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, 27072006 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 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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