Elisabetta Barberio University of Melbourne Beauty 2006: Oxford September 2006 Measurements of V cb...

Elisabetta Barberio University of Melbourne

Beauty 2006: Oxford September 2006

Measurements of Vcb

and Form Factors

September 2006 E. Barberio 2

Standard Model Consistency Tests

Vcb provide a test of CP violation in the Standard Model comparing the measurements on the () plane


Semileptonic B decaysSemileptonic B decays

tree level, short distance:

decay properties depend directly on |Vcb|,mb

perturbative regime (s

n)

Vcb

u

+ long distance:

,u

But quarks are bound by softgluons: non-perturbative (QCD) long distance interactions of b quark with light quark


heavy quark symmetry

heavy quark: the energy of soft gluon QCD~250 MeV << mb,c

heavy quark spin and mass (flavour) are good symmetry as mQ/QCD ∞

departure from the heavy quark symmetry can be expressed as (QCD/mQ)n corrections

Two methods to extract Vcb

Inclusive b + Br(b cl) + shapes

Exclusive

€

(Br B→D(*)lυ)+HQET


Inclusive semileptonic decays

Short distance is calculable Long distance leading order and short distance contribution are cleanly separated

Operator Product Expansion predictions: integration over neutrino and lepton full phase space provides smearing over the invariant hadronic mass of the final state

Many theorists love inclusive semileptonic decays

Most accurate Vcb determination from inclusive decays: precision limited by theory error


Vcb from inclusive semileptonic decays

sl described by Heavy Quark Expansion in (1/mb)n and sk

€

(B→ Xcl) =GF

2mb5

192π 3Vcb

2

1+ Aew[ ]Anonpert Apert ⎡ ⎣ ⎢

⎤ ⎦ ⎥

The expansion depend on mb definition: non-perturbative terms depend on the choice of mb definition

exp. |Vcb|<1%

€

sl(b→ cl −) =γth Vcb

2

=BR(b → cl −ν )

τb

non perturbative parameters need to be measured

Theory error is dominated by 1/mb3 terms and

above

Parameters of HQEParameters of HQEDecay rate in are express in terms of OPE up to 1/mb

3

Calculations available in different renormalization schemes (mb definition):

• Kinetic running mass (P. Gambino, N.Uraltsev, Eur. Phys. J. C 34, 181 (2004))

• 1S mass (C.Bauer, Z.Ligeti, M.Luke, A.Manohar, M.Trott PRD 70 094017)

• Pole mass not used anymore: not well behaved, irreducible error on mb


Difficulty to go from measured shape to true shape: e.g. QED corrections, accessible phase space, resolution, background

Inclusive SL decays

rate

shape

shape

|Vcb|

mc, G,

mb, 2

1.5


non-perturbative parameters are extracted from the spectral moments

moments in semileptonic decays

Xn are evaluated either on the full lepton spectrum or part of it: p > pmin in the B rest frame

€

Xn

=X− Xo( )

n∫

dΓ

dXdX

dΓ

dXdX∫

= f 'OPE mb ,mc ,α s( )

E : lepton energy spectrum (BaBar Belle CLEO Delphi)

MX: hadronic mass spectrum (BaBar Belle CDF CLEO Delphi)

10

Full reconstruction

flavour - charge - momentum

B+ and B0 decays studied separately

fully reconstruct the tag-side B meson by searching the decay modes e.g. B→D(*), B→ D(*)ρ, and B→D(*)a1

Bsig→Xl

K γ

γ

l-

BB0 0

Υ(4S)

Btag→DX

BXc

But low efficiency < 1%


Most recent measurements from Belle

moments in BXc

Plmin = 0.4

GeV

P*l (GeV)P*

l (GeV)

from the moments of these distributions we get Vcb and HQ parameters

140 fb-1

sample


Moments with threshold

Belle unfolded

spectrum:

B0 and B+ combined

(statistical errors only)

0.4 GeV electron energy threshold

Measure up to 4th moment!


Electron energy moments and partial BR

Decrease of truncated

BR

Incr

ease

of th

e

mea

n

Decrease of the

width

Belle-Conf-0667Belle final results

Systematics: b->c model, background, electron detection

Br(B+)0.4GeV=(10.79±0.25±0.27)%

Br(B0)0.4GeV=(10.09±0.30±0.22)%


BR(B→Xcl) ~ 10.5%

21 %

54%

~25%

Grounds states Broad states Narrow states

Hadronic Xc system

Important to understand the shape and branching fractions of each hadronic contribution: B→D**l not measured well

Select (4S) decays with fully reconstructed hadronic B decays “Btag”

Select events with one identified lepton (electron or muon)

Constrain neutrino mass to zero:

pX = pbeam-pBtag-pl-pν

K γ

γ

l-

ν

B B00

Υ(4S)

Mx

M2miss < 3 GeV2/c4

Belle hadronic mass moment analysis

Bsig→Xlν

Btag→DX

Measure Mx mass on signal side of the event:


Hadronic-Mass Spectrum

Measured Mx2

spectrum for different El

*cut

Main systematics: b→c model, background subtraction

Belle ICHEP06


Results and systematic uncertainties

The moments are derived from the unfolded spectrum down to 0.7 GeV minimum lepton energy in the B rest frame

0.7 GeV

El*cut

1.5 GeVdecrease in higher mass final

states

D*

D**

D

BelleUnfolded Mx

2 spectrum

Mx2 (GeV2/c4)

Vcb extraction

mkinb ,mkin

c (m1Sb) - mass of b and c

quarks

ΛQCD2/mb

2μ

2(λ1) - kinetic energy of b quark,

μG2

(λ 2) - chromomagnetic coupling

ΛQCD3/mb

3 ρD, ρLS (ρ1,τ1-3)

well behaving renormalization schemes are used:• Kinetic running mass• 1S mass

both schemes have 7 free parameters:

higher moments are sensitive to 1/mb3 terms

reduce theory error on Vcb and Heavy Quark parameters

Kinetic SchemeBelle

/dof =17.8/24

mb = 4.564 ± 0.076 GeV, mc = 1.105 ± 0.116 GeV

Contours =1

|Vcb| = (41.93 ± 0.65fit ± 0.48αs ± 0.63th )×10-3

BRBR EEe,1e,1

EEe,2e,2

EEe,3e,3

MMxx22

EEγγ,1,1

MMxx44

EEγγ,2,2

Yellow band: theory errorYellow band: theory errorFilled circles: used in Filled circles: used in fitfit

Preliminar

Preliminaryy

Belle ICHEP06


|Vcb| = (41.5 ± 0.5fit ± 0.2 )×10-3

1S Scheme

mb1s= 4.73 ± 0.05 GeV

1 = -0.30 ± 0.04 GeV

Belle ICHEP06

EEe,3e,3

MMxx22

EEγγ,1,1

MMxx44

EEγγ,2,2

2020

Yellow band: fit errorYellow band: fit errorRed band: Theory + FitRed band: Theory + Fit

BRBREEe,1e,1

EEe,2e,2

Filled circles: used Filled circles: used in fitin fit

/dof = 6/17

Contours =1

Preliminar

Preliminaryy


Vcb and HQ parameters

Exp HQ sl

Global fit Kinetic scheme expansion - all experiments (Buchmuller, Flasher PRD73:073008 (2006))

Belle new measurements missing

Vcb @ 2%

mb < 1% crucial for

Vub

mc @ 5%

|Vcb|

=(41.96±0.23exp±0.35HQE±0.59SL)10-3


c

q

-

w=1

HQET and B D*l

w=1 D* produced at rest in B rest frame

€

w=mB2+m

D*2 −q2

2mBmD*

l

Vcb

b c

q2q2 4-momentum transfer

Heavy Quark Effective Theory (HQET):simplified description of processes involving heavy heavy quark transitions

B D(*)l transitions non-perturbative effects are described by one form factor , Isgur-Wise function, as a function of w

c

q

-

w>1


Vcb from B D*l

d(B→D*l)

dw=K(w)F (w)V

cb

measure d/dw and extrapolate at w=1 the slope is important

fit for both intercept F(1)|Vcb| and slope 2

when mQ∞ (1)=1 Vcb extraction

F(1

)Vcb

w

F(1)~(1)~ 1K(1) =0

DelphiK(w): phase space (known function)F(w): unknown form factor F(1)•g(w)

in the heavy quark limit

F(1)=(1)=1


signal and w reconstruction

B D*lD* +

slowD0: m(D*)-m(D0)~m(+): + is almost at rest in the B rest frame difficult to reconstruct when the B is almost at rest

Main physics background BD**l, D** resonant and non resonant

CLEO

Signal region

cos(θB−D* l

) =E

BE

D* l−m

B

−mD* l

pBp

D* l

cos(θ

B−D* l)

cos(θ

B−D* l)


€

F (w)=hA1(w) f1 (r, w) 1 +R1 (w)

w−1

w +1

⎛

⎝⎜⎜

⎞

⎠⎟⎟+ f (r, w) 1 + 1−R (w)

w−1

r−1

⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

⎧

⎨⎪

⎩⎪

⎫

⎬⎪

⎭⎪

extrapolation: form factor shape expansion around w=1 up to second order:

Caprini,Lellouch,Neubert NP B530(98)153 and Boyd,Grinstein,Lebed PRD56(97)6895

use dispersive relations to constraint the shape

R1,R2 calculated using QCD sum rules

R1(w)1.27-0.12(w-1)+0.05(w-1)2 R2(w) 0.80+0.11(w-1)-0.06(w-1)2

measured by CLEO:

R1(1)=1.18±0.30±0.12 R2(1)=0.71±0.22±0.07

For long time R1,R2 uncertainty was the major source of systematic on A

2

used in the oldworld average


form factor shape

one-dimension projection

of fitted distributions:

Fit w and 3 angles


form factor and Vcb

Simultaneous fit of the Form factors and Vcb

F (1)|Vcb|=(34.680.321.15)10-3

Br(B0 D*+l)=(4.840.39)%


F (1)|Vcb|

2/dof = 38.7/14

2=1CL=37%

New HFAG average uses R1, R2

from Babar: this decrease F (1)|Vcb|

F (1)|Vcb|=(36.20.8)10-3 A2

=1.190.06


non-perturbative QCD calculations

F(1) =0.9070.0070.0250.017

F(1) =0.9000.0150.0250.025

F(1) =0.919

-0.035

+0.030

|Vcb|excl=(39.40.9exp1.5theo)10-3

F(1) and Vcb

from lattice and sum rule


Vcb from Bd0D+ decays

BELLE

G(1)|Vcb|=(42.64.5) x 10-3

G2 =1.17 0.18

large combinatorial background but very good prospective on the theory side for G(1)

Worth to measure as it will may cross-check Vcb excluisve


(BD*,**)/(BDX) Measurement

There is disagreement between inclusive and exclusive b cl branching fractions

(BD*,**)/(BDX) is sensitive to non resonant states

Measure simultaneously D, D* and D** components using the fully reconstructed events

211 fb-1


(BD*,**)/(BDX) Measurement

This measurement is not solving the puzzle …

RD*

=Br (B

−

→ D*0

l)

Br (B0

→ D* −

l)=1.3 ±0.07


Conclusions

|Vcb|

inc=(41.96±0.23exp±0.35HQE±0.59SL)10-3

|Vcb|excl=(39.40.9exp1.5theo)10-3

Vcb is now a precision measurement:

The measurement of mb from the inclusive spectrum arecrucial for the precise extraction of Vub

BD** are still a puzzle and a concern….

Inclusive and exclusive analyses give consistent results

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Elisabetta Barberio University of Melbourne Beauty 2006: Oxford September 2006 Measurements of V cb...

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