Meeting on Shape Function Parameters
When: July 07, 2004, 07:00 AM PDT
Meeting ID: 8160
o Central values and errors of shape function parameters
o Error on mb (see e.g. hep-ex/0404017)
o Some theoretical aspects
o BABAR's note: ps pdf
and the other plots as eps A B
and as pdf A B
o Belle's SF extraction: ps pdf
KEK: Toru Iijima, Hidekazu Kakuno, Tadao Nozaki, Yoshi Sakai
Melbourne: Elisabetta Baberio, Antonio Limosani
Dresden: Heiko Lacker, Kerstin Tackmann
Frascati: Ikaros Bigi
Heidelberg: Urs Langenegger
Cornell: Stefan Bosch, Bjoern Lange, Gil Paz
SLAC: Riccardo Faccini, Bob Kowalewski, Francesca di Lodovico
In the following SF = shape function; dF/N = de Fazio/Neubert
1. Short theoretical statement
Stefan emphasized that there *is* a relation between *SF moments* and
HQET parameters. The HQET parameters are universal quantities and can
be extracted from many different experiments like inclusive b -> c l nu
decays, b -> s gamma decays, or Upsilon spectroscopy. They can be
extracted using different (physical) mass schemes, like the kinetic
mass or the 1PS mass. A proper physical scheme for the moments of the
SF is the SF mass scheme introduced in section 5.2 of hep-ph/0402094
where also its relations to other physical mass schemes are given. The
knowledge of two moments of the shape function (like m_b and mu_pi^2)
constrains model-building of the SF but does not determine its
functional form. Once a complete theoretical treatment of the b -> s
gamma photon spectrum is available, we'll have crucial information on
the functional form of the SF.
Ric raised the point whether we should just resort to using dF/N to
unfold the measured spectra and quote partial branching fractions
only, from which the extraction of Vub would be done with MC
generators but more directly at the order available for a calculation
and scheme. The point here is that dF/N is curretnly the only
triple-differential MC generator covering the entire phase space.
Improvements to dF/N are work in progress (Bjoern).
2. Belle: B-> s gamma analysis and extraction of SF parameters
Tadao discussed the note sent around before the meeting and linked
above and proposed a weighted average of the central values extracted
from the Belle and CLEO, independently using positive and negative
variations. He raised the point of the "old" parametrizations of the B
-> s gamma photon spectra.
There was a clarifying discussion as what the "extreme1 e_1" and
"extreme2 e_2" points in table 2 of the Belle note are: They
correspond to the upper left and lower right extreme points on the
contours shown in fig 4 of that note.
Ikaros inquired into the large uncertainty on mu_pi^2, as the range
between 0.23 and 0.96 seems "absurdly" large. The reply stated that
the current data of the B->s gamma photon spectrum do not provide
sensivity to this parameter in the parametrizations used.
The extraction of the SF parameters will be publicly available from
the HFAG webpages. In addition, it will be posted to hep-ex by BELLE.
3. Miscellaneous issues
Ric again raised the point of the combination of Belle's result with
CLEO's in order to go beyond the weighted average. The summary of the
discussion is that Belle will provide a functional form of the delta
Chi2 in the relevant parameter space by next week. We'll try to get
the same information from CLEO and eventually from BABAR. This
information will be made available on the HFAG webpages.
As the quoted error on Vub should represent a 68%CL, the agreement was
to use the delta Chi2 = 2.3 contour. Because delta Chi2 = 1 was used
in the last average, we'll remark about this. After the meeting, BABAR
statisticians are in disagreement:
I think that it has been done correctly using the deltaChisq=1
In a linear approximation (ie, keeping linear order in a Taylor
series expansion of Vub in mb,a), the Vub variable picks out a
direction in the mb,a plane. The "basis vector" in Vub direction is
a rotation of the mb,a coordinates. The 68% confidence interval of
the rotated "basis vector" corresponds to taking the extreme points
(ie, remaximizing likelihood wrt to the orthogonal directon) on the
error ellipse along that direction. This interval gets scaled
appropriately when Vub is computed.
A way to check that everything is behaving as hoped is to use the
Belle deltachisq=1 contour to read off Var(mb), Var(a), Cov(mb,a),
Var(Vub) ~ (dVub/dmb)^2 Var(mb)
+ (dVub/da)^2 Var(a)
+ 2 (dVub/dmb) (dVub/da) Cov(mb,a)
Ric raised another point whether not separating out the exclusive
component is right. The discussion showed that also BELLE uses a fully
inclusive mass distribution for there SF parameter determination. The
theoretical advice here is that this is the correct approach,
including the resonant component adds an ad-hoc model dependence and
the advantages are not clear.
Ikaros raised two more points:
(1) A cautionary note: the universality of the distribution or shape
functions holds only to leading order in 1/m_Q; thus only in leading
order can you measure it in b -> s gamma and use it in b -> u l
nu. There are nonperturbative contributions in order 1/m_Q -- unlike
for fully integrated rates, where they arise only in order 1/m_Q^2 --
that affect b-> s gamma and b-> u l nu differently; furthermore the
connection to observables becomes much more scheme dependent
then. Those 1/m_Q corrections are not known (yet).
(2) Just to be more specific and accurate, it should always be stated
whether the energies and energy cuts are given for the Y(4S) rest
frame or the B meson rest frame.
4. Improvement of charmless semileptonic rate -> |Vub|
There was agreement that the measurement of the b->c l nu moments by
BABAR should be used to improve the extraction of Vub from the total
charmless semileptonic rate, which previously had been "fixed" at the
CERN CKM workshop. This is currenty under discussion in BABAR, Urs
will send out a note once that is settled.
5. Action Items
1. Belle will circulate their delta Chi2 function by next week
2. We will ask CLEO for the same information. And inquire about the
delta Chi2 = 1.
3. The HFAG webpage will be updated to contain the information
necessary for each experiment to perform the SF systematic
uncertainty as soon as possible.
4. Urs will circulate a short note on the extraction of Vub from the
full charmless semileptonic rate based parameters mu_pi^2 and mb as
determined in the b->c l nu moments measurements by BABAR.