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Discussion on theoretical inputs for the extraction
of Vcb and Vub.
Discussion on theoretical inputs for the extraction
of Vcb and Vub.
Minutes of the Feb. 18th meeting
Organisers: Marco Battaglia and Pauline Gagnon for
the LEP b physics steering group.
Were present: D. Abbaneo, U. Aglietti, P. Ball, M. Battaglia,
G. Buchalla, M. Calvi, J. Fischer, P. Gagnon, A. Hoang,
S. Mele, G. Nardulli, F. Palla, G. Ricciardi, R. Tenchini,
W. Venus, N. Uraltsev
Agenda:
1) Uncertainties in the prediction of the lepton spectrum:
present status and perspectives
(Pauline Gagnon)
2) Determination of mu_pi**2, m_b - m_c, and Lambda bar based on
the moment analysis of the lepton spectrum
(Marco Battaglia)
3) Parton-hadron duality violation in semileptonic and hadronic
B decays (Nicolai Uraltsev)
4) Present status on theoretical inputs for Vcb and Vub
(Pauline Gagnon) (this last point was skipped for lack of time)
1) Lepton spectrum modelling in semileptonic b decays
Presentation: Pauline Gagnon showed transparencies on the
experimental determination of b to l decays as presented in Tampere. She
showed how the uncertainty on the modelling of the lepton spectrum
feeds into the systematic uncertainty on this measurement. Most
determination techniques rely on information from the transverse
lepton momentum w.r.t. to the jet (which is affected by the decay
modelling of the lepton momentum spectrum) and the full momentum
(which is affected by the fragmentation function). This information
is used differently in the various analyses used at LEP
and contributes accordingly. To assess
the contribution of the lepton spectrum modelling on this measurement,
the EWWG suggested in 1993 to use the ACCMM model tuned to
CLEO data for central value
and the ISGW and ISGW** for the +1 and -1 sigma errors. The
ISGW** model is a modified version of the ISGW model where the
contribution from D** states was left as a free parameter
and fitted to the CLEO data, leading to 32% contributions from
D** states instead of the 9% from the initial model. This
prescription was chosen for lack of a better choice. The ISGW and
ISGW** models provide a variation on the each side of the
shape of the ACCMM spectrum. This prescription is used by all
LEP experiments, including L3 for their new measurement. (L3 had used
a different approach at the time of the Tampere conference).
Attempts were made at OPAL to discriminate between the various
existing models. The ACCMM model was refitted to OPAL data and yielded
different model parameters: the Fermi momentum p_f was found to be
(837 +/- 210) MeV for OPAL data instead of 298 MeV for CLEO data.
The charm quark mass m_c was fitted to be (1287 +/- 139) MeV/c**2 for
OPAL data, compared to 1673 MeV/c**2 for CLEO data. The ISGW model
was revised recently by its authors in the framework of HQET. The new
model ISGW2 did not provide a better description of the
OPAL data. In the end, there was not enough sensitivity to
discriminate between all these models, except to say that the
ISGW2 model was disfavoured. Similar attempts are underway at Delphi.
When the results from all
LEP experiments are combined in the LEP electroweak working group
(EWWG) global fit to all electroweak parameters, the modelling error
is taken to be completely correlated and is not reduced by the combination.
After combination of all results, the modelling error comes second
to errors from detector event reconstruction and lepton identification.
These errors are uncorrelated between the four experiments and are reduced
by the combination.
Discussion: There are still no new theoretical models available.
An alternative model based on resonant states with constraints from
sum rules was developed at U. Minn. but this activity has been discontinued.
This was done by one of N. Uraltsev's student.
Nicolai said he could work on it if there is interest in the community.
Patricia Ball tried last year to improve the situation
but her attempts failed as well.
2) Using lepton energy and hadronic moments to determine
theoretical inputs
Presentation: Marco Battaglia.
The analysis of the moments of the lepton energy and the hadronic mass in
semileptonic B decays was proposed a long ago as a mean of estimating m_b and
m_b - m_c.
A preliminary analysis was performed by CLEO but the results were not
conclusive. The feasibility of the moment analysis for the lepton energy will
be studied at LEP where there are some advantages (i.e. accessing the full
energy spectrum) and disadvantages (unfolding the B boost) compared to CESR.
Discussion:
It was pointed out that it is advantageous to use up to the fifth
moment. The higher moments are sensitive to higher order operators.
Patricia Ball suggested also
to use moments around the end-point E_max instead of the average
energy, namely (E - E_max) and m_b instead of Lambda bar.
Marco has established
contact with Voloshin to get the necessary programs to perform
this analysis on Delphi data.
3) Quark-hadron duality violation in semileptonic b decays
Presentation:
Nicolai Uraltsev presented results from a recent
study he has conducted with I. Bigi using a 't Hooft model in (1+1)
dimensions with N_c --> infinity. This model has
built-in confinement and infinitely narrow resonances.
He found that for heavy-to-heavy transitions, duality holds
to better than 1% as soon as there is enough energy to excite the D**
states. For heavy-to-light transitions, the maximum duality
violation found was about 2%. General assumption dictates that
duality holds after having
integrated several resonances. The 't Hooft model shows
the first P-wave state to be sufficient.
Discussion:
Gerhard Buchalla mentioned other studies
(Aleksan (1995) and Deandrea (1997)) that have given proof
of quark-hadron duality in (3+1) dimensions QCD in the limit
of large N_c and small velocity. Possible tests of duality
were discussed:
- by looking at D - D bar mixing
- by studying the lepton spectrum for B_u --> X_u l nu and
B_d --> X_u l nu. This would test non factorizable contributions to
the matrix element. The effect is expected at E_l - m_B/2 of the
order of Lambda_QCD.
4) Present status on theoretical inputs for Vcb and Vub
Presentation:This last point was skipped for lack of time.
All details on the current status of theoretical inputs can be found
in the
note written by the LEP b steering group
Comment: From several informal discussions
held before and after the meeting,
it appears that all theorists consulted
agree on the size of the errors used to derive
Vcb and Vub by the LEP b steering group (see the
latest draft on the b
steering group page).
The main (if not only) remaining pending issue is to
determine the validity on the quark-hadron duality which is
explicitly used (but not yet proven to hold) for the
determination of Vub and Vcb through the inclusive semileptonic
rates b --> X_c l nu and b --> X_u l nu. The good agreement found
for Vcb and Vub derived from either
the inclusive or exclusive methods (see draft above)
suggests that if duality violation occurs, it is only at a
few percent level. This will be the starting point of the
next meeting
scheduled for 17 March 2000 at CERN.