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 nth order polynomial, just take the values as they
> come out of the single binbybin 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/numsum*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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