# New Inorganic Scintillators' Application in the Electromagnetic Calorimetry in High-Energy Physics
## 2 Simulations in Geant4
### Results of the Simulations for Combined Calorimeters  
It is crucial to determine whether it is possible to distinguish between photons and other types of particles with the proposed combined GAGG + PWO-calorimeter. There are a few methods that provide such an opportunity. The first one is based on a pulse shape analysis of different particles, for instance, positrons and neutrons [21,22] or photons and \(\alpha\)-particles [23]. The second way to separate gammas and neutrons considers the difference in their radiation/interaction lengths. This can be achieved by the usage of different crystals such as PWO and GAGG [22], or two identical GAGG:Ce crystals with one of them codoped with Mg [21]. The third option is to discriminate photons by their shower shape and suppress the charged pion and antineutron background. This is achieved by calculating the eigenvalues (\(\lambda_{short}\), \(\lambda_{long}\)) of the dispersion tensor [1]. Examples of such distributions for photon energies of 500 MeV and 5 GeV, obtained by the GAGG + PWO calorimeter with a 10 cm long GAGG section, are depicted in the Figure 7. At high photon energies, electromagnetic showers are rather compact and localized in a narrow region in the plane (\(\lambda_{short}\), \(\lambda_{long}\)). The distribution broadens with a decrease in the photon energy. Analogous distributions can be constructed for other types of particles, such as charged pions and antineutrons. Projection examples for particles with energies of 5 GeV and  
Figure 6: Energy resolution of PWO crystals with and without the noise simulation [20]. Figure 7: Examples of (\(\lambda_{short}\), \(\lambda_{long}\)) distributions for a photon impact into GAGG + PWO-calorimeter with the photon energy of 500 MeV (**left**), 5 GeV (**right**). 500 MeV are represented in the Figures 8 and 9, respectively. It can be concluded that \(\pi^{+}\) and \(\bar{n}\) distributions are much broader than \(\gamma\) distributions, which provides an opportunity for an efficient gamma-hadron separation based on a \(\lambda\) cut. In addition, the distribution of antineutrons remains broad, regardless of the primary photon energy. After applying a cut (\(\lambda_{short}\leq 1.5\) cm\({}^{2}\), \(\lambda_{long}\leq 2\) cm\({}^{2}\)) for 5 GeV particles, only 1.8% of \(\gamma\) are lost, but 89.9% of \(\pi^{+}\) and 98.7% of \(\bar{n}\) are rejected. After applying a cut (\(\lambda_{short}\leq 2.2\) cm\({}^{2}\), \(\lambda_{long}\leq 5\) cm\({}^{2}\)) for 500 MeV particles, only 7.2% of \(\gamma\) are lost, but 55.9% of \(\pi^{+}\) and 96.2% of \(\bar{n}\) are removed. The level of possible \(\gamma/\pi^{+}\) and \(\gamma/\bar{n}\) differentiation is shown in Figure 10. Here, the accepted fraction of particles with \(\lambda_{long}>0\) and a less than varying cut as a function of this cut is shown. At the same time, \(\lambda_{short}\) is fixed at the value of 2.2 cm\({}^{2}\). A \(\lambda\) cut, which depends on the deposited energy, can be used to obtain an energy-independent acceptance level for electromagnetic showers while providing a maximum hadronic shower rejection. To determine the spatial resolution of the GAGG and GAGG + PWO calorimeters, the procedure described above for the calculation of PWO calorimeter resolution was carried out. Figure 11 shows a comparison of the spatial resolution in the PWO-, GAGG-, and GAGG + PWO-calorimeters, excluding noise. The spatial resolution of the combined calorimeter is slightly worse than that of the calorimeter consisting only of PWO crystals, but not significantly. The resolution of the pure GAGG-calorimeter is noticeably worse in the range of energies of 1-100 MeV and above 5 GeV. A comparison of the spatial resolution obtained for GAGG + PWO-calorimeter with different GAGG-section lengths is depicted in Figure 12. For the energies above 1 MeV, the spatial resolution of the GAGG + PWO-calorimeter is nearly the same as the resolution of the PWO-calorimeter.