Transcript Inclusive b -> ulnu and b

Inclusive b → uℓv and
b → sg Spectrum
Masahiro Morii
Harvard University
BABAR Collaboration
SLAC/INT Workshop on Flavor Physics and QCD
May 11–14, 2005
Experimental Program
Inclusive rate Gu = G(B  Xuℓv)  |Vub|2


Total rate not measurable due to b  c background
Measure partial rate in the “charm-free” regions of phase space
Expect theory to calculate G = G u V ub

Inputs required for the shape function (SF)
 Eg spectrum in b  sg



2
Eℓ and mX spectra in b  cℓv
11 May 2005
Shape Function
Partial Gu
Perturbative
 Sub-leading SF
 Weak annihilation (WA)
b → cℓv

2

SF errors considered “experimental”
Theoretical errors include:

b → sg
G
|Vub|
M. Morii, Harvard
2
Measurements of b → sg
Eg spectrum depends on the shape function


Measure Eg moments (1st, 2nd, 3rd)  fit with theory, or
Fit the spectrum itself with theory

Is there a preference?
Two types of measurements:

Inclusive measurement detects only the photon

Poor S/B ratio forces tight selection cuts
 Efficiency depends strongly on Eg

Sum-of-exclusive measurement reconstructs
a large number of exclusive decay channels and add them up

Better S/B ratio
 Efficiency depends on the s-quark fragmentation model
11 May 2005
M. Morii, Harvard
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Inclusive b → sg
Inclusive Eg spectrum can be measured above ~1.9 GeV
Belle
Belle, efficiency-corrected
Data
Eg cut
<Eg>
BABAR 80 fb-1 1.9 GeV 2.288 ± 0.033
Belle
BABAR, partial BF
<Eg2> − <Eg>2
Ref.
not yet
Mommsen, Moriond talk
140 fb- 1.8 GeV 2.292 ± 0.043 0.0305 ± 0.0097
1
11 May 2005
M. Morii, Harvard
PRL 93:061803,2004
4
Sum of Exclusive B → Xsg
BABAR uses 38 channels: (K± or KS) plus ≤4 pions, etc.
BABAR preliminary


Data sample is 80 fb-1
Measure Eg spectrum and the
first three truncated moments

Table of values in R. Mommsen’s
talk at Moriond Electroweak
Eg cut (GeV)
11 May 2005
M. Morii, Harvard
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Shape Function Parameters
Fit the Eg spectrum from the BABAR S(excl.) measurement with


Kinetic scheme by Benson, Bigi, Uraltsev (Nucl.Phys.B710:371,2005)
Shape-function scheme by Neubert (Eur.Phys.J.C40:165,2004)
Kinetic
 (G eV )
b → sg
 0.06
0.59  0.04
Shape-function
  (G eV )
2
2
 0.07
0.30  0.05
 (G eV )
  (G eV )
0.63 ± 0.04
0.19  0.05
2
2
 0.06
Preliminary
b → cℓv 0.67 ± 0.07 0.45 ± 0.06 0.65 ± 0.08 0.15 ± 0.07
BABAR PRL 93:011803,2004
Neubert PLB612:13,2005
b → sg and b → cℓv agree, and have comparable precision
 Final results based on the moments in the works

|Vub| results in this talk use the SF parameters from b → cℓv

Caveat: Error on  is 80 MeV (BABAR) vs. 70 MeV (Belle)
11 May 2005
M. Morii, Harvard
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Measurements of b → uℓv
Three degrees of freedom in B  Xuℓv



Lepton energy Eℓ : Easy to measure
Hadronic system mass mX : Efficient for b  c rejection
Lepton-neutrino mass squared q2 : Mild dependence on the SF


Inclusive lepton sample  Eℓ
Lepton + missing momentum  Eℓ and q2
Recoil of reconstructed B  Eℓ, mX, and q2
Purity

Efficiency
Sample selection technique determines the available variable(s)
Experiments measure partial branching fraction DB
2
 Translation to |Vub| requires tB and G = G u V ub

BABAR/Belle use Bosch, Lange, Neubert, Paz (NPB699:335,2004) for
the latter
11 May 2005
M. Morii, Harvard
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Lepton Endpoint
Experiments push the Eℓ cut as low as possible
Data
BABAR 801fb

Eℓ
(GeV)
|Vub| × 103
Ref.
2.0-2.6
3.93 ± 0.34exp ± 0.38SF ±
0.18theo
hep-ex/0408075
4.49 ± 0.42exp ± 0.32SF ±
0.20theo
Belle
hep-ex/0504046
Better efficiency
27
fb
Belle
1.9-2.6
1 SF dependence
 Weaker
 Smaller WA error

S/B < 1/10  Background modeling!
on-peak
off-peak
Pushing below 1.9 GeV difficult

Hit poorly-understood B → D**ℓv
11 May 2005
M. Morii, Harvard
on – off
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Lepton + Neutrino
Find lepton with Eℓ > 1.9 GeV and assume pv = pmiss of the event

Now we have Eℓ and q2
Define charm-free space by calculating
Maximum hadronic
mass squared
m ax
 sh


m ax
sh
2


q
2
2
= mB  q  2mB  E 
 + correction for
4E 

B motion in
 m D rejects the charm background
2
the c.m.s.
Actual cut is shmax < 3.5 GeV2
Signal/background = 1/2
Data
|Vub| × 103
Ref.
3.89 ± 0.40exp ± 0.45SF ±
hep-ex/0408045
BABAR 801fb
0.21theo
 Final result will have smaller experimental errors
11 May 2005
M. Morii, Harvard
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Recoil B Analysis
Reconstruct one B completely in B → D(*) + hadrons

Efficiency ~0.2%/B
Recoil gives a clean and unbiased sample of B

Fully reconstructed
B  hadrons
Charge and 4-momentum known
Find a lepton in the recoil B and require


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Charge conservation
Missing mass = 0
Veto against K (likely from D)
We get complete event kinematics


Leave Eℓ cut loose (>1 GeV)
Use mX and/or q2 to select signal
11 May 2005
M. Morii, Harvard
v
lepton
X
Recoil B
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mX and
2
q
Spectra
Experiments plan to measure the mX and q2 spectra in b → uℓv
No q2 cut
mX < 1.7 GeV
Belle, background-subtracted distributions


BABAR, corrected for efficiency
and resolution
Potential goal: determine the SF parameters with b → uℓv
What else can we learn?
11 May 2005
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mX vs.
2
q
Select mX < 1.7 GeV and q2 > 8 GeV2

Proposed by Bauer, Ligeti, Luke (PRD64:113004, 2001)
b → uℓv outside
the signal region
signal
background
Data
BABAR 80 fb-1
|Vub| × 103
Ref.
4.45 ± 0.49exp ± 0.40SF ±
0.22theo
hep-ex/0408068
4.34 ± 0.34exp ± 0.33SF ±
253
fb
CKM05 talk
Belle

Reminder:
is
different
1 SF errors differ because the error on Bizjak,
0.22
theo
11 May 2005
M. Morii, Harvard
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P+ Variable
Define P+ = EX – PX and cut at P+ < 0.66 GeV

Proposed by Bosch, Lange, Neubert, Paz (PRL93:221801,2004)
Belle
Data
|Vub| × 103
3.87 ± 0.33exp ± 0.35SF ±
Belle 2531 fb
0.13theo
Note small theoretical error
11 May 2005
M. Morii, Harvard
Ref.
Bizjak, CKM05 talk
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Inclusive |Vub| in May 2005
Cuts
|Vub| × 103
BABAR 80 fb-1
Eℓ > 2.0 GeV
3.93 ± 0.34exp ± 0.38SF ±
0.18theo
27 fb-1
Eℓ > 1.9 GeV
4.49 ± 0.42exp ± 0.32SF ±
0.20theo
Data
Belle
BABAR 80 fb-1 Eℓ > 1.9 GeV, shmax < 3.5 GeV2
3.89 ± 0.40exp ± 0.45SF ±
0.21theo
4.45 ± 0.49exp ± 0.40SF ±
0.22theo
 Experimental errors 8–11%  5% if combined
4.34 ± 0.34exp ± 0.33SF ±
 Shape-function
errors
7–12%
8% 2on average
253
fb
2 >
Belle
m
<
1.7
GeV,
q
8
GeV
1
X
0.22theo
BABAR 80 fb-1

mX < 1.7 GeV, q2 > 8 GeV2
Theoretical errors 3–5%  4% on average
3.87 ± 0.33exp ± 0.35SF ±
Belle
<
0.66
GeV
We have1 determinedP|V
|
to
5%

8%

4%theo0.13
 10%
+ ub
exp
SF
253 fb-

We said this last summer – Do we believe it now?
11 May 2005
M. Morii, Harvard
theo
14
Inclusive |Vub| at Moriond 2007
Experimental error (5%) in |Vub| will shrink with the statistics


Even syst. errors improve with larger control samples
500 fb-1/expt. by summer 2006  2.5%?
Largest uncertainty (8%) comes from the shape function
Will improve as soon as we start using the new b → sg results
 BABAR S(excl.) result alone can halve the error on 


2 expts. × 2 methods × more data  3%?
Theory error (4%) will be the largest error (again)


We’d better be darn sure about them
We’d better have a strategy to shrink them
11 May 2005
M. Morii, Harvard
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Questions + Remark
How robust are the current theory errors?

BABAR/Belle rely on calculation by one group

Error estimates come from Lange, Neubert, Paz, hep-ph/0504071
 We’d love to have an independent calculation or two


Sub-leading SF error small (0.5% for mX-q2)  Do we all agree?
P+ cut has small theo. error (3%)  Will another group confirm?
What can we do to shrink the theory errors?



Leading error is perturbative  Any hope for improvement?
We will pursue B+-B0 difference  Precision unknown yet
Experimental handles on sub-leading SFs?
|Vub| will be determined to a 5% precision in 2 years if the theory
error becomes 3%, and we believe it
11 May 2005
M. Morii, Harvard
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