[Halld-cal] MC Michel Spectra selection cuts

[semenov at jlab.org]

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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