Hello,
Alessio and I have rerun enforcing the overall normalization of the
weights all over the lambda_bar and lambda_1 plane and there have been
small adjustments to the results. Since the previous posting was unclear I
will go through the description again.
We have performed fits to the mX distribution in a grid of values of
lambda_bar and lambda_1. We reweight the hybrid in each configuration and
we perform a chi^2 test between data and MC on the mX distribution after
background subtraction.
An example of such a fit is in
http://www.slac.stanford.edu/~asarti/recoil/rewchisq/RicQ2_b3l10_var.eps
where the data are the black dots and the MC the red ones.
The raw results as obtained by Alessio are summarized in
http://www.slac.stanford.edu/~asarti/recoil/rewchisq/
expressed in terms of values of mb and of bins of the 'a' parameter.
Lambda_1 is related to the 'a' bin index (l) by
lambda_1=[(5.28mb)/(5.3mb)]^2(1.1+l*0.1)
(I apologize for the awkward formula, I made a small mistake in generating
the points...).
I translated them in terms of countours in the lambda_1 and lambda_bar
plane of the deltaChi2, the distance of the chi^2 for each point from the
minimum:
http://www.slac.stanford.edu/~rfaccini/phys/vub/SF/ll_cont_new.eps
The black,red and green lines correspond to deltaChi2=1,2.25 and 5 (i.e.
the red line corresponds to 1 sigma). The plot is limited in range because
it already arrives at very high values of deltaChi2 and we need not know
to go further.
As you can see the huge tail at high values of lambda_bar and
lambda_1 allowed by CLEO's analysis (see
http://www.slac.stanford.edu/cgibin/lwgate/VUBRECOIL/archives/vubrecoil.200306/Author/article21.html
) is not allowed by us.
If one wanted to extract constraints on the HQE parameters from our data,
one should plot the values of deltaChi2 obtained as a function of
lambda_bar
http://www.slac.stanford.edu/~rfaccini/phys/vub/SF/lbproj_new.eps
and lambda_1
http://www.slac.stanford.edu/~rfaccini/phys/vub/SF/l1proj_new.eps
There are several values of deltaChi2 for each value of the variable which
is considered because the other variable is allowed to vary.
The 68% C.L. interval is given by the intercept of the deltaChi2=1 line
(which is drawn) and the envelope of the deltaChi2 distribution.
For comparison I added the currently assumed 68% C.L. intevals as arrows.
It can be seen that our data are consitent with the value we assume,
although slightly offset towards higher values of lambda_bar and less
negative values of lambda_1.
The sae game can be played in terms of BRBR:
http://www.slac.stanford.edu/~rfaccini/phys/vub/SF/brbr_new.eps
It can be seen that the minimum of the chi^2 is well within the allowed
C.L.
ciao
ric
