How to use the "Gas Cherenkov" and "Total Shower" detectors for $e/$ rejection.

The following instruction has been elaborated recently and represents a general description of how to use "Gas Cherenkov" (GC) and "Total Shower" (TS) detectors of the Hall A electron spectrometer for identification electrons and pions. The work is in progress, so we hope to develop user oriented more convenient program by taking into account possible suggestions and corrections about current code. Also, we plane to add an ESPACE variable, which value would determine particle type.

Present version consists of several stages to reach consequentially definite goals:

1.

Energy calibration of "Total Shower" detector.

2.

The determination of parameters (pshe, , , , ) of shower detector by means of electrons and pions rejected by "Gas Cherenkov" detector.

3.

The determination of the identifications characteristics of the "Gas Cherenkov" detector for electrons and pions identified by "Total Shower" detector on the basis of parameters, which have been found on step #2.

4.

The determination of the identification characteristics of the "Total Shower" detector by using identification characteristics of the "Gas Cherenkov" detector, obtained on step #3.

In "Total Shower" detector particles are identified by their energy deposition in the detector, so one needs to have precise values of the calibration coefficients, i.e. it is better to perform calibration for given data file. Then sometime the calibration has to be done as mentioned. Electrons are defined by summing up amplitudes provided by all PMT-s of "Gas Cherenkov" detector. So one needs to have calibration coefficients for each PMT. At present time due to the absence of calibration code for "Gas Cherenkov" detector the calibration coefficients from database are used. In case one can get them by PMT amplitude spectrum analysis.

Our analysis of the "PreShower" and "Shower" detectors responses have shown that it is convenient to use the function dependent on momentum of particles (P ), energy deposition in "PreShower" detector ($E$_presh ), integral energy deposition in "Total Shower" detector ($E$_tot ) given as

$$fen={E_tot / P } × {lg(E_presh ) / lg(pshe )}

where pshe is the average energy deposition of electrons with momentum P_e=P_centr .

As soon as the dependence pshe(P) analytically is not known and due to the incompleteness of data, we recommend to use step #2 procedures once the value of P_centr gets change.

On step #2 the mean values and the corresponding standard deviations of energy deposition for electrons and pions with P=P_centr must be found as well (, , , ).

To separate electrons and pions the response of "Gas Cherenkov" detector was used. The parameters , , , are needed in step #3 to extract "pure electron" (| - E_tot | < / 2 ) and "pure pions" (| - E_tot | < / 2 ) events by implementing certain conditions on E_tot . Besides of that on step #3 the mean value of the fen function (meanfen) and standard deviation of fen (sigmafen) are defined for electrons.

And finally, on step #4, first of all the conditions to chose electrons and pions are defined as

meanfen - × sigmafen < fen < 2 -- for electrons

0 < fen < meanfen - × sigmafen -- for pions

where is task dependent, and second of all the identification characteristics of "Total Shower" detector are investigating.

Calibration process is initiated, when a File/scan command with option "s" is executed.

.................
File/scan/ [dir]/[run].dat FIRST=1 LAST=50000 -s
.................

The first and last entries given in this command show the range of entries, among which events for calibration will be selected.

Using KUMAC file, which containing following commands:

..................
define/cut/1d spec_e.gas.adcsum_c-1 0.0 10000.0
..................
define/logical cer_elec spec_e.gas.adcsum_c-1
define/logical cer_pion!spec_e.gas.adcsum_c-1
..................
Define/variable eshow:(spec_e.show.cl_e+spec_e.preshow.cl_e)
..................
set/spectrum/bins/x1 100
set/spectrum/windowx1 0. 2500.
spectra/save eshow-1 cer_elec
spectra/save eshow-2 cer_pion
spectra/save spec_e.preshow.cl_e-1 cer_elec
..................

and analysis spectrum, one can obtain parameters pshe, , , , .

Using KUMAC file, which containing following commands:

...................
Define/variable eshow:(spec_e.show.cl_e+spec_e.preshow.cl_e)
Define/variable epi:(spec_e.show.cl_e+spec_e.preshow.cl_e)/spec_e.p_kin
Define/variable ddd:(log10(spec_e.preshow.cl_e))/log10(pshe)
...................
define/cut/1d spec_e.u1.clus-1 0.5 1.5
define/cut/1d spec_e.v1.clus-1 0.5 1.5
define/cut/1d spec_e.u2.clus-1 0.5 1.5
define/cut/1d spec_e.v2.clus-1 0.5 1.5
define/cut/1d spec_e.beta-1 0.7 1.3
define/cut/1d eshow-1 [ - / 2 ] + / 2 ]
define/cut/1d eshow-2 [ - / 2 ] + / 2 ]
define/cut/1d spec_e.preshow.part_id-1 -0.5 0.5
define/cut/1d spec_e.show.part_id-1 -0.5 0.5
...................
define/logical goodel eshow-1
define/logical goodpi eshow-2
define/logical partid1 spec_e.preshow.part_id-1&&spec_e.show.part_id-1
define/logical no_cosmic spec_e.beta-1
define/logical one_cluster_e _

spec_e.u1.clus-1&&spec_e.v1.clus-1&&spec_e.u2.clus-1&&spec_e.v2.clus-1 ...................
set/spectrum/bins/x1 10
set/spectrum/window/x1 0. 10000.
spectra/save spec_e.gas.adcsum_c-1
spectra/save spec_e.gas.adcsum_c-2 _
one_cluster_e&&partid1&&no_cosmic&&goodel spectra/save spec_e.gas.adcsum_c-3 _
one_cluster_e&&partid1&&no_cosmic&&goodpi set/spectrum/bins/x1 200
set/spectrum/window/x1 0. 2.
spectra/save fen-4 one_cluster_e&&partid1&&no_cosmic&&cer_elec

(where instead of [ - / 2 ], + / 2 ], [ - / 2 ] and + / 2 ] must be set real numbers, computed through the parameters , , , , obtained before), one can obtain efficiency identification electrons and pions by formulas

= {number of events in spectrum 2} / {number of events in spectrum 1}

1 - = {number of events in spectrum 3} / {number of events in spectrum 1}

and calculate meanfen and sigmafen by analysis spectrum 4.

Using KUMAC file, which containing following commands:

....................
define/cut/1d fen-1 (meanfen-sigmafen/2) 2.
define/cut/1d fen-2 0. (meanfen-sigmafen/2)
....................
define/logical sh_elec fen-1
define/logical sh_pion fen-2
....................
spectra/save eshow-1 one_cluster_e&&partid1&&no_cosmic
spectra/save eshow-2 one_cluster_e&&partid1&&no_cosmic&&cer_elec
spectra/save eshow-3 one_cluster_e&&partid1&&no_cosmic&&sh_elec
spectra/save eshow-4 _

one_cluster_e&&partid1&&no_cosmic&&cer_elec&&sh_elec

one can obtain efficiency identification electrons and pions by formulas

where: n -- number of events in spectrum 1;
n_cerel -- number of events in spectrum 2;
n_shel -- number of events in spectrum 3;
n_cerel^shel -- number of events in spectrum 4.