1. Inclusive semileptonic B decays: experimental
Elisabetta Barberio
University of Melbourne
FPCP: Vancouver April 2006

2. Standard Model Consistency Tests
Vub and Vcb provide a test of CP violation in the Standard
Model comparing the measurements on the (r, h) plane
The width of the green ring
need to be reduced to
match sin2b and other
measurements
The error on the ring width
is dominated by Vub
Goal: Accurate determination of |Vub|
April 2006
E. Barberio

3. Semileptonic B decays Vcb ,Vub tree level, short distance:
decay properties depend
directly on |Vcb|, |Vub|,mb
perturbative regime (asn)
Vcb ,Vub u
+ long distance: ,u
But quarks are bound by soft
gluons: non-perturbative (LQCD)
long distance interactions of b
quark with light quark
April 2006
E. Barberio

4. Inclusive semileptonic decays
Many theorists love inclusive semileptonic decays
Short distance is calculable
Long distance leading order and short distance contribution
are cleanly separated and probability to
hadronnize is 1
To compare Operator Product Expansion predictions
with experiments:
integration over neutrino and lepton phase space provides
smearing over the invariant hadronic mass of the final state
April 2006
E. Barberio

5. Inclusive semileptonic decays
Vcb vs Vub
Vcb: most accurate determination from the inclusive decays
2% precision limited by theory error
precise Heavy Quarks parameters, tests of OPE
Vub: 7.5% precision shared between experimental and
theoretical errors
small rate and large bcln background
space cuts to remove bcln background which introduce
O(1) dependence on non-preturbative b-quark distribution
function
April 2006
E. Barberio

6. Vcb from inclusive semileptonic decays
exp. D|Vcb|<1%
Gsl described by Heavy Quark Expansion in (1/mb)n and ask
non perturbative parameters need to be measured
The expansion depend on mb definition: non-perturbative terms are expansion dependent
Theory error was dominated by 1/mb3 terms and above
April 2006
E. Barberio

7. Bc moments in semileptonic decays
Xn are relate to non-perturbative parameters
moments evaluated on the full lepton spectrum or part of it: p > pmin in the B rest frame
higher moments are sensitive to 1/mb3 terms  reduce theory error on Vcb and HQ parameters
April 2006
E. Barberio

8. Inclusive SL decays
rate
shape
|Vcb|
mc, m2G,
mb, m2p
Difficulty to go from measured shape to true shape: e.g. QED corrections, accessible phase space, resolution, background
April 2006
E. Barberio

9. moments in semileptonic decays
E : lepton energy spectrum in BXc n (BaBar Belle CLEO Delphi)
MX 2: hadronic mass spectrum in BXc n (BaBar CDF CLEO Delphi)
Most recent measurements from Belle
mx (GeV)
P*l (GeV)
P*l (GeV)
Plmin =0.7 GeV
Plmin =0.4 GeV
from the moments of these distributions we get Vcb and HQ parameters
April 2006
E. Barberio

10. Parameters Extraction
BABAR: up to 1/mb3: fit ~90 measurement to extract HQ parameter and Vcb at the same time
MX moments
o= used, •= unused in the nominal fit
BABAR
c 2/ndf =20/15
M1x
M2x
M3x
M4x
M0l
M1l
M2l
M3l
Red line: HQE fit Yellow band: theory errors
P.Gambino, N.Uraltsev
hep-ph/
hep-ph/
April 2006
E. Barberio

11. Vcb and HQ parameters
Global fit Kinetic scheme expansion (hep-ph/ ) 2%
mb < 1%, 5%
U(1S) expansion scheme has similar results
Exp HQ Gsl
used measurements:
April 2006
E. Barberio

12. Vub inclusive determination
B Xuln rate tree level from OPE  corrected for perturbative as and non-perturbative 1/mb terms
In principle main uncertainty
from mb5
Tree-level rate was calculated at the quark level, but what we observe is the hardrons.
BUT…..
Br(BXuln)/Br(BXcln) =1/50
April 2006
E. Barberio

13. Shape Function Limited phase space to reduce the B  Xcln background:
OPE doesn’t work everywhere in the phase space  non-perturbative Shape Function F(K+) to extrapolate to the full phase space
F(K+)
L = MB -mb K+
Detailed shape not constrained,
in particular the low tail
Mean and r.m.s. are known
Shape Function need to be determined from experimental data
April 2006
E. Barberio

14. Inclusive B  Xuln mu << mc  exploits different kinematics l
q2 = lepton-neutrino mass squared
mX = hadron system mass
El = lepton energy
P+ = EX -|PX|
Signal events have smaller MX and P+  Larger El and q2
bu
bc
Not to scale!
April 2006
E. Barberio

15. Lepton Endpoint First measurement from CLEO El>2.3 GeV
BABAR PRD 73:12006 Belle PLB 621:28 CLEO PRL 88:231803
First measurement from CLEO El>2.3 GeV
BaBar
BaBar El>2.0 GeV
Belle El> 1.9 GeV
Crucial accurate subtraction of
background is crucial!
S/B ~1/10 eff~ 40%
DB (10-4)
BABAR 80fb-1
5.72 ± 0.41stat ± 0.65sys
Belle 27fb-1
8.47 ± 0.37stat ± 1.53sys
CLEO 9fb-1
2.30 ± 0.15stat ± 0.35sys
April 2006
E. Barberio

16. Measuring mX q2 P+
BABAR hep-ex/ Belle PRL 95:241801
Reconstruct all decay products to measure MX ,q2 or P+
fully-reconstructed B meson
flavor and momentum known
lepton in the recoil-B
mmiss consistent with a neutrino
lepton charge consistent with B flavor
left-over particles belong to X
equal mB on both sides; mmiss = 0
S/B ~ 2 Eff~ 0.1%
April 2006
E. Barberio

17. Measuring Partial Branching Fraction
P+ BLNP PRL93:221802
DB (10-4)
BABAR 211fb-1
mX < 1.7, q2 > 8
8.7 ± 0.9stat ± 0.9sys
Belle 253fb-1
first measurement of P+ spectrum
mX < 1.7
12.4 ± 1.1stat ± 1.0sys
8.4 ± 0.8stat ± 1.0sys
P+ < 0.66
11.0 ± 1.0stat ± 1.6sys
April 2006
E. Barberio

18. |Vub| Turning DB into |Vub| Eg mb mX El HQE Fit El q2 mX
b → sg
Shape Function Eg mb
Inclusive b → clv mX El
HQE Fit
SSFs
Inclusive b → ulv El
HFAG main results:
HQ parameters form
b  Xcln and b  Xsg
hep-ph/
|Vub| q2 mX
duality WA

19. Dealing with Shape Function
easy to fit shape function
Better resolution  K* peak (more difficult for SF)
Belle
Eg>1.8 GeV
E*g (GeV)
Eg (GeV)
Solution  use directly the g spectrum:
theory
April 2006
E. Barberio

20. Inclusive |Vub|: BLNP framework
|Vub| world average as of Winter 06
Inputs:
mb(SF) = 4.60  0.04 GeV
mp2(SF) = 0.20  0.04 GeV2
|Vub|BLNP=(4.45  0.20  0.26) 10-3
d|Vub| =  7.3%
Statistical
2.2%
Expt. syst.
2.7%
B  Xcln model
1.9%
B  Xuln model
2.1%
Subleading SF
3.8%
other theory error
4.5%
April 2006
E. Barberio

21. Theory Errors Quark-hadron duality is not considered (cut dependent)
b cln and b  sg data fit well HQ predictions
Weak annihilation   1.9% error
Expected to be <2% of the total rate
Gw.a./G(b  u) < 7.4 % from CLEO
HQ parameters   4.1% mainly mb; kinematics cuts depend on mb,!
Sub-leading shape function   3.8% dominated by the lepton endpoint measurements B u b l n q
April 2006
E. Barberio

22. Inclusive |Vub|: DGE framework
Dressed Gluon Exponentiation (DGE)
on-shell b-quark calculation converted into hadronic variables
used as approximation to the meson decay spectrum
Still digesting the method
|Vub|DGE = (4.41  0.20  0.20) 10-3
DGE theory  2.9% matching scheme method and scale
mb(MS)   1.3% on event fraction mb(MS)=4.200.04 GeV
as   1.0% on event fraction
total GSL   3.0 %
April 2006
E. Barberio

23. Vub without Shape Function
Babar
Based on Leibovich, Low,
Rothstein, PLB 486:86
First proposal by Neubert
Weight function
Babar
Babar
mxcut
OPE mx<2.50 GeV
LLR mx<1.67 GeV
April 2006
E. Barberio

24. |Vub|: inclusive vs exclusive
W.A. Winter 06
|Vub| exclusive
W.A. Winter 06
April 2006
E. Barberio

25. |Vub|: CKM consistency
Most probable value of Vub from measurements of other CKM parameters Standard Model predictions with
Dms measurement
(thank to Pierini)
Vub from exclusive
measurements
Vub from inclusive
April 2006
E. Barberio

26. Conclusions b cln b uln
Vcb 2% error dominated by theory, (kinetic and U(1S) schemes), (kinetic scheme)
but how well do we know the B Xcln spectrum?
b uln
Vub ~7.4% error shared between theoretical and experimental
inclusive vs exclusive less than 1.4 s difference, depending on the inclusive extracting method
We have now different methods to extract Vub
5% possible? Improve knowledge of B Xcln, B Xuln and more work on the theoretical error
April 2006
E. Barberio

27. Inclusive |Vub|: comparisons
HQ parameters from cln and sg
HQ parameters from sg only
April 2006
E. Barberio

28. Mx unfolded spectrum for B  Xc l n
Belle
April 2006
E. Barberio

29. photon energy spectrum
Eg : photon energy spectrum in Bsg (BaBar Belle CLEO Delphi)
u, c, t
photon energy spectrum in B Xsg not sensitive to new physics and give information on B structure
Belle
Eg>1.8 GeV
Eg>2 GeV
CLEO
April 2006
E. Barberio