Hi Concezio, Concezio Bozzi wrote: > Hi, > Wolfgang, why should we apply 50% and 100% > correlations? The mX bins should be statistically independent, no? True, the bins are statistically independent, but I assume that having more peaking background in one bin means also more peaking background in the other bins. 100% correlation will be too conservative but it will give the worst case number. Cheers, Wolfgang > Concezio. > > Il giorno gio, 27-07-2006 alle 11:27 +0200, Wolfgang Menges ha scritto: >> 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 [log in to unmask] ------------------------------------------------------------------------