Elastic collision events: e + p → e’ + p’

• Scattered electrons (e’) are detected in the calorimeter
• Recoil protons (p’) are detected in the HMS

Calibration coefficient

• According to energy conservation, the energy $E_i$ of scattered electron in event $i$ is:

  $E_i = E_b + M_p - E^p_i$

  where $E_b$ is the beam energy, $M_p$ is the mass of target proton, $E^p_i$ is the energy of proton detected in the HMS

• By comparing $E_i$ with $\Sigma_j C_jA^i_j$

  • $C_j$ is the calibration coefficient of block $j$ in the caloremeter
  • $A^i_j$ is the amplitude (deposited energy) if block $j$ in event $i$

  we can build $\chi^2=\Sigma_i(E_i-\Sigma_j C_jA^i_j)^2$

• The calibration coefficient $C_j$ can be calculated by minimizing the $\chi^2$:

  ${\partial\chi^2\over\partial C_k}=-2C_k\Sigma_i(E_i-\Sigma_jC_jA^i_j)A^i_k=0$

  which can be witten as:

  $\Sigma_iE_iA^i_k=\Sigma_j[\Sigma_iA^i_jA^i_k]C_j$

• Then, $C_j$ can be calculated by inverse the matrix $[\Sigma_iA^i_jA^i_k]$ and multiply $\Sigma_iE_iA^i_k$

The matrix and the calibration coefficients

• Because of an correction of depodited energy when generating the events in the simulation, edep_corr = edep*1.04, most of the calibration coefficiencts are close to 1