Comparison of Pi0's reconstructed
with SF=60 ch/GeV (best pi0 invM) and 50ch/GeV (from MIP calib)

> What do you get for the reconstructed p_T for these
> two triggers if instead you use gains determined from
> the MIP calibrations, assuming 5.0% sampling fraction?


Prescription of converting the MIP peak to absolute energy calibration for
tower

Assumptions and definitions:

* tower consist of 24 scint layers 4 mm each, total depth D=9.6cm
 ( the 3 pre/post shower layers have 5 mm, but the light collection
efficiency is lower)

* energy loss for MIP in scint is 1.8 MeV/cm ( in the minimum of
ionization, scint=carbon with density of 1g/cm3)

* relative gain of i-th tower is denoted g_i

* scale factor (SF) is overall energy calibration for EM energy

* sampling fraction for electromagnetic energy SamplFrac=0.05

The peak value of MIP ADC (total energy)  is given by:

Emip(ch)=   dE/dX *  D /tanh(eta)* g_i  * SF(ch/GeV)/SampFrac

The reconstructed EM energy:

Eem(GeV) = ADC/g_i /SF

This definition is little awkward, but the EM sampling fraction is hidden
in SF for reconstruction of EM energy.

Note, I'm not taking about transverse energy at any moment, the total 
energy is meant at all places.
 
If all of the above makes sens, then

for the  tower 5TB09 the values are

MIP peak at ADC=19.8
g_i=1 per definition
eta=1.3 for the etaBin=9 

SF = Emip * tanh(eta) * SamplFrac / ( dE/Dx * D * g_i)
SF = 19.8 * 0.86 *0.05 /(0.0018 *9.6 ) = 49.3 ch/GeV

This is just 20% below the value needed to get the pi0 peak & invM at the right
place.

The events taken with ppTrans-1 trigger were sorted according to the trigger: 1000=MinB, 1152= EHT2, 1150=1151+1152+1154=EHT1&2(fast+slow).
The params for pi0 reconstruction: seed energy of 0.6 GeV, seed/total energy >0.7, pi0 inv mass cut=0.07-0.22 GeV, relative gains from MIPs (for eta bin 1-4) & slopes (1-4).

Six panels below show:
-top left: invariant mass spectrum for all events,
-top mid: energy of pi0, after invM cut =0.05,0.22 GeV
-top right: transverse momentum of pi0, after invM cut
-bottom left: energy shearing Z=|E1-E2|/(E1+E2) of 2 gammas, after invM cut
-bottom mid: opening angle of 2 gammas, after invM cut
-bottom right: pseudo-rapidity distrib. of pi0, after invM cut
Green histos represent mixed events

Runs used: R4123094

SF=50 ch/GeV;    trig=1151+2+4    Npeak= 2492 ;     invM fit=0.173 +/- 0.002 GeV;

SF=60 ch/GeV;    trig=1151+2+4    Npeak= 1905 ;     invM fit=0.157 +/- 0.002 GeV;