Inclusive b → uℓv andb → s Spectrum

Masahiro Morii

Harvard University

BABAR Collaboration

SLAC/INT Workshop on Flavor Physics and QCD

May 11–14, 2005

11 May 2005 M. Morii, Harvard 2

Experimental Program

Inclusive rate u (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 Inputs required for the shape function (SF)

E spectrum in b → s Eℓ and mX spectra in b → cℓv

SF errors considered “experimental” Theoretical errors include:

Perturbative Sub-leading SFWeak annihilation (WA)

2

u ubV

|Vub|

Partial u

b → s b → cℓv

Shape Function

2

11 May 2005 M. Morii, Harvard 3

Measurements of b → sEspectrum depends on the shape function Measure Emoments (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 E

Sum-of-exclusive measurement reconstructsa 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 4

Inclusive b → sInclusive E spectrum can be measured above ~1.9 GeV

Belle, efficiency-corrected

Data E cut <E> <E> − <E>2 Ref.

BABAR 80 fb-1 1.9 GeV2.288 ± 0.033

not yetMommsen, Moriond

talk

Belle 140 fb-1 1.8 GeV2.292 ± 0.043

0.0305 ± 0.0097

PRL 93:061803,2004

BABAR, partial BF

Belle

11 May 2005 M. Morii, Harvard 5

Sum of Exclusive B → XsBABAR uses 38 channels: (K± or KS) plus ≤4 pions, etc.

Data sample is 80 fb-1

Measure E spectrum and thefirst three truncated moments Table of values in R. Mommsen’s

talk at Moriond ElectroweakE cut (GeV)

BABAR preliminary

11 May 2005 M. Morii, Harvard 6

Shape Function Parameters

Fit the E spectrum from the BABAR (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)

b → s 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)

Kinetic Shape-function

b → s 0.63 ± 0.04

b → cℓv0.67 ± 0.07

0.45 ± 0.060.65 ± 0.08

0.15 ± 0.07

(GeV) 2 2(GeV )0.060.040.59

0.070.050.30

0.060.050.19

(GeV) 2 2(GeV )

BABAR PRL 93:011803,2004 Neubert PLB612:13,2005

Preliminary

11 May 2005 M. Morii, Harvard 7

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

Sample selection technique determines the available variable(s) Inclusive lepton sample Eℓ

Lepton + missing momentum Eℓ and q2

Recoil of reconstructed B Eℓ, mX, and q2

Experiments measure partial branching fraction Translation to |Vub| requires B and

BABAR/Belle use Bosch, Lange, Neubert, Paz (NPB699:335,2004) for the latter

Eff

icie

ncy

Puri

ty

2

u ubV

11 May 2005 M. Morii, Harvard 8

Lepton Endpoint

Experiments push the Eℓ cut as low as possible

Better efficiencyWeaker SF dependence Smaller WA error

S/B < 1/10 Background modeling!

Pushing below 1.9 GeV difficult Hit poorly-understood B → D**ℓv

Data Eℓ (GeV) |Vub| × 103 Ref.

BABAR 80 fb-1 2.0-2.6 3.93 ± 0.34exp ± 0.38SF ± 0.18theo hep-ex/0408075

Belle 27 fb-1 1.9-2.6 4.49 ± 0.42exp ± 0.32SF ± 0.20theo hep-ex/0504046

Belle

on-peak

off-peak

on – off

11 May 2005 M. Morii, Harvard 9

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

rejects the charm backgroundActual cut is sh

max < 3.5 GeV2

Signal/background = 1/2

Final result will have smaller experimental errors

2max 2 2 2

4h B B

qs m q m E

E

Maximum hadronicmass squared

+ correction for B motion in the c.m.s.max 2

h Ds m

Data |Vub| × 103 Ref.

BABAR 80 fb-1 3.89 ± 0.40exp ± 0.45SF ± 0.21theo hep-ex/0408045

11 May 2005 M. Morii, Harvard 10

Recoil B Analysis

Reconstruct one B completely in B → D(*) + hadrons Efficiency ~0.2%/B

Recoil gives a clean and unbiased sample of B Charge and 4-momentum known

Find a lepton in the recoil B and require 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

Fully reconstructedB hadrons

lepton

v

X

Recoil B

11 May 2005 M. Morii, Harvard 11

mX and q2 Spectra

Experiments plan to measure the mX and q2 spectra in b → uℓv

Potential goal: determine the SF parameters with b → uℓv What else can we learn?

No q2 cut mX < 1.7 GeV

Belle, background-subtracted distributionsBABAR, corrected for efficiency

and resolution

11 May 2005 M. Morii, Harvard 12

mX vs. q2

Select mX < 1.7 GeV and q2 > 8 GeV2

Proposed by Bauer, Ligeti, Luke (PRD64:113004, 2001)

Reminder: SF errors differ because the error on is different

Data |Vub| × 103 Ref.

BABAR 80 fb-1 4.45 ± 0.49exp ± 0.40SF ± 0.22theo hep-ex/0408068

Belle 253 fb-1 4.34 ± 0.34exp ± 0.33SF ± 0.22theoBizjak, CKM05

talk

signal

background

b → uℓv outside the signal region

11 May 2005 M. Morii, Harvard 13

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 Ref.

Belle 253 fb-1 3.87 ± 0.33exp ± 0.35SF ± 0.13theoBizjak, CKM05

talkNote small theoretical error

11 May 2005 M. Morii, Harvard 14

Inclusive |Vub| in May 2005

Experimental errors 8–11% 5% if combined Shape-function errors 7–12% 8% on average Theoretical errors 3–5% 4% on average

We have determined |Vub| to 5%exp 8%SF 4%theo 10% We said this last summer – Do we believe it now?

Data Cuts |Vub| × 103

BABAR 80 fb-1 Eℓ > 2.0 GeV 3.93 ± 0.34exp ± 0.38SF ± 0.18theo

Belle 27 fb-1 Eℓ > 1.9 GeV 4.49 ± 0.42exp ± 0.32SF ± 0.20theo

BABAR 80 fb-1 Eℓ > 1.9 GeV, shmax < 3.5 GeV2 3.89 ± 0.40exp ± 0.45SF ± 0.21theo

BABAR 80 fb-1 mX < 1.7 GeV, q2 > 8 GeV2 4.45 ± 0.49exp ± 0.40SF ± 0.22theo

Belle 253 fb-1 mX < 1.7 GeV, q2 > 8 GeV2 4.34 ± 0.34exp ± 0.33SF ± 0.22theo

Belle 253 fb-1 P+ < 0.66 GeV 3.87 ± 0.33exp ± 0.35SF ± 0.13theo

11 May 2005 M. Morii, Harvard 15

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 functionWill improve as soon as we start using the new b → s results BABAR (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 16

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/0504071We’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