Semileptonic B Decays Masahiro Morii Harvard University Determination of |V ub | and |V cb | with Inclusive and Exclusive b u and b c Decays APS Meeting,

Semileptonic B Decays

Masahiro MoriiHarvard University

Determination of |Vub| and |Vcb| withInclusive and Exclusive

b u and b c Decays

APS Meeting, April 22-25, 2006

APS April Meeting 2006 M. Morii, Harvard 2

The Unitary Triangle The goal: Over-constrain the apex to test the

completeness of the Cabibbo-Kobayashi-Maskawa model

Let’s measure the opposite side precisely!

( , )

Angles: CP violation

Right side: md /m

s

Left side: |Vub /Vcb|

1.31.221.7 degrees


B

uX

b

u

ubVB

, cuX X

Hadron level

Semileptonic B Decays Natural probe for |Vub| and |Vcb|

Decay rate x (b x) |Vxb|2

c larger than u by a factor ~50 Extracting b u signal challenging

Sensitive to hadronic effects Must understand them to extract |Vub|, |Vcb|

Use data to bolster theory

b

,u c

, cub bV V

Parton level

W


Inclusive vs. ExclusiveInclusive B Xc

Inclusive B Xu

B

W

cX

cbV

B

W

uXubV

Exclusive B D*

B

W

*DcbV

Exclusive B

B

W

ubV


Inclusive Measurements Operator Product Expansion

predicts total rate u as

Dominant error from mb5

mb measured to 1% 2.5% on |Vub|

Total rate can’t be measured due to B Xcbackground Must enhance S/B with cuts

5

2

22

31

192

1

b

b sF ubG V

m

m

OO

Perturbative terms known to (s

2)Non-perturb. terms suppressed by 1/mb

2

Inclusive B Xc

Inclusive B Xu

B

W

cX

cbV

B

W

uXubV


Three independent kinematic variables in B → Xv

Measure partial rates in favorable regions of the phase space Caveat: Spectra more sensitive to non-perturbative effects than

the total rate (1/mb) instead of (1/mb2)

Need to know the Shape Function (= what the b-quark is doing inside the B meson)

Solution: Measure B Xcspectra Non-perturb. effects

Kinematical Cuts

q2 = mass squared mX = hadron system massE = lepton energy

b c

b u

b c

b ub c

b u

Not to scale!

No detector resolution!

Not to scale!

No detector resolution!

deca

y ra

te


Inclusive B Xc Spectra

Observables: E (lepton energy) and mX (hadron system mass) Measurements by BABAR, Belle, CDF, CLEO, DELPHI

OPE predicts observables integrated over large phase space

Moments:

Belle, hep-ex/0508056

E (GeV) E (GeV)

1 c

c

n n dE E d

dEE E

1n

Xn cX X

c X

dm dm

dmm

mX2 (GeV2/c4)

Belle, hep-ex/0509013


Global OPE Fit OPE predicts total rate c and moments E

n, mXn as functions

of |Vcb|, mb, mc, and several non-perturb. params Each observable has different dependence

Can determine all parameters from a global fit

E spectrum in B Xs decays connected directly to the SF Small rate and high background makes it tough to measure Measured by BABAR, Belle, CLEO

BABAR

preliminary

E (GeV)

Par

tial

BF

(10

-4/1

00 M

eV)

hep-ex/0507001

Par

tial

BF

(10

-3/1

00 M

eV)

BABAR PRD 72:052004

E (GeV)


OPE Fit Results Buchmüller & Flächer (hep-ph/0507253)

fit data from 10 measurements with an OPE calculation by Gambino & Uraltsev (Eur. Phys. J. C34 (2004) 181)

Fit parameters: |Vcb|, mb, mc, 2, G

2, D3, LS

3, BR(B Xc

Goodness of the fit and the consistencybetween Xc and Xs add confidenceto the theory

Needed for |Vub|3

exp OPE

exp OPE

exp OPE

2 2exp OPE

exp OPE

(41.96 0.23 0.35 0.59 ) 10

4.590 0.025 0.030 GeV

1.142 0.037 0.045 GeV

0.401 0.019 0.035 GeV

10.71 0.10 0.08 %

slcb

b

c

V

m

m

BR

2%

1%

BABARPRD69:111103 PRD69:111104 PRD72:052004 hep-ex/0507001

Belle PRL93:061803 hep-ex/0508005

CLEO PRD70:031002 PRL87:251807

CDF PRD71:051103

DELPHI EPJ C45:35

combined

b s

b c


Inclusive B Xu Measure partial BF (B Xu in a region where ...

the signal/background is good, and the partial rate u is reliably calculable

Many possibilities – Review a few recent results

0.5 1 1.5 2 2.5

5

10

15

20

25

b cv

E (GeV)

q2 (G

eV2 )

b uv

E endpoint

E -q2 cut

q2 (G

eV2 )

mX (GeV)

b cv

b

uv

mX cut

mX-q

2 cut

Large u generally good, but not always


Lepton Endpoint Find leptons with large E

Push below the charm threshold Larger signal acceptance Smaller theoretical error

S/B ~ 1/15 (E > 2 GeV) Accurate subtraction of background is crucial!

E (GeV) |Vub| (10-3)

BABAR 80fb-1 2.0–2.6 4.41 0.29exp 0.31SF+theo

Belle 27fb-1 1.9–2.6 4.82 0.45exp 0.30SF+theo

CLEO 9fb-1 2.2–2.6 4.09 0.48exp 0.36SF+theo

BABAR PRD 73:012006Belle PLB 621:28

CLEO PRL 88:231803

BABAR

MC bkgd.b cv

Data

Data – bkgd.

MC signalb uv

Shape Function: determined from the OPE fit

Theory errors: Lange et al. PRD72:073006

Hadronic B Tag Fully reconstruct one B in hadronic decays

Use the recoiling B with known charge and momentum Access to all kinematic variables

BABAR hep-ex/0507017Belle PRL 95:241801

lepton

v

X

253M BB

X XP E P

Region |Vub| (10-3)

Belle 253M BB

mX < 1.7 GeV, q2 > 8 GeV2 4.70 0.37exp 0.31SF+theo

mX < 1.7 GeV 4.09 0.28exp 0.24SF+theo

P+ > 0.66 GeV 4.19 0.36exp 0.28SF+theo

BABAR 210M BB mX < 1.7 GeV, q2 > 8 GeV2 4.75 0.35exp 0.32SF+theo

reconstructed B

Prelim.


|Vub| from Inclusive B Xu |Vub| determined to 7.4%

Expt. and SF errors will improve with more data

Theory errors from Sub-leading SF (3.8%)

Higher-order non-perturbative corrections

Weak annihilation (1.9%) Can be constrained with

future measurements

Experimental 4.5%

SF params. 4.1%

Theory4.2

%

World Average 4.45 0.33

2/dof = 5.5/6


SF-Free |Vub| Measurement

Possible to combine b uv and b s so that the SF cancels

BABAR applied Leibovich, Low, Rothstein(PLB 486:86) to 80 fb-1 data

Trade SF error Stat. error mX < 2.5 GeV is almost (96%) fully

inclusive Theory error reduces to 2.6%

2

2 ( )( )

( ) ub su

ts

W EV d B X

B X dEdEV

Weight function

BABAR hep-ex/0601046

mX cut (GeV)1.67

Theory error

Expt. errormX cut |Vub| (10-3)

1.67 GeV

4.43 0.45exp 0.29theo

2.5 GeV 3.84 0.76exp 0.10theo

Fullrate


Inclusive vs. ExclusiveInclusive B Xc

Inclusive B Xu

B

W

cX

cbV

B

W

uXubV

Exclusive B D*

B

W

*DcbV

Exclusive B

B

W

ubV


Exclusive Measurements Exclusive rates determined by

|Vxb| and Form Factors Theoretically calculable at

kinematical limits Lattice QCD works if D* or

is ~ at rest relative to B Empirical extrapolation is

necessary to extract |Vxb| from measurements

Measure differential rates to constrain the FF shape Then use FF normalization

from the theory

Exclusive B D*

B

W

*DcbV

Exclusive B

B

W

ubV


Exclusive B D* Decay rate is

(1) = 1 in the heavy-quark limit; lattice QCD: (w) shape expressed by 2 (slope at w = 1) and

R1, R2 (form factor ratios) Curvature constrained by analyticity

Measure decay angles , V, Fit 3-D distribution in bins of w

to extract 2, R1, R2

22*2

3

( )( ) ( )

48F cbG Vd B D l

w wdw

d F G phase space

form factor

D* boost in the B rest frame0.0300.035(1) 0.919

FHashimoto et al,PRD 66 (2002) 014503

Caprini, Lellouch, NeubertNPB530 (1998) 153


B D* Form Factors BABAR measured FF params. with 79 fb-1

R1 and R2 improved by a factor 5 over previous CLEO measurement PRL 76 (1996) 3898

Will improve all measurements of B D*

BABAR hep-ex/0602023

Signal MC vs. bkgd.-subtracteddata, 1D projections

w cos cosV

1 stat syst

2 stat syst

2stat syst

1.396 0.060 0.044

0.885 0.040 0.026

1.145 0.059 0.046

R

R

Using BABAR measurements only


|Vcb| from B D* HFAG average still uses FF from CLEO

New BABAR FF

c.f. (42.0 0.7)10-3 from inclusive OPE fit

Average 37.6 0.8 2/dof = 30.2/14

|Vcb| = (40.9 0.9 1.5(1)) 10-3


Exclusive B B v rate is given by

Form factor f+(q2) has been calculated using Lattice QCD

Unquenched calculations by Fermilab (hep-lat/0409116) andHPQCD (PRD73:074502)

12% for q2 > 16 GeV2

Light Cone Sum Rules Ball & Zwicky (PRD71:014015) 13% for q2 < 16 GeV2

22 223

2 3

( )

24( )F

ub

Gd BV f

dqqp

One FF for B → vwith massless lepton

Ball-ZwickyFermilabHPQCD

ISGW2

Quark model, PRD52 (1995) 2783


Untagged B Missing 4-momentum = neutrino

Reconstruct B v and calculate mB and

BABAR 80fb-1 PRD72:051102

dataMC signalsignal withwrong b uvb cvother bkg.

BABAR PRD 72:051102

Measured q2 spectrum starts to constrain the FF shape LQCD/LCSR favored over ISGW2

BABAR0 4

stat syst( ) (1.38 0.10 0.18 ) 10B B

2BE E s


D(*)-tagged B Reconstruct one B in D(*)v and look for B v in the recoil

B D*BF large; two neutrinos in the event Event kinematics determined assuming

known mB and mv = 0

vv

D

soft

BABAR hep-ex/0506064, 0506065Belle hep-ex/0508018

253fb-1

Signal appears in 0 < xB2 < 1

Mode BF (10-4)

Belle

B0 1.38 0.24

B+ 0.77 0.16

BABARPrelim.

B0 1.02 0.28

B+ 1.86 0.44


|Vub| from B Average BF measurements and apply FF calculations

Consistent within (large)FF errors

Experimental errors already competitive

Form Factor q2 (GeV2) |Vub| (10-3)

Ball-Zwicky < 16

HPQCD > 16

FNAL > 16

exp theo0.550.373.36 0.15

exp theo0.630.434.20 0.29

exp theo0.650.433.75 0.26

LCSR

UnquenchedLQCD

Inclusive: 4.45 0.20exp 0.26SF+theo

(q2 < 16) (10-4) (q2 > 16) (10-4) Total (10-4)

0.94 0.06stat 0.06syst

0.39 0.04stat 0.04syst

1.34 0.08stat 0.08syst


Summary Semileptonic B decays offer exciting physics opportunities

|Vub /Vcb| complements sin2 to test (in)completeness of the SM

Challenge of hadronic physics met by close collaboration between theory and experiment Inclusive B Xc & Xs fit precisely determines |Vcb|, mb, etc.

Dramatic progress in both measurement and interpretation of inclusive B Xu in the last 2 years

Inclusive |Vub| achieved 7.4% accuracy Room for improvements with additional data statistics

B D* form factors have improved by a factor 5 Measurements of B becoming precise

Improved form factor calculation needed

Backup Slides


Weak Annihilation WA turns B+ into + soft hadrons Size and shape of WA poorly known Minimize the impact

Measure Xu with v. loose cuts

Cut away large q2 region Measure WA contribution

sl(D+) vs. sl(Ds) CLEO-c

Distortion in q2

CLEO hep-ex/0601027

(B+ Xu) vs. (B0 Xu) Work in progress

Documents

Semileptonic B Decays Masahiro Morii Harvard University Determination of |V ub | and |V cb | with Inclusive and Exclusive b u and b c Decays APS Meeting,