I also understand the question about the correlations.
Heiko
On Thu, 27 Jul 2006, Wolfgang Menges wrote:
> Hi Concezio,
>
> as Heiko said, very promissing. Can you run with 50% and 100% correlation?
>
> Cheers,
>
> Wolfgang
>
> Concezio Bozzi wrote:
> > Hi all,
> >
> > I run a test to estimate the systematic uncertainty due to the
> > uncertainty on S/P in mES data fits in the following way:
> >
> > 1) Take the S/P ratios determined as
> >
> > S/P(data_enriched) = [S/P(MC_enriched) / S/P(MC_depleted)] * S/P
> > (data_depleted)
> >
> > I have used the values which I have been recently playing with, i.e.
> > #mx_l mx_h corr err_corr
> > 0.00 1.55 1.499 +- 0.495
> > 1.55 1.90 2.688 +- 0.655
> > 1.90 2.20 1.801 +- 0.296
> > 2.20 2.50 1.896 +- 0.611
> > 2.50 2.80 1.165 +- 0.468
> > 2.80 3.10 0.637 +- 0.311
> > 3.10 3.40 19.367+- 34.585
> > 3.40 3.70 1.524 +- 1.610
> > 3.70 4.20 8.180 +- 31.833
> > 4.20 5.00 0.555 +- 6.639
> >
> > No attempt to fit a n-th order polynomial, just take the values as they
> > come out of the single bin-by-bin fits on data depleted, MC enriched and
> > depleted.
> > Note that the relative errors are quite large (e.g. 33% on the first
> > bin, 25% on the second, 22% on the third, 32% on the 4th, higher and
> > higher as mX increases).
> >
> > 2) Randomize simultaneously the 10 above values according to a gaussian
> > distribution whose mean is the correction (column corr) and whose sigma
> > is the uncertainty (err_corr). The random number is of course different
> > for each mX bin.
> >
> > 3) Fit with VVF by using the randomized S/P of point 2)
> >
> > 4) go to 2), change the random seed, repeat 100 times
> >
> > Results of the 100 jobs are in
> > http://www.slac.stanford.edu/~bozzi/scra/Ibu_SP_*
> > *=1,...,100
> >
> > Take the (width/mean) ratio of the resulting 100 fits as systematic
> > uncertainty:
> >
> > yakut02(~:) grep "BRBR " ~bozzi/scra/Ibu_SP_*/*dat | awk
> > 'BEGIN{sum=0; sum2=0}{sum+= $3; sum2+=$3*$3; num++}END{print sum/num;
> > print sqrt(sum2/num-sum*sum/num/num)}'
> > 0.0291231
> > 0.00188286
> >
> > The relative uncertainty is 0.00188/0.02912 = 6.46% i.e. 3.2% on Vub.
> > This is somewhat lower than a naive argument which can be used (see
> > below) to give the error on the fitted Vub events in the first bin and
> > which give about twice (13.2%) the error on BRBR. I think the reason for
> > this is that the errors on the first 4 bins are comparable, which
> > reduces the lever arm and therefore the variation in the first bin.
> >
> > Quite promising, isn't it?
> >
> > Concezio.
> >
> >
> > PS: here is the naive argument on the uncertainty on the number of
> > signal events in the first bin, which translates in the uncertainty on
> > BRBR. We have
> >
> > N_signal = N_data - N_argus - N_peaking
> >
> > N_peaking = N_signal * 1/corr
> > (corr is the S/P correction factor)
> >
> > Solving for N_signal:
> >
> > N_signal = [corr / (1+ corr)] * [N_data - N_argus]
> >
> > Error propagation gives:
> >
> > delta(N_signal) / N_signal = [delta(corr) / corr] / (1+corr)
> >
> > Taking corr = 1.499, delta(corr)/corr = 0.33 we get
> >
> > delta(N_signal) / N_signal = 13.2%
> >
>
> --
> ------------------------------------------------------------------------
> Wolfgang Menges
> Queen Mary, University of London SLAC, MS 35
> Mile End Road 2575 Sand Hill Road
> London, E1 4NS, UK Menlo Park, CA 94025, USA
> +44 20 7882 3753 ++1 650 926 8503
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