[Halld-cal] MC Michel Spectra selection cuts

[Elton Smith]

Hi Andrei,

Thanks for the plots. These are very nice. (By the way, I resolved my 
confusion from this morning)

1. Would you please send us the data from the histograms, e.g. the 
histograms in a root file.

2. It would also be interesting to see the total energy deposited in the 
module(s) as a function of the ratio and thresholds.

Thanks, Elton.

On 12/16/15 6:25 PM, semenov at jlab.org wrote:
> 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_layer
>
> 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.
>>
>>
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