Meeting on Shape Function Parameters

Connection Details

  When: July 07, 2004, 07:00 AM PDT 
  Call: 510-665-5437
  Meeting ID: 8160

Discussion Items

o Central values and errors of shape  function parameters

   - BABAR
   - BELLE 

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),
  and compute:

  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.