4/13/00
Sudeshna Banerjee
Supriya Jain

 The Calorimeter package
--------------------------

 Eight parts.

 1. Input info:
   For each track - particle ID, energy, theta, phi.
   to be obtained after the track has passed through the tracker.

 2. check the particle ID :
    EM objects (electrons, photons, pi zeroes), muons and hadrons
    have to be treated separately.
    
 3.        For a muon minimum ionizing energy will be lost in ecal and hcal
        (.5 GeV in ECAL and 2 GeV in HCAL)

       For an electron 99% of the energy will go into ECAL

       Table of energy division for a hadron:
      (rough numbers based on test beam data of the CMS calorimeter)
    Energy division between ECAL and HCAL (needs random number gen).

   S. No.     % of total events      % Energy in ECAL    % Energy in HCAL

     1.           25%                    0                  100
     2.           16%                   20                   80
  Right now for the next 59% events an average amount of energy is deposited
  into 4 ECAL and 4 HCAL layers
  (obtained from shower profile, fig. 40, pa 212, D0 detector paper)
    
     0 in ECAL should be minimum ionising energy in ecal (.5 GeV) 

 4. Response efficiency of ECAL and HCAL (only 0.5% difference from being 
    linear, so ignore for the time being).

 5. Smearing of the energy according to ECAL and HCAL resolution
    (needs random number generator).

 6. Decide which tower is the central tower according to the eta phi of the
     track (consider effect of magnet (to be done)).

 7. Showering - 
 
   Hadrnic showers:
       Longitudinal shower development for a hadron:
    
  Case 1. in item 2 above --
    0.5 GeV divided equally among four ECAL layers
         Late showers
       HCAL 1  35%
            2  30%
            3  20%
            4  10%
           Missing 5%

  Case 2. in item 2 above --
       ECAL 1  1%
            2  5%
            3  6%
            4  8%
         (total=20%)
       HCAL 1  28%
            2  22%
            3  17%
            4  8%
           Missing 3%
          total=80%

     All the other cases

       ECAL 1  3%
            2  10%
            3  25%
            4  22%
         (total=60%)

       HCAL 1  20%
            2  12%
            3   7%
           4   1%
         (total=40%)

  Lateral shower development of a hadron:
 
     Width W(E) = -17.3 + 14.3 ln (E), Width is in cm, E is in GeV
     Fernow, p. 277, eqn. 11.19
 (Assume this is the width at shower max, 99% energy will be inside this width)

  For 300 GeV, it is 64 cm. at shower max. How many towers will it be ?
  (D0 detector note, page = 202, shower size = 10 cm for electrons)
  HCAL starts after 20 X0 (=280 cm).
  tan(theta) = (280+78)/64, theta = 79.3 deg., eta span = .18
  (With 10 cm shower radius, eta span = .06, same as EM)

     In ECAL:

      First 2 layers, energy will be in the central tower.
      Next two layers

      Central tower = 80%
      Outer 3X3 (8 towers) = 20%  (2.5% each tower)

     In HCAL:

       In all four layers
      Energy will be spread over 3X3 towers (for the time being)

       Central tower = 80%
       Outer 3X3 (8 towers) = 20%  (2.5% each tower)

     Shower development for electrons:

     longitudinal development of the showers:

  Shower maximum will occur at t = ln(E0/Ec)/ln(2) rad. lengths
  (Fernow, p. 262)
  Ec for liquid argon =18 (calculated above)
  For a 100 GeV particle t=1.3 X0, For a 300 GeV particle t=2/.69=2.89 X0,
  So, it shifts a little.
  First EM Layer =10% of total energy,
  Second EM Layer =19% of total energy,
  Third EM Layer = 58% of total energy,
  Fourth EM Layer = 2% of total energy,
  1% of total energy leaks out
 (From Fig. 11.3, p. 265, Fernow)

  Lateral shower development of electrons:

      95% of the shower energy is within 2*Rm (moliere radius)
      99% of the shower energy is within 3.5*Rm

      Rm = X0*(Es/Ec)  eqn. 23.21, P. 148 (Blue book)
    For liquid argon, X0=14 cm
    Es = 21 MeV, Ec = 800/(Z+1.2), for Ar, Z = 18
 (formula valid for high energy electrons where electrons interact with
  matter by emitting radiation, not by ionising)
    So, Rm = 14*20/40 = 7 cm approx.
  (D0 detector note, page = 202, shower size = 1-2 cm for electrons)
  How many towers is this in the Dzero calorimeter ?
  Inner radius of the Central Calorimeter = 78 cm
  shower max is at 10X0 (=140 cm) into the EM calorimeter.
   eta span = -ln(tan(theta/2))
  tan(theta)=(140+78)/14, theta=86.3 deg., eta span=.06
  The tower size at shower max is 0.05X0.05.
                                                                    
      Energy will be spread over 3X3 towers (for the time being)
      Energy spread is as follows :

      Central tower = 95%
      Next layer (3X3 = 8 towers) = 5%

     1. First EM Layer, = all the energy in the central tower
     2. Second EM Layer, = all the energy in the central tower
     3. Third and Fourth EM Layer = 95% energy in the central tower,
        5% Energy in the next 8 towers

 8. Output energy in different eta-phi towers.
   Different geometry depending on Central Calorimeter or endcap.

    In CC
     eta spans from -1.2 to 1.2

     EM (electromagnetic) has four longitudinal readouts 
     at 2X0, 4X0, 10.8X0, 20.5X0
     24 divisions in eta (each 0.1), 64 divisions in phi (each about 0.1)
     3rd EM segment has cell divisions .05X.05

     FH (fine hadronic) has three longitudinal readouts 
     of widths 1.3 int. length, 1.0 int. length, 0.9 int. length
     24 divisions in eta (each 0.1), 64 divisions in phi (each about 0.1)

     CH (course hadronic) has one longitudinal readout 
     of width 3.2 int. length
     24 divisions in eta (each 0.1), 64 divisions in phi (each about 0.1)

     In EC (yet to be incorporated in the present version of the program)

      eta range means on both sides of the centre.

      One EM (electro magnetic) module contains four readouts 
      at (0.3, 2.6, 7.9, 9.3)X0, side by side in Z.
      Total number of readout channels - 7488
      Each cell is .1X.1 in eta X phi
      (7488/4 readouts in 360 degrees of phi, eta varies from 1 to 4,
       so, 3/.1=30 concentric rings in phi. Full phi range is 2*pi =6.28.
       6.28/.1= 62 divisions in phi)      
       Inner radius = 5.7 cm. Outer radius varies from 84 cm to 104 cm. 

      One IH (Inner Hadronic) module contains 
      one FH (fine hadronic) section with four readouts (1.1 Lambda each).
      eta varies from 1.6 to 4.5
      one CH (coarse hadronic) section with one readout (4.1 Lambda).
      eta varies from 2.0 to 4.5
      The five IH sections are side by side in Z.
      The full ECIH module provides 5216 signals.
      (5216/5 readouts in each section)
      ( 62 sections in phi, 16 sections in eta. )

      MH (middle hadronic) module has 
      one FH (fine hadronic) section with four readouts (0.9 Lambda each).
      eta spans from 1.0 to 1.7.
      one CH (coarse hadronic) section with one readout (4.4 Lambda).
      eta spans from 1.3 to 1.9
      The five IH sections are side by side in Z.
      The full ECIH module provides 1856 signals.
      (1856/5 readouts in each section)
      ( 62 sections in phi, 7 sections in eta.)

      CH (coarse hadronic) module has three sections side by side in Z.
      960 signals.
      62 channels in phi, 3 in eta
      960 signal channels. span in eta = .7 to 1.4