10-15° ? (rB …)
LHC-b will have initial data
The heavy flavor program will
restrict the space in which
theories for the new physics to be
seen at LHC can operate
Kowalewski
39
Backup slides
ICHEP '06
Kowalewski
40
Tale of two fitters
CKMfitter (frequentist)
ICHEP '06
UTFit (Bayesian)
Kowalewski
41
|Vub| from inclusive decays
Theory calculations

Bosch, Lange, Neubert, Paz (BLNP)





Andersen and Gardi: Dressed gluon exponentiation (DGE)




ICHEP '06
Decompose into Hard, Jet and Shape functions using HQE and
SCET: H×J ×S
Same formalism used to extract mb and μπ2 from bsγ
Predictions over full phase space, reasonable error analysis
Critique: 3 scales between ΛQCD and mb
Only mb and αS as input parameters
Gives good description of bsγ spectrum
Agrees fairly well with BLNP on buℓν rates
Critique: some (but not all) consider it a model;
Kowalewski
42
|Vcb| from inclusive decays
Global fit: Input
measurements

Moments used in fit, from B  Xcℓν and b  sγ
Buchmüller and Flächer,
Phys.Rev. D73 (2006) 073008
\ Moment
Experiment
Electron energy
Hadronic mass
Delphi
3
3
CLEO
need full covar
4
CDF
Belle
BaBar
ICHEP '06
Photon energy
1
2
need full covar
need full covar
4
14
13
3
Kowalewski
43
|Vcb| from exclusive decays
BXcℓν using
tagged samples


Reconstruct D(*)Xℓ-ν across from a fully reconstructed
B+ or B0 meson; Mmiss2 provides new kinematic handle
Belle reported last year
Belle
BFs for B  D(*)πℓν:
BF (in %)
Phys.Rev.D72:051109,2005
Also report BF(B-D*0ℓ-ν) = 6.06 ± 0.25stat%;
and
BF(B0D*+ℓ-ν) = 4.70 ± 0.24stat%.


ICHEP '06
New BaBar preliminary result:
BF(B-D*0ℓ-ν) = 6.8 ± 0.4%
BF(B-D0ℓ-ν) = 2.3 ± 0.3%
BF(B-D**0ℓ-ν) = 1.9 ± 0.3%
(includes D(*)πℓν; translated from relative
fractions into BFs by this speaker assuming
these modes saturate bcℓν)
New D0 result
D
D*
D(*)π
(preliminary)
BF(BsDs1(2536)ℓν) = 0.86 ± 0.16 ± 0.16
Kowalewski
44
|Vcb| from exclusive decays
The BF(BD*ℓν) puzzle



The largest B BF is BD*ℓν (~6%), yet B  K*γ (~4×10-5) is known as
well, and perhaps better…
(HFAG winter) average: BF(B0D*+ℓ-ν) = 5.35 ± 0.20%; CL=3.8%
Consider RD* = BF(B-D*0ℓ-ν) / BF(B0D*+ℓ-ν);
we expect RD* = τ+ / τ0 = 1.071 ± 0.009
Total BF(BXℓν)
consistent with isospin

Naively combining Belle and BaBar
results: RD* = 1.32 ± 0.07
(20% and 3.5σ from isospin!)
BaBar
preliminary
Ee
BF(B+Xeν) / BF(B0Xeν)
= 1.084 ± 0.041 ± 0.025
ICHEP '06
Kowalewski
45
Importance of rB


The uncertainty on γ (φ3) depends strongly on the value of
rB, which is currently not well known
Predictions for how σγ will evolve with luminosity have
significant uncertainty
rB
Belle
φe
ICHEP '06
Kowalewski
46