Some studies on the sampling fraction in EEMC

EEmc Slow Simulator

The EEmc slow simulator uses a fixed value of 0.048 (changed from 0.05 on Aug 5th, 2010).  The change is given the comment:

// Updated to 4.8% from Ilya's study http://drupal.star.bnl.gov/STAR/node/16426

The code also contains the comment:

ADC=4095 * geantEnergy / samplingFrac / 60GeV / cosh(eta) is recorded as in StEvent

Computing the Sampling Fraction in Monte Carlo

One can take the energy deposition in the active layers of the towers, as given by GEANT, and divide by the true energy of the incident particle to get the sampling fraction for that individual track.  Since the slow simulator uses a fixed value, the question arises how accurate and precise is the practise of using a fixed value.  One method of looking at this is to use our photon gun Monte Carlo runs, cut to events where the photon survives, and see if there are obvious variations.  The sampling fraction is fit to a Gaussian distribution.  For the details of the sets and runs, see Hal's blog.

The results are presented in five columns, the columns being:

1. run identifier
2. mean of sampling fraction fit
3. sigma of sampling fraction fit
4. sigma/mean,
5. 0.135 x mean sampling fraction / 0.0048 (the expected pi0 mass in MC if the real sampling fraction is the computed one, and the slow simulator used 0.048)

Set 1: variation of pT

gamma_set1_run1 0.0495836 0.00162706 0.0328145 0.139454
gamma_set1_run2 0.0499655 0.00117374 0.023491 0.140528
gamma_set1_run3 0.0494833 0.00183164 0.0370154 0.139172
gamma_set1_run4 0.0497436 0.00132769 0.0266907 0.139904
gamma_set1_run5 0.0490026 0.00238983 0.0487694 0.13782
gamma_set1_run6 0.0492095 0.00217645 0.0442282 0.138402
gamma_set1_run7 0.0494093 0.00202034 0.0408898 0.138964
gamma_set1_run8 0.0496854 0.0014128 0.028435 0.13974

Set 3: variation of phi (centers of towers)

gamma_set3_run1 0.0495928 0.00160402 0.0323438 0.13948
gamma_set3_run2 0.0495287 0.0015915 0.0321328 0.1393
gamma_set3_run3 0.0496194 0.00160141 0.032274 0.139555
gamma_set3_run4 0.04957 0.00160574 0.0323935 0.139416

Set 4: variation of eta (centers of towers)

gamma_set4_run1 0.0483132 0.00202343 0.0418816 0.135881
gamma_set4_run2 0.049866 0.00154533 0.0309896 0.140248
gamma_set4_run3 0.049432 0.00175275 0.0354578 0.139027
gamma_set4_run4 0.048069 0.0021796 0.0453431 0.135194
gamma_set4_run5 0.0490934 0.00193636 0.0394424 0.138075
gamma_set4_run6 0.0497378 0.00148069 0.02977 0.139887
gamma_set4_run7 0.0497771 0.00130106 0.0261378 0.139998

Set 6: variation of phi across sector border near 45 degrees (1 degree steps, tower is 6 degrees wide)

gamma_set6_run1 0.0459611 0.00336098 0.0731266 0.129266
gamma_set6_run2 0.0401131 0.00601934 0.150059 0.112818
gamma_set6_run3 0.0370409 0.00673546 0.181838 0.104177
gamma_set6_run4 0.0445517 0.00444481 0.0997673 0.125302
gamma_set6_run5 0.0497631 0.00160697 0.0322924 0.139959

Set 9: variation of phi across sector border near 195 degrees (1 degree steps, tower is 6 degrees wide)

gamma_set9_run1 0.049568 0.0016513 0.0333138 0.13941
gamma_set9_run2 0.046044 0.00333002 0.0723225 0.129499
gamma_set9_run3 0.040398 0.00615378 0.152329 0.113619
gamma_set9_run4 0.0369067 0.00676837 0.183392 0.1038
gamma_set9_run5 0.0442734 0.00411616 0.0929714 0.124519
gamma_set9_run6 0.0498417 0.00160342 0.0321702 0.14018
gamma_set9_run7 0.0496929 0.00160153 0.0322284 0.139761

Set 10: variation of phi across sector border near 195 degrees (1 degree steps, tower is 6 degrees wide)

gamma_set10_run1 0.0496011 0.00162192 0.0326992 0.139503
gamma_set10_run2 0.0456848 0.00329248 0.0720694 0.128489
gamma_set10_run3 0.0403972 0.00582031 0.144077 0.113617
gamma_set10_run4 0.0379398 0.00676107 0.178205 0.106706
gamma_set10_run5 0.0440862 0.00469935 0.106595 0.123992
gamma_set10_run6 0.0498203 0.00156307 0.0313741 0.14012
gamma_set10_run7 0.0495991 0.00165578 0.0333833 0.139498

Set 11: variation of phi across sector border near 195 degrees (1 degree steps, tower is 6 degrees wide)

gamma_set11_run1 0.0496345 0.0016008 0.0322517 0.139597
gamma_set11_run2 0.04576 0.00326454 0.0713405 0.1287
gamma_set11_run3 0.0400603 0.00624559 0.155905 0.11267
gamma_set11_run4 0.0372306 0.00706105 0.189657 0.104711
gamma_set11_run5 0.0443147 0.00435016 0.0981654 0.124635
gamma_set11_run6 0.0498479 0.00162017 0.0325023 0.140197
gamma_set11_run7 0.0496045 0.00153951 0.0310356 0.139513

Set 12: variation of phi across sector border near 195 degrees (1 degree steps, tower is 6 degrees wide)

gamma_set12_run1 0.0495947 0.00161524 0.0325688 0.139485
gamma_set12_run2 0.0459623 0.00331676 0.0721627 0.129269
gamma_set12_run3 0.0403233 0.00609595 0.151177 0.113409
gamma_set12_run4 0.0368674 0.00656452 0.178058 0.103689
gamma_set12_run5 0.0440541 0.00438683 0.0995782 0.123902
gamma_set12_run6 0.0498375 0.00164122 0.0329313 0.140168
gamma_set12_run7 0.0496009 0.00159756 0.0322082 0.139502

Conclusions

While this study is by no means exhaustive, it seems that the sampling fraction is fairly stable (around 0.049) with eta, phi, and pT, as long as the photons are centered in the towers.  As the photons near sector boundaries, the sampling fraction decreases.  The use of a constant 0.048 would cause the MC energy to be reported too high for photons in the centers of towers, and thus push the pi0 mass peak high by about 4-5 MeV.  Near sector boundaries, the sampling fraction drops, causing the reported energy and computed pi0 mass peak to appear low, by as much as 32 MeV.