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Measurement of |V ub | using Inclusive Semileptonic B Decays at the B-Factories Wolfgang Ehrenfeld University of Hamburg/DESY, Germany Theoretical Calculations Experimental Methods Latest Results Uncertain Future

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SLIDE 1

Measurement of |Vub| using Inclusive Semileptonic B Decays at the B-Factories

Wolfgang Ehrenfeld University of Hamburg/DESY, Germany

  • Theoretical Calculations
  • Experimental Methods
  • Latest Results
  • Uncertain Future
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SLIDE 2

2

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

Semileptonic B Decays

l ν

u

X B

u quark turns into

  • ne or more hadrons

B → Xlv decays are described by 3 variables

2 2

( ) 1 ( ) 50

ub cb

V b u b c V ν ν Γ → ≈ ≈ Γ → l l

q2 = lepton-neutrino mass squared q2 = lepton-neutrino mass squared mX = hadron system mass mX = hadron system mass El = lepton energy El = lepton energy P+ = EX - |pX| P+ = EX - |pX|

b , c u

−

l ν W ,

cb ub

V V

Semileptonic B decays allow measurement of |Vcb| and |Vub| from tree level processes. Presence of a single hadronic current allows control of theoretical uncertainties. b → clv is background to b → ulv:

favoured by theory

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SLIDE 3

3

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

B Factories

Čerenkov Detector (DIRC)

144 quartz bars 11000 PMTs

1.5 T solenoid ElectroMagnetic Calorimeter

6580 CsI(Tl) crystals

Drift CHamber

40 stereo layers

Instrumented Flux Return

iron/RPCs/LSTs (muon/neutral hadrons)

Silicon Vertex Tracker

5 layers, double sided strips

e+ (3.1 GeV) e- (9 GeV)

BaBar Detector PEPII: Lpeak ~ 1.234cm-2s-1 Lint ~ 390 fb-1 KEKB: Lpeak ~ 1.7 1034cm-2s-1 Lint ~ 690 fb-1

TOF counter

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SLIDE 4

4

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

Luminosity at the B-factories

BaBar: 1.2x10-34 -> 17 fb-1/month

  • Run 1-2:

~94 fb-1

  • Run 3-4: ~148 fb-1

~242 fb-1

  • Run 5:

~149 fb-1 ~391 fb-1

  • Run 6/7: ~550 fb-1

~910 fb-1 Belle: 1.7x10-34 -> 29 fb-1/month

  • Now:

~694 fb-1

  • At least: ~1000 fb-1
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SLIDE 5

5

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

The standard approach is to choose a method to tag the semileptonic event and a set of kinematic variables to suppress the large b->clv

  • background. From this a partial branching fraction is measured.

Tagging:

  • untagged
  • semileptonic tag
  • hadronic tag

Suppress b->clv events:

  • Ee
  • Ee/q2
  • mx, mx/q2, p+

Experimental Approach

q2 (GeV2) Ee (GeV) bc allowed

Points are buℓν simulation

low purity, high statistics high purity, low statistics low acceptance high acceptance

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SLIDE 6

6

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

OPE gives good results for full phase space but breaks down in the so-called shape function (SF) region (low mx and low q2). There are three approaches to solve this problem:

BLNP (Bosch, Lange, Neubert, Paz) Handle SF region by introducing a parameterization

  • Shape function form is unknown -> assume form
  • Shape function moments are related to HQE parameters (mb, μπ

2) -> can be measured

  • Leading shape functions universal in b->clv, b->ulv, b->sγ
  • Subleading shape functions depend on decay

BLL (Bauer, Ligeti, Luke) OPE based calculation excluding the region of sizable non-perturbative effects.

  • Residual dependence on SF effects
  • Only depend on mb
  • Only valid in non-SF region (mx < mD and q2 > 8)

DGE/AG (Anderson, Gardi) Using Dressed Gluon Exponentiation (DGE) to convert on-shell b-quark calculations into meson decay spectra

  • Only depend on mb

Traditional Theoretical Calculations

( )

B u ub

X B B V τ ζ ν ⋅ Δ → Δ = l

Take your favorite theory calculations and convert the partial branching fraction into |Vub|:

PRD72:073006(2005) PRD64:113004(2001) JHEP0601:097(2006)

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SLIDE 7

7

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

Alternative Approaches

LLR (Leibovich, Low, Rothstein)

  • Relates |Vub|2/|VtbVts

*| to mx or El spectrum in b->ulv and Eγ spectrum

in b->sγ

  • Includes higher order corrections

Neubert

  • Similar to LLR

BLNP/Lange

  • Relates |Vub| to the measured partial BF(b->ulv) and normalised Eγ

spectrum in b->sγ decays BFMP (Boos, Feldmann, Mannel, Pecjak)

  • Relate |Vub|/|Vcb| to measured spectrum in b->ulv and b->clv decays

The fact that the leading shape functions are universal to first order allows the direct use of information from either b->clv or b->sγ decays in the measurement of |Vub|. The spectrum of a kinematic variable in b->ulv decays is relate to the spectrum in b->clv or b->sγ decays using a weighting function.

JHEP0601:104(2006) PLB513:88(2001) PRD61:053005(2000), PLB513:83(2001) JHEP0605:056(2006)

Results!

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SLIDE 8

8

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

Select electrons with Elow < El < 2.6 GeV

– Push below the charm threshold Larger signal acceptance Smaller theoretical error – Accurate subtraction of b->clv background is crucial

  • off-resonance data
  • events with pe > 2.8 GeV
  • fit b->clv composition in bkg subtraction

– Measure partial BF

Untagged Lepton Endpoint

BABAR MC signal b → ulv Data – bkgd. Data MC bkgd. b → clv

|Vub| [10-3]: BLNP BaBar: El = 2.0-2.6 GeV 4.39 ±0.16stat±0.19exp±0.32SF±0.24theo Belle: El = 1.9-2.6 GeV 4.82 ±0.11stat±0.44exp

SF±0.23theo

CLEO: El = 2.1-2.6 GeV 4.09 ±0.14stat±0.46exp

SF±0.26theo

+0.17

  • 0.23

+0.20

  • 0.27

PRD73:012006(2006) PLB621:28(2005) PRL88:231803(2002)

9.7M BB 29M BB 88M BB

HFAG HFAG HFAG

15% 12% 11%

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SLIDE 9

9

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

Untagged El and q2

  • Try to improve signal-to-background
  • Use pv = pmiss in addition to pe calculate q2

– Define sh

max(El, q2) = the maximum mX squared

  • Cutting at sh

max < mD 2 removes

b → clv while keeping most of the signal

– S/B = 1/2 achieved for El > 2.0 GeV and sh

max < 3.5 GeV2

– Measured partial BF

. 5 1 1 . 5 2 2 . 5 5 1 1 5 2 2 5

b → clv El (GeV) q2 (GeV2) b → ulv BABAR

Extract signal normalize bkg Extract signal normalize bkg

|Vub| [10-3]: BLNP BaBar: 4.57 ± 0.22stat ± 0.22exp

SF ± 0.30theo

PRL95:111801(2005), PRL97:019903(2006)

HFAG

88M BB

+0.23

  • 0.31

12%

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SLIDE 10

10

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

  • fully reconstruct one B in hadronic decay mode
  • study the recoiling B -> known momentum and flavour
  • access to all kinematic variables (mx, q2, P+)

mX<1.7GeV, q2>8GeV

|Vub|= (4.75 ±0.25stat ±0.25sys

SF ±0.25theo) x 10-3

hep-ex/0507017

210M BB

P+=EX-|pX| <0.66 mX<1.7GeV, q2>8GeV mX<1.7GeV PRL95:241801(2005)

253M BB

|Vub| = (4.70 ± 0.24stat ± 0.28syst ± 0.20SF

theo) × 10-3

|Vub| = (4.09 ± 0.19stat ± 0.20syst ± 0.18SF

theo) × 10-3

|Vub| = (4.19 ± 0.20stat ± 0.30syst ± 0.24SF

theo) × 10-3

lepton

v

X

Hadronic B Tag

253M BB

+0.23

  • 0.24

+0.14

  • 0.16

+0.14

  • 0.15

10% 9% 11%

error[%]

HFAG

+0.23

  • 0.31

11%

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SLIDE 11

11

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY theory uncertainties

  • relate charmless SL rate to b→sγ spectrum
  • reduced dependence from shape function

2 2

( ) ( ) ( )

ub s u ts

W E V d B X B X dE dE V

γ γ γ

γ ν Γ → Γ → =

∫

l

Weight function

mX cut LLR : MX < 1.67 GeV: |Vub| = (4.43 ± 0.38stat ± 0.25syst ± 0.29theo) 10-3 OPE: MX < 2.50 GeV: |Vub| = (3.84 ± 0.70stat ± 0.30syst ± 0.10theo) 10-3

L = 80 fb-1

Reducing Model Dependence

Acceptance: 72% 98%

NEW!

PRL96:221801(2006)

88M BB

12% 20%

PRD61:053005(2000) PLB513:83(2001)

Following LLR

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SLIDE 12

12

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

Reinterpretation of Lepton Endpoint

Take the partial branching fraction from the BaBar lepton endpoint measurement and use the BaBar semi-inclusive photon spectrum from b->sγ and calculate |Vub|:

  • Try different methods (LLR, Neubert, BLNP/Lange)
  • Try different cuts

Do we see the effect of SSF here?

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SLIDE 13

13

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

Status of Inclusive |Vub|

|Vub| world average summer 2006

±2.2% Statistical Error ±4.2% Theory Error ±3.7% Experimental Error ±4.1% SF parameters (mb,μπ

2)

|Vub| determined to ±7.3% BLNP 4.45 ± 0.20exp ± 0.18SF ± 0.19theo |Vub| [x10-3]:

Numbers rescaled by HFAG.

SF parameters from hep-ex/0507243, predicted partial rates from BLNP

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SLIDE 14

14

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

Comparision of Theory

6% theory error 4.5% theory error Perfect agreement! Good agreement! 7.4% theory error 4.7% theory error 6.7% theory error All Measurements mx-q2 Measurements 6.5% theory error Why is DGE so good? Can BLL improve?

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SLIDE 15

15

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

Theoretical Uncertainties Breakdown

BLNP:

  • Shape Function

4.2% -> 2.1 %

  • Subleading shape function

3.8% -> ? %

  • Weak Annihilation

1.9% -> ? % total: 6.0% ->

DGE:

  • mb

1.2% -> 0.6%

  • αs

1.0%

  • Total semileptonic B width

3.0% -> ? %

  • Method/scale of matching theory

2.9% -> ? % total: 4.5% ->

BLL:

  • Residual shape function effects

3.0% -> ? %

  • Higher order terms in αs expansion

3.0% -> ? %

  • mb

4.5% -> 2.2%

  • 3rd order terms in OPE expansion

4.0% -> 2.0% total: 7.4% ->

Can we half the errors on Δmb and Δμπ

2?

What to do with the SFF? Measurement of / limit on WA BLL: Improve calculations?

What can we improve in the future?

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SLIDE 16

16

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

Extrapolation of Uncertainties

What can be achieve on the experimental side?

  • Detector effects are understood and small (maybe not in the future)
  • Selection usually involves complex fitting techniques (mES)

– More data increases statistics – More data shows more details -> need to be accounted for

  • Dominant systematics are the modeling of signal and background

– b->ulv (resonances, non-resonant contribution (SF-dependent)) – b->clv (D, D*, D**) – Continuum background

4,1 7,5 3,2 6,8 3,0 5,7

total

1,3 2,6 1,1 2,2 0,3 0,6

b->ulv

1,3 2,5 1,3 2,5 1,0 1,9

b->clv

2,6 3,8 2,3 3,4 2,6 3,9

sys

2,6 5,3 1,5 4,8 1,2 3,6

stat mx/q2 El/q2 Endpoint

Statistics scales with luminosity Systematics scaled by 2/3 (not all will gain from pure luminosity) b->clv and b->ulv description will improve with better (exclusive) measurements

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SLIDE 17

17

Wolfgang Ehrenfeld, Univ. of Hamburg/DESY

Summary

  • At lot of work has been done on the experimental and theoretical

side:

– Many different methods on how to suppress background – Many different theoretical calculations

  • Try all combinations to understand which one is good and why others

are wrong?

  • Most collected data is not analyses yet and more is to come
  • Statistics alone will not be enough but will help

– Shape function parameters – Weak annihilation constraints – b->clv and b->ulv modeling

  • Improvements on experimental and theoretical systematics are

needed

– How to estimate – What to estimate

  • At the end we want to get to the 5% (or better!)