1. E.Barberio University of Melbourne Daphne04: Frascati 7-11 June 2004
measurements of Vcb
E.Barberio
University of Melbourne
Daphne04: Frascati 7-11 June 2004

2. precision electroweak tests
e.w. process at tree level are computed from 3 parameters , GF , mZ
and the CKM matrix elements Vij.
aem = ppm
Gm = 9 ppm
mZ = 23 ppm
very well measured!
Vij are less well known (if at all):
extraction limited by theory error
CP Violation
8 June 2004
E. Barberio

3. physics motivation Vcb governs bc transition
ultimate goal: precise determination of Vcb !
quarks are inside hadrons bound by soft gluons  both
perturbative (mb) and non-perturbative (LQCD) QCD effects
Tools:
Heavy quark symmetry and lattice QCD
8 June 2004
E. Barberio

4. heavy quark symmetry u/d b LQCD<<mb asymptotic freedom
when the energy of soft gluon LQCD~250 MeV << mb,c heavy quark
heavy quark is ‘invisible’ to gluon probes with de Broglie wavelegnth lg>>1/mc,b:
heavy quark spin and mass (flavour) are good symmetry as
(mQ/LQCD) ∞
- departure from the heavy quark symmetry can be expressed as (LQCD/mQ)n corrections
8 June 2004
E. Barberio

5. Heavy Quark Effective Theory
Heavy Quark Effective Theory (HQET):
simplified description of processes involving heavy  heavy quark transitions
non-perturbative effects described by form factors
all B D(*)ln transitions are described by one form factor  (Isgur-Wise function) as a function of w: the D* boost in B rest frame c q n -
w=1
q2  4-momentum transfer l
Vcb b c n q2 c q n -
w>1
w=1 D* produced at rest in B rest frame
in mQ∞ (1)=1 Vcb extraction with little model dependence
bonus: BD(*)ln largest branching fraction of B decay modes
8 June 2004
E. Barberio

6. Vcb from B D*ln F(w): unknown form factor= F(1)•g(w) F(1)Vcb w
in HQET
F(1)Vcb w
DELPHI
K(w): is the phase space (known function)
F(w): unknown form factor= F(1)•g(w)
in the heavy quark limit mQ∞ F(1) =(1)=1
measure dG/dw(w) and extrapolate at w=1  g(w) slope important
fit for both intercept F(1)|Vcb| and slope (r2)
[Caprini, Lellouch, Neubert, Nucl.Phys.B530(98)]
8 June 2004
E. Barberio

7. signal and w reconstruction
Belle
D*  Dp
DKp(p)
B  D*ln
D*  p+slowD0:
m(D*)-m(D0)~m(p+): the p+ is almost at
rest close to K(w=1) in the B rest frame
p+ difficult or impossible to reconstruct
if the B is produced at rest or has
little boost
w  pn and En need good resolution for En+pn: easy if the B is produced at rest of with little boost l
Vcb b c n q2
8 June 2004
E. Barberio

8. B D(*)ln U(4S)  B0 at rest or almost LEP Z bb: B0 large variable
momentum ~30 GeV
good efficiency at w~1: less
extrapolation uncertainty at w=1
U(4S)  B0 at rest or almost
large data sample, good w resolution, low D** background
poor efficiency at w~1 w
CLEO
B-D*0-
Bd0D*+-
poorer w resolution
large background from higher D**
8 June 2004
E. Barberio

9. background from BD**ln
BD**ln with D** pD*/pD0 resonant (narrow and wide) and non resonant
LEP: resonant D**:different form factors depending on assumption on quark decay dynamics [Leibovich,Ligeti,Stewart,Wise]
D** shape from constraints on D** rates: Br(BD*2ln )/ Br(BD1ln) <0.4
U(4S):
CLEO
cosB,D*l
D*l  (73.5%)
D**l  (7.5%)
fake lep (0.3%)
uncorr (6.2%)
correlated (1.5%)
contin. (3.2%)
fake D* (7.75%)
BABAR
events/01
8 June 2004
E. Barberio

10. F(1)Vcb CLEO Bd0D*- and B-D*0- OPAL BELLE w w 8 June 2004
E. Barberio

11. F (1)|Vcb|
F (1)|Vcb|=(36.50.3tat0.8syst)x rA2 =1.470.02stat0.13syst
8 June 2004
E. Barberio

12. F(1) and Vcb
non-perturbative QCD calculations
F(1) =0.9070.0070.0250.017
F(1) =0.9000.0150.0250.025
F(1) =0.913
future error reduction from unquenched calculations
from lattice and sum rule
F(1)=0.91  0.04
|Vcb|excl=(40.10.9exp1.8theo) 10-3
8 June 2004
E. Barberio

13. Vcb from Bd0D+- decays
large combinatorial background
non-zero 1/mQ corrections to G(1)
BELLE
consistency check and test of the theory:
from Belle D* and D+ results
r2D-r2D*=-0.230.29 0.20
G(1)/F(1)=1.160.14 0.12
compatible with expectations
G(1)|Vcb|=(41.83.7) x 10-3
rG2 =1.15  0.16
8 June 2004
E. Barberio

14. Vcb from inclusive semileptonic decays
exp. D|Vcb|~1%
Gsl described by Heavy Quark Expansion in (1/mb)n and ask
non perturbative parameters to be measured and arise at each order
expansions depend on mb definition: different expation different non-perturbative terms, but they related
pole mass
low scale running quark masses L
l1 l2 or mp2 mG2 at 1/mb2
rD3,rLS3 or r1,r2,T1-4 at 1/mb3
8 June 2004
E. Barberio

15. inclusive Vcb W rate |Vcb| shape mb,mc m2G,m2p shape
from the shape get non-perturbative parameters though the ‘moments’:
8 June 2004
E. Barberio

16. moments of kinematic variables
how much is there? (area)
where is it? (mean)
how wide is it? (width)
skewness
8 June 2004
E. Barberio

17. moments in semileptonic decays
E : lepton energy spectrum in BXc n (CLEO, DELPHI)
MX 2: hadronic mass spectrum in BXc n (CLEO, BaBar, DELPHI)
Eg : photon energy spectrum in B Xsg (CLEO,Belle)
On=1,2,..: different sensitivities to non-perturbative parameters evaluated on the full spectrum or part of it (p > pmin)
OPE predictions can be compared with experiments after smearing 
integration over neutrino and lepton phase space provides smearing over the
invariant hadronic mass of the final state:
test of OPE predictions, quark-hadron duality
higher moments used to get sensitivity to 1/mb3 parameters:
reduced uncertainty on |Vcb| from inclusive semileptonic decay
8 June 2004
E. Barberio

18. photon energy spectrum
u, c, t
photon energy spectrum in B Xsg is not sensitive to new physics and give information on B structure
Belle
Eg>1.8 GeV
Eg>2 GeV
without Belle
8 June 2004
E. Barberio

19. hadronic moments hadronic mass spectra Mx
Mx from ln: MX2 = mB2+mn2-2EBEn
fit relative contributions of D,D*,D**
CLEO 3.2 fb-1
B-meson fully reconstructed
MX2
BABAR 51 fb-1
BXn
P*min= 1.5 GeV
8 June 2004
E. Barberio

20. lepton energy spectrum
spectra background subtracted
ratios of truncated lepton spectra
Gremm,Kapustin
e m
Cleo
BABAR
Babar, lower momentum cut in the B rest frame:
small B boost and larger statistics
8 June 2004
E. Barberio

21. moments at LEP
large momentum of b-hadron ~30 GeV: full lepton energy spectrum in B rest
frame  non-truncated spectra
lepton spectrum
unfolded spectrum
background subtracted
e+m
D**D0+
D**D*+-
D**D+-
Bd0 D**- decays exclusively reconstructed
M=M(D(*))-M(D(*)) fits with resonant and non resonant states
8 June 2004
E. Barberio

22. parameters extraction
CLEO: photon spectrum and hadronic mass spectrum evaluated at 1/mB3 and as2 bo
[Ligeti,Luke,Manohar,Wise] [Falk,Luke,Savage]
L = 0.350.07  0.1 GeV
l1=-0.238 0.0710.078 GeV2
1s theo.
photon, hadronic mass and lepton energy spectrum evaluated at 1/mB3and as2 bo
L= stat+0.06sys+0.12th GeV
l1= stat+0.05sys+0.14th GeV2
from 1/mB3 + as
8 June 2004
E. Barberio

23. moments at LEP
multi-parameter c2 fit to determine relevant 1/mb3 parameters
mp2 (GeV2)
mb (GeV)
rD3 (GeV3)
M1(Mx)
M2(Mx)
M3(Mx)
M1(El)
M2(El)
M3(El)
c2/d.o.f.=0.96
input:
mG2= GeV2
rLS3= GeV3
mc= 1.05  0.30 GeV
mb= 4.57  0.10 GeV
equivalent to B Xsg
mb,kin (1GeV)= fit+0.01sys GeV
mc,kin (1GeV)= fit+0.03sys GeV
mp2 (1GeV) = fit+0.02sys GeV2
rD3 (1GeV) = fit+0.01sys GeV3
mb(mb)= GeV mc(mc)= GeV
present accuracy: no need of higher order terms
L = fit+ 0.02sys GeV l1= fit+ 0.03sys GeV2
r1= fit+ 0.03sys GeV3
r2= fit sys GeV3
pole mass expantion:
(compatible with CLEO)
similar results with mb1S-l1 formalism
Bauer, Ligeti, Luke, Manohar
8 June 2004
E. Barberio

24. parameters extraction
BABAR: up to 1/mb3
fit all parameter and Vcb as function of pcut
mb,kin (1GeV) = exp+0.05HQE +0.02as GeV
mc,kin (1GeV) = exp+ 0.06HQE +0.02as GeV
mp2 (1GeV) = exp HQE +0.01as GeV2
mG2 (1GeV) = exp HQE +0.02as GeV2
rD3 (1GeV) = exp HQE GeV3
rSL3 (1GeV) = exp HQE +0.01as GeV3
p*min=1.5GeV +  from CLEO bsg: l1=-0.17±0.06±0.07 GeV2 in agreement with CLEO
8 June 2004
E. Barberio

25. derivation of inclusive Vcb
+ tB
LEP: BR(BXc -) = (10.420.26) 10-2
8 June 2004
E. Barberio

26. derivation of inclusive Vcb
Vcb dependence on non-perturbative parameters in running quark mass scheme:
N.Uraltsev hep-ph/
|Vcb| = |Vcb|0 { [ mb(1)-4.6 GeV] [mc(1)-1.15 GeV]
+ 0.01[ mp GeV2] [ rD GeV3]
+ 0.05[ mG GeV2] [ rLS GeV3] }
using sl(world) and Babar:
|Vcb| = 41.9 [1±0.009Gsl±0.010fit ±0.005pert]10-3
mb,mc,mp2,mG2,rD3,rLS3
as scale
8 June 2004
E. Barberio

27. conclusion |Vcb| from exclusive B decays
Bd0D(*)- more statistics available and new measurements coming
present precision (5%) systematics limited: slow p, D’s BR, D**?
need to understand the “exeprimental” spread of F(1)Vcb
error on F(1)=1 can be reduced in the future by lattice calculations
|Vcb|excl=(40.1 0.9exp 1.8theo) 10-3
|Vcb| from inclusive B decays
small error on BR(BXc-) and tB
quark-hadron duality violation? no evidence of any effects with the present sensitivity: constraints on non-perturbative parameters reduce the uncertainty on |Vcb| to ~2.%
more measurements will consolidate the picture
8 June 2004
E. Barberio

28. CKM mixing matrix Wolfenstein parameterization: unitarity (A†A = 1)
8 June 2004
E. Barberio

29. G(bXcln) Word average GBXc-= (0.441 0.008) 10-10 MeV U(4S):
BR(BXc -) = (10.830.25) 10-2
tB = (1.5980.01) ps
GBXc -= (0.4460.0100.003)10-10 MeV
LEP:
BR(BXc -) = (10.420.26) 10-2
tb = (1.573  0.01) ps
GBXc -= (0.4360.010 0.006)10-10 MeV
Word average
GBXc-= (0.441 0.008) MeV
8 June 2004
E. Barberio

30. Systematics
BELLE
CLEO
8 June 2004
E. Barberio

31. extrapolation: form factor shape
· expansion around w=1 up to second order:
· use dispersive relations to constraint the shape
Relate F (w) to the ratios of HQET form factors R1(w), R2(w)
Caprini,Lellouch,Neubert NP B530(98)153 and Boyd,Grinstein,Lebed PRD56(97)6895
R1,R2 calculated using QCD sum rules
R1(w) (w-1)+0.05(w-1) R2(w) (w-1)-0.06(w-1)2
or measured by CLEO: R1(1)=1.18±0.30± R2(1)=0.71±0.22±0.07
R1,R2 uncertainty is the major source of systematics on rA2, which should improve with future new measurements
8 June 2004
E. Barberio

32. Systematics
LEP
8 June 2004
E. Barberio