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Semileptonic B Decays at BaBar

Wolfgang MengesQueen Mary, University of London, UK

Teilchenphysik Seminar, Bonn, 4th May 06

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Outline

• Introduction & motivation– CKM Matrix & Unitarity

Triangle– PEP-II and BABAR– Why semileptonic decays?

•Measurements– Inclusive b cl– Exlusive B D*l– Inclusive b ul– Exclusive B l

•Howit all fitstogether

•Outlook / Conclusions

|Vcb|

|Vub|

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B Decays – a Window on the Quark Sector

•The weak and mass eigenstates of the quarks are not the same•The changes in base are described by unitarity transformations Cabibbo Kobayashi Maskawa (CKM) matrix

The only 3rd generation quark we can study in detail

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

1-c2 c A c

3(-i)

= -c 1- c2/2 A c

2

Ac3(1- -i) -A c

2 1 + O(c

4) [ c= sinc ]CP violation

| Vub| e-i

| Vtd| e-i

|Vub|

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Unitarity Triangle

Unitarity of VCKM

– this is neatly represented by the familiar Unitarity Triangle

– angles can be measured with CPV of B decays– side from semileptonic B decays (|Vcb| and |Vub|)

0ud ub cd cb td tbV V V V V V

*

*

*

*

*

*

arg

arg

arg

td tb

ud ub

cd cb

td tb

ud ub

cd cb

V V

V V

V V

V V

V V

V V

1

td tb

cd cb

V V

V V

†CKM CKM 1V V

ud ub

cd cb

V V

V V

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Unitarity Triangle Fits

Bd mixing: md

Bs mixing:ms / md

J/K0: sin2

bul: |Vub|

D*l: |Vcb|

kaon decays: εK

http://ckmfitter.in2p3.fr

charmless two-body:

interference in

BDK:

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Consistency tests

•Compare measurements in the ()-plane

– If the SM is the whole story,they must all overlap

•The tells us that this is true (status winter 2005)

– But still large enough for New Physics to hide

•Precision of sin2 from B factories dominates determination of

– Must improve the others to get more stringent tests

•Left side of the UT is

– Uncertainty dominated byca. 7% error on |Vub|

ud ub cd cbV V V V

Measurement of |Vub| is complementary to

sin2

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Experiments

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Collides 9 GeV e−

against 3.1 GeV e+

– ECM = 10.58 GeV = mass of (4S)

– Boost = 0.56 allows measurement of B decay times

PEPII Asymmetric B Factory

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The BaBar Detector

Čerenkov Detector(DIRC)

144 quartz bars11000 PMTs

1.5 T solenoid

ElectroMagnetic Calorimeter

6580 CsI(Tl) crystals

Drift CHamber40 stereo

layers

Instrumented Flux Returniron/RPCs/LSTs

(muon/neutral hadrons)

Silicon Vertex Tracker5 layers, double sided

strips

e+ (3.1 GeV)

e- (9 GeV)

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Run 1/2: ~80 fb-1

Run 3/4: ~140 fb-1

Run 1-4: ~220 fb-1

Data Taking

Run 5

Run 4

Run 3

Run 2

Run 1

Run 5:

collected: ~100 fb-

1

expected: ~230 fb-1

Peak luminosity 1×1034/cm2/s BB production ~10 Hz

Belle:

collected: ~560 fb-

1

1 fb-1 -> 1.1 x 106 BB

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KEKB and Belle Detector

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Physics

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Semileptonic B Decays

uX

B

c/u quark turns into one or more hadrons

B → Xlv decays are described by 3 variables

2

2

( ) 1

( ) 50ub

cb

Vb u

b c V

q2 = lepton-neutrino mass squaredq2 = lepton-neutrino mass squared

mX = hadron system massmX = hadron system mass

El = lepton energyEl = lepton energy

b

,c u

W

,cb ubV 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:

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|Vcb |

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free-quark rate

|Vcb| & the „Atomic Physics“ of B Decays

•Contains b- and c-quark masses, mb and mc

2 related to kinetic energy of b-quark

G2 related to chromomagnetic operator (B/B* mass splitting)

•Darwin term (ρD3) and spin-orbit interaction (ρLS

3) enter at 1/mb3

= scale which separates effects from long- and short-distance dynamics

r = mc/mb; z0(r), d(r): phase space factors; AEW = EW corrections; Apert = pert. corrections (sj , s

k0)

Strategy: Global fit of all parameters measure rate, moments(NB: Several HQE schemes exist; operators and coeff’s are scheme dependent)

Inclusive rate described by Heavy Quark Expansion (HQE) in terms of as(mb) and 1/mb

43

3

2

332

45

2

3322

3

23

52

1)()1(2)),(1(

21),(1)(

1||192

)(

bb

D

b

b

LSDG

pert

b

b

LSDG

pert

EWcbbF

c

mO

mr

m

mrrA

m

mrAr

AVmG

XB

d

z 0

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Inclusive Decays: |Vcb| from b clv

•Fit moments of inclusive distributions: lepton energyhadronic mass

– Determine OPE parameters and |Vcb|

•Measurements from B Factories, CDF, Delphi•We’ll look at an example: Hadronic Mass Moments

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5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 mES[GeV/c2]

225020001750150012501000750500250

0

Eve

nts

/ 1.8

MeV

/c2

BABARL = 81 fb-1

• Select events with a fully-reconstructed B– Use ca. 1000 decay chains B D(*) + (n) + (mK)– Flavor and momentum of “recoil” B are known

• Find a lepton with E > Ecut in the recoil B– Lepton charge consistent with the B flavor– mmiss consistent with a neutrino

• All remaining particles belong to Xc

– Improve mX with a kinematic fit (require mB2=mB1 and mmiss=0)

– Yields resolution (mX) = 350 MeV

Hadronic Mass Moments

Fully reconstructedB hadrons

lepton

v

X

BABAR PR D69:111103

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Hadronic Mass Moments

• Unmeasured particles measured mX < true mX

– Calibrate using simulation– Depends (weakly) on decay multiplicity and mmiss

– Validate in MC after applying correction– Validate on data using partially reconstructed D *± D 0±, tagged

by the soft ± and lepton

• Calculate 1st-4th mass moments with Ecut = 0.9 … 1.6 GeV

input to HQE fit

BABARValidation:

high mass charm states

Mx2[GeV2/c4]

D,D*

BABAR PRL 93:011803

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• Calculation by Gambino & Uraltsev

– Kinetic mass scheme to– Eℓ moments

– mX moments

• 8 parameters to determine:

• 8 moments available with several Ecut

– Sufficient degrees of freedom to determineall parameters without external inputs

– Fit quality tells us how well HQE works

Fit Parameters

cbV bm cm 2

2G

3D

3LS( )cB X B

kinetic

chromomagnetic

Darwin

spin-orbit

2(1/ )bmO

3(1/ )bmO

3(1/ )bmO

( )sO

2( )sO

Benson, Bigi, Mannel, Uraltsev, hep-ph/0410080Gambino, Uraltsev, hep-ph/0401063

Benson, Bigi, Uraltsev, hep-ph/0410080

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Results

Global fit in thekinetic scheme

|Vcb| < 2%mb < 1%mc = 5%

Buchmüller, Flächer: hep-ph/0507253

|Vcb| = (41.96

± 0.23 ± 0.35 ± 0.59) 10-3

BRclv = 10.71 ± 0.10 ± 0.08 %

mb = 4.590 ± 0.025

± 0.030

GeV

mc = 1.142 ± 0.037

± 0.045

GeV

μπ2 = 0.401 ±

0.019± 0.035

GeV2

μG2, ρD

3,ρLS3

exp HQE SL

b→sb→clνcombined

Based on:

Babar: • PRD69, 111103 (2004)• PRD69, 111104 (2004)• PRD72, 052004 (2005)• hep-ex/0507001

Belle:• PRL93, 061803 (2004)• hep-ex/0508005

CLEO: • PRD70, 032002 (2004) • PRL87, 251807 (2001)

CDF: PRD71, 051103 (2005)

DELPHI: EPJ C45, 35 (2006)

Use inputs from BaBar, Belle, CLEO, CDF &

DELPHI:

b->clv and b->s

b

s

b

c

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v

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•Shape of F(w) unknown•Parametrized with 2 (slope at w = 1) and form factor

ratios R1, R2 ~ independent on whA1 expansion a-la Caprini-Lellouch-Neubert

Exclusive |Vcb| and Form Factors

Reconstruct B -> D*+ev as D*+ D0+ with D0 K

G(w) known phase space factorF(w) Form Factor (FF)w = D* boost in B rest frame

BaBar hep-ex/0602023

+0.030

-0.035

•F(1)=1 in heavy quark limit; lattice QCD says: F(1) = 0.919 Hashimoto et al, PRD 66 (2002)

014503

-> measure form factors from multi-dimensional fit to diff rate-> measure |Vcb| with

21222

2

*

,,,,,,coscos

RRqfVddddq

DBdVcb

V

Nucl. Phys. B 530, 153 (1998)

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B D*l Form Factors and |Vcb|

hep-ex/0602023

Using latest form factors with previous BaBar analysis: PRD71, 051502(2005)

|Vcb| = (37.6±0.3±1.3 ) x 10-3

+1.5-1.3

Reducing FF error: 2.8% -> 0.5% Total sys error: 4.5% -> 3.5%

80 fb-1

80 fb-1Factor 5 improvement of FF uncertainty from previous

CLEO measurement (1996).

1D projections of fit resultR1 = 1.396 ± 0.060 ± 0.035 ± 0.027

R2 = 0.885 ± 0.040 ± 0.022 ± 0.013

2 = 1.145 ± 0.059 ± 0.030 ± 0.035

stat MC sys

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Summary of |Vcb| Results

Excl: |Vcb| = (40.9±1.0exp F(1)) x 10-3 (D*lv)

Incl: |Vcb| = (42.0±0.2exp±0.4HQE±0.6) x 10-3

+1.1-1.3

The new BaBar form factors and |Vcb| result are not included. Work is going

on.

B->D*lv B->Dlv

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|Vub |

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How to Measure b → ul

•Need to suppress the large b → clbackground (×50)

• Inclusive: – mu << mc differences in kinematics– Maximum lepton energy 2.64 vs. 2.31 GeV– < 10 % of signal accessible

• How accurately do we know this fraction?

•Exclusive: – Explicit reconstruction of final-state hadrons– B lv, B lv, B lv, B lv, …– Need form factors (FF) to describe hadronization effects– Example: the rate for B lv is

• How accurately do we know the FF ?(for vector mesons 3 FFs)

222 3 2

2 3

( )( )

24F

ub

Gd BV p f q

dq

Form Factor

E

b c

b u

2.64

2.31

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Inclusive b → ulStrategies

Use kinematic cuts to separate bulv from bclv decays:

2q

b c

b u

E

b c

b u

Xm

b cb u

Not to scale!Not to scale!

•smaller acceptance -> theory error increase• OPE breaks down• shape function to resum non-pert. corrections

•measure partial branching fraction B

•get predicted partial rate from theory

Experimental resolution not included!Experimental resolution not included!

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Lepton Endpoint

•Select electrons with 2.0 < El < 2.6 GeV– Push below the charm threshold

Larger signal acceptance Smaller theoretical error

– Accurate subtraction of background is crucial!

– S/B =1/15 for the endpoint El > 2.0 GeV– Measure the partial BF

L(fb-1) E (GeV) (10-4)

BABAR: 80 2.0–2.6 5.72 ± 0.41stat ± 0.65sys

Belle: 27 1.9–2.6 8.47 ± 0.37stat ± 1.53sys

CLEO: 9 2.2–2.6 2.30 ± 0.15stat ± 0.35sys

BABAR

total BF is ~2103

BABAR hep-ex/0602023

MC signalb ulv

Data – bkgd.

Data

MC bkgd.b clv

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El and q2

• Try to improve signal-to-background

• Use pv = pmiss in addition to pe calculate q2

– Define shmax(El, q2) = the maximum mX squared

• Cutting at shmax < 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

(10-4)

BABAR 80fb-1 3.54 ± 0.33stat ± 0.34sys

0.5 1 1.5 2 2.5

5

10

15

20

25

b clv

El (GeV)

q2 (G

eV2 )

b ulv

Smaller systematic errors

BABAR

Extract signal normalize bkg

•Measured partial BF

BABAR PRL 95:111801

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mX and q2

•Must reconstruct all decay products to measure mX or q2

– Use (fully-reconstructed) hadronic B tag

•Suppress b → c lv by vetoing against D (*) decays– Reject events with K– Reject events with B 0 → D *+(→ D0 +)l−v

•Measure the partial BF in regions of (mX, q2)– mX < 1.7 GeV and q2 > 8 GeV2:

(10-4) = 8.7 ± 0.9stat ± 0.9sys (211fb-1)

BABAR hep-ex/0507017

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Theory for b → ul

•Tree level rate must be corrected for QCD• Just like b → cl…, and with similar accuracy

•…until limited experimental acceptance is considered•Poor convergence of HQE in region where b → cl decays

are kinematically forbidden•Non-perturbative Shape Function (SF) must be used to

calculate partial rates

= scale which separates effects from long- and short-distance dynamics

AEW = EW corrections; Apert = pert. corrections (sj , s

k0)

32

2

52

22

32

3

52 12))(1(

21)(1||

1921)(

bb

Gpert

b

Gpertub

bFEWu m

Om

Am

AVmG

AXB

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Light-cone momentum distribution of b quark: f(k+)– Fermi motion of b quark inside B meson– Universal property of the B meson (to leading order);

subleading SFs arise at each order in 1/mb

•Consequences: changes effective mb smears kinematic spectra

•SF cannot be calculated must be measured

Rough features (mean, r.m.s.) are known

k

( )f k

B bM m

Details, especially the tail, are unknown

0

Shape Function – What is it ?

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Extracting the Shape Function

•We can fit inclusive distributions from b → s or b → clv decays with theory prediction

– Must assume a functional form of f (k+)

•Example:

•New calculation connects SF moments with b-quark mass mb and kinetic energy

2 (Neubert, PLB 612:13) – Determined precisely from b → s and b clv decays

• from b → s, and from b c lv– Fit data from BABAR, Belle, CLEO, DELPHI, CDF:

•Use SF together with calculation of triple-diff. decay rate Bosch, Lange, Neubert, Paz (BLNP) to get |Vub|

(1 )( ) (1 ) ;a a x kf k N x e x

nEnE

nXm

2 2(4.60 0.04)GeV, (0.20 0.04)GeVbm Buchmüller & Flächerhep-ph/0507253

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|Vub| from Branching Fraction

Results of different calculations/ HQE parameters using the same partial branching fraction:

For converting a branching fraction into |Vub|the phase space acceptance is needed:

3) |Vub|=(4.82±0.36exp±0.46SF+theo)10-3

2) |Vub|=(4.65±0.34exp ±0.23theo)10-3+0.46–0.38SF

1) |Vub|=(5.00±0.37exp±0.46SF±0.28theo)10-3

4) |Vub|=(4.86±0.36exp±0.22theo)10-

3

Example for mx/q2

1) BLNP: BaBar BXcl moments

mb(SF) = 4.61 ± 0.08 GeV

π2(SF) = 0.15 ± 0.07

GeV2

3) BLL: BaBar BXcl momentsmb(1S) = 4.74 ± 0.06 GeV

2) BLNP: Belle BXs spectrum

mb(SF) = 4.52 ± 0.07 GeV

π2(SF) = 0.27 ± 0.23

GeV2

4) DGE: HFAG averagemb(MS) = 4.20 ± 0.04 GeV

BLL – Bauer, Ligeti, LukeDGE – Anderson, Gardi

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Status of Inclusive |Vub|

|Vub| world average winter 2006

Experimental Error 4.5%

SF parameters (mb,

2)4.1%

Theory Error 4.2%

|Vub| determined to 7.6%

Numbers rescaled by HFAG.SF parameters from hep-ex/0507243,

predicted partial rates from BLNP

BLNP: Shape Function PRD72:073006(2005) 4.45 0.20exp 0.18SF 0.19theo

Andersen-Gardi: DGE JHEP0601:097(2006) 4.41 0.20exp 0.20theo

NEW!

|Vub| [x10-3]:

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Summary

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Exclusive b → ulv

B → lvInclusiveb → ulv q2

lv, lv ?

b → s

ShapeFunction

E

mb

Inclusive b → clv

mXEl

HQE Fit

mX

El

WA

duality

|Vub|

SSFs

FF

LCSR LQCDunquenching

How it all fits togetherExclusive b → clv

|Vcb| B → Dlv

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Conclusions

• |Vcb| determined with high precision (2%)

Now |Vub| is important!

• Precise determination of |Vub| complements sin2 to test the validity of the Standard Model– 7.6% accuracy achieved so far 5% possible?

• Close collaboration between theory and experiment is importantInclusive |Vub| : – Much exp. and theo. progress in the last 2 yearsExclusive |Vub| : – Significant exp. progress in the last year, but further improvement in B → FF calculations needed (also new calculations for B → lB → lB → l– Accuracy of for exclusive |Vub| in the next few years (?)

• Important to cross-check inclusive vs. exclusive results

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The Unitarity Triangle: 2004 2005

•Dramatic improvement in |Vub|

•sin2 went down slightly Overlap with |Vub/Vcb| smaller