[Halld-cal] MC Michel Spectra selection cuts

Tue Jan 12 18:25:34 EST 2016

Elton and Will:

The attachment contains four "mudecay2_#.##.root" files with requested
histograms with attenuated energy depositions in all materials of readout
cells as well as whole calorimeter (I do believe that the histogram names
are self-explanatory). Because the muons were seeded randomly in the whole
BCAL volume, "upstream-attenuated" and "downstream-attenuated" histograms
are almost the same.

Another four "mudecay3_#.##.root" files in the attachment contain similar
histograms but for the deposited energies without attenuation (just in
case you need it too).

Please let me know if you need something else.

Andrei

> Elton and Will:
>
> The requested histograms and data files are in the attachment.
>
> Each of the data files is made for specific threshold ( of 1.15, 2.3,
> 3.45, and 4.6 MeV) on the attenuated energy deposition in the whole
> readout cell.
>
> Format of each line is ("m_" means "mean", and "s_" means RMS):
>
> m_layer1 s_layer1 m_layer2 s_layer2 m_layer3 s_layer3 m_layer4 s_layer4
>
> Each file contains 6 lines:
>
> Upstream for 0.4<Ratio<=0.6
> Downstream for 0.4<Ratio<=0.6
> Upstream for 0.6<Ratio<=0.8
> Downstream for 0.6<Ratio<=0.8
> Upstream for 0.8<Ratio<=1.0
> Downstream for 0.8<Ratio<=1.0
>
> The units are "attenuated-MeV", and all spectra and numbers correspond to
> the energy deposited in all materials of readout cell.
>
> Cheers,
> Andrei
>
>
>
>>
>> -------- Forwarded Message --------
>> Subject: 	Re: [Halld-cal] MC Michel Spectra selection cuts
>> Date: 	Wed, 4 Nov 2015 10:53:47 -0500
>> From: 	Elton Smith <elton at jlab.org>
>> To: 	wmcginle at andrew.cmu.edu, semenov at jlab.org
>> CC: 	elton at jlab.org, Andrei Semenov <andrei.semenov at uregina.ca>, Zisis
>> Papandreou <Zisis at uregina.ca>, Mark Dalton <dalton at jlab.org>
>>
>>
>>
>> Hi Andrei and Will,
>>
>> In order to calibrate using the Michel electrons, it seems the most
>> useful quantity is the full energy spectrum (Ed and Emc below). But
>> since the energy is distributed over several cells, this complicates the
>> gain assignment. The energies in each cell are denoted by Ed_i and
>> Emc_i, for data and MC, respectively. Here is an outline (for
>> comments/feedback) for a strategy to determine the gain factors
>> iteratively.
>>
>> We can write the total energy for the data as follows:
>>
>> Ed = Sum_k (g0_k * Ed_k) = g0_i*Ed_i + Sum_j.ne.i (g0_j * Ed_j); [Note:
>> Ed has units of MeV, Ed_i has units of fADC channels]
>>
>> where i is the channel that we wish to calibrate. The 'g0' constants
>> denote the current value to be optimized. It also makes sense to choose
>> the channel i that has the largest amount of energy deposition. Of
>> particular interest is the faction of energy deposited in channel i:
>>
>> Rd_i = g0_i*Ed_i/Ed
>>
>> We can also compute the same quantities in MC, where the gain factors
>> are set to unity
>>
>> Emc = Sum_k (Emc_k) = Emc_i + Sum_j.ne.i (Emc_j), and correspondingly
>> [Note: Emc and Emc_i have units of MeV]
>>
>> Rmc_i = Emc_i/Emc
>>
>> Suppose we plot Ed, Ed_i for bins in Rd_i (e.g. 0.4 < Rd_i < 0.6, 0.6 <
>> Rd_i < 0.8, 0.8 < Rd_i < 1.0), and correspondingly for the MC data.
>>
>> (1)   If we assume that on average the channels for j.ne.i have the
>> correct calibration, i.e. <Sum_j.ne.i (g0_j * Ed_j)> = < Sum_j.ne.i
>> (Emc_j)>, then
>>
>> <Emc> - <Ed> = <Emc_i> - c*g0_i <Ed_i> = 0, where g_i = c*g0_i is the
>> correct gain factor for channel i. Then
>>
>> c = <Emc_i> / (g0_i * <Ed_i>)
>>
>> Of course, assumption (1) above may not be correct in general, but the
>> conclusions still follow for the case that Rd_i = Rmc_i = 1 (i.e. sums
>> j.ne.i are zero).
>>
>> Now, since we have plotted Emc_i and Ed_i in bins of Rd_i and Rmc_i, one
>> play plot c vs R_i. The correct gain factor will be given by g_i =
>> c(R_i=1) * g0_i.
>>
>> The process may be repeated with updated gain factors, and if they are
>> converging, then the value of c should become independent of R_i.
>>
>> If we agree that this procedure makes sense, Andrei should produce the
>> plots of Emc_i for different bins in Rmc_i and Will would generate the
>> corresponding histograms for the data and complete this procedure. Of
>> course all other selection cuts, which have been discussed, should be
>> common for both data and MC.
>>
>> Suggestions/comments?
>>
>> Elton.
>>
>>
>> _______________________________________________
>> Halld-cal mailing list
>> Halld-cal at jlab.org
>> https://mailman.jlab.org/mailman/listinfo/halld-cal
>>
>
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