NOT FINISHED

Definitions of quantities used for empirical calibration of BSMD.

Revised January, 26, 2009

A) Model of the physics process (defines quantities: E, eta, smdE, smdEp, smdEe, C0, C1)

1. gamma particle with fixed energy E enters projectively EMC at fixed pseudo-rapidity eta. Eta is defined in detector ref. frame.
2. EM showers develops and BSMD (consisting of 2 planes) captures smdEtot of shower energy. Single plane captures smdE=0.5*smdEtot. The SMD cluster energy from single plane is denoted as smdE.
3. SMD consist  of 2 planes : eta-plane closer to IP and the outer phi-plane. Each plane captures non-equal fraction ofenergy  deposited in BSMD: smdEp, smdEe, respectively.  
   
   The following relation holds:
                smdEp(E,eta) =smdE(E) * [1-C1(eta)] 
                smdEe(E,eta) =smdE(E) * [1+C1(eta)] 
   where  theta-dependent coefficient C1 accounts for all physical processes differentiating fraction of captured shower energy by eta vs. phi-planes along Z-direction. 
   allows reconstruction of full BSMD energy deposit independent on gamma angle theta if cluster energy in both plane is measured 
4. BSMD Cluster energy is measured in each plane by few consecutive strips which:
   1. response is linear and
   2. strip-to-strip local  hardware gain variation is negligible (the "long-wave" is accounted for in C1(theta))
      Note, there are 4 low gain strip (id=50,100) in the eta-plane , seen in fig 2 of 08) SMD-E gain equalization , ver 1.1, which require ADC to be rescaled appropriately.
   
   
5. The overall conversion constant C0=6.5e-8 (GeV/ADC chan) allows reconstruction of BSMD cluster energy in given plane based on the sum of ADCs from all strips participating in the cluster  
            smdEp(E,eta)=C0* sum{ ADC_i - ped_i}, over cluster of few strips , similar formula for smdEp(E,eta)=....
   The value of C0 was determined based on 19) Absolute BSMD Calibration, table ver2.0, Isolated Gamma Algo description, table 2. Gammas with ET=6 GeV were thrown at EMC and resulting SMD cluster ADC sum was matched to the average value seen for 2008 pp data.

To summarize
The reconstructed cluster energy in each plane with use of C0 & C1 should have eta dependence 

             smdE(E) =C0* sum{ ADC_i - ped_i}/[1-C1(eta)] for phi-plane cluster

             smdE(E) =C0* sum{ ADC_j - ped_j}/[1+C1(eta)]  for eta-plane cluster
              
Those 2 quantities are well suited to place cuts. 

B) Determination of C1(eta) was based on 19) Absolute BSMD Calibration, table ver2.0, Isolated Gamma Algo description, from crates 1,2,and 4. 

Data analysis was done for 10 pseudo-rapidity  ranges [0,0.1], [0.1,0.2] ,..., as shown in table 2, row labeled 'DATA'. 

For practical application analytical approximation is provided

    C1(eta)= C1_0 + C1_1*|eta| + C1_2*eta*eta

symmetric versus positive/negative pseudo-rapidity.  

The numerical values of expansion coefficients are: C1_0=0.014, C1_1=0.015, C1_2=0.333

 

C) Modeling of BSMD response in STAR M-C

1. find  geantDE geant energy deposit for given BSMD strip
2. undo simulated by GEANT +/-7% difference between eta/phi planes (see 19) Absolute BSMD Calibration, table ver2.0, Isolated Gamma Algo description, row 'M-C') 
          geantDEp=geantDE*0.93
          geantDEe=geantDE*1.07
3. compute ADC for every i-th strip & plane
       ADCp_i= geantDEp/[1-C1(eta)]/C0 
       ADCe_i= geantDEe/[1+C1(eta)]/C0
   1. If NO saturation is assumed that is all - use ADC-values in reconstruction.
   2. To simulate full ADC saturation at 1024 assume pedestal is at ADC=100 and saturate values of ADCp_i, ADCe_i at 924. Then proceed to reconstruction.