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Vub measurement using recoil of fully reconstructed Bs

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From:
Wolfgang Menges <[log in to unmask]>
Date:
27 Jul 2006 11:27:43 +0200Thu, 27 Jul 2006 11:27:43 +0200
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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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