Hi,
on Dec 9th we had shown a preliminary unfolded m_X spectrum, where
some things still needed to be changed.
1) At that time the unfolding treated the data as if it just had
normal sqrt(N)-errors on each bin. We changed this such that
now the actual error from the fit is taken.
2) We are no longer performing the fit with our equidistant binning.
Instead, we just feed in the results from fits with the default
binning for vubcomp, vcbcomp, errvcbcomp, othcomp and errothcomp
and do all the other things with our binning (m_ES-subtraction,
bkgd-subtraction, ...).
3) Third, we now unfold taking into account the multiplicity categories.
For this, we use the m_X spectra from data and signal MC divided
up into the five usual multiplicity categories.
This is done as follows:
* We determine weights for the reconstructed signal MC such that its
relative multiplicity category population is the same as in data,
i.e. we apply the following weight to signal MC to multiplicity
category (mc) i
w_mc^i = dr_mc^i / br_mc^i
where dr_mc^i is the relative population of multiplicity category i
in data and br_mc^i is the relative population of reconstructed
multiplicity category i in signal MC.
* The (m_X!) detector response matrix (that is used for the
unfolding) is determined for each multiplicity category
separately A_mx^i and these matrices are added up with the same
weight w_mc^i per multiplicity category that is applied to the
reconstructed signal MC:
A_mx = A_mx^i * w_mc^i (sum over i)
to give the detector response matrix that is used for the
unfolding.
* We then determine the weights for the generated multiplicity
categories by requiring that the resulting spectrum (i.e.
reweighted generated multiplicity category spectrum x_mc^rew)
yields the reweighted reconstructed multiplicity category spectrum
b_mc^rew when applying the multiplicity category detector response
matrix, i.e. the requirement is
A_mc x_mc^rew = b_mc^rew.
(same principle as for m_X, A_mc is the matrix mediating between
the generated and the reconstructed distribution
A_mc x_mc = b_mc
with x_mc being a vector with the population of the generated
multiplicity categories, b_mc being the vector for the reco mc.)
We use the weights we obtained this way for the generated
multiplicity categories to reweight the generated m_X spectrum,
which we use for the unfolding.
Here is the current plot:
http://www.slac.stanford.edu/~kerstin/mult24_4.eps
where the blue distribution is the reweighted generated m_X distribution
that is used for the initialization, the black data points are the
unfolded spectrum and the green distribution is the scaled measured
spectrum, which is unfolded.
Assuming that the data sample contains about 89 Mio BBbar pairs and
taking the branching fractions from PDG assuming equal numbers of
neutral and charged B one would expect to see about 24000 pis and
35000 rhos. We do not see any inconsistency between these numbers and
the unfolded spectrum.
We will be glad to get some feedback on this as well as your opinion
concerning the dominant systematic errors (what they are and how they
should be evaluated).
Kerstin
