Evaluation of clustering algorithms at the < 1 GeV energy scale for the electromagnetic calorimeter of the PADME experiment

A possible solution to the Dark Matter problem postulates that it interacts with Standard Model particles through a new force mediated by a "portal". If the new force has a U(1) gauge structure, the "portal" is a massive photon-like vector particle, called dark photon or A'. The PADME experiment at the DAΦNE Beam-Test Facility (BTF) in Frascati is designed to detect dark photons produced in positron on fixed target annihilations decaying to dark matter (e⁺e^-→γA′) by measuring the final state missing mass. One of the key roles of the experiment will be played by the electromagnetic calorimeter, which will be used to measure the properties of the final state recoil γ. The calorimeter will be composed by 616 21×21×230 mm³ BGO crystals oriented with the long axis parallel to the beam direction and disposed in a roughly circular shape with a central hole to avoid the pile up due to the large number of low angle Bremsstrahlung photons. The total energy and position of the electromagnetic shower generated by a photon impacting on the calorimeter can be reconstructed by collecting the energy deposits in the cluster of crystals interested by the shower. In PADME we are testing two different clustering algorithms, PADME-Radius and PADME-Island, based on two complementary strategies. In this paper we will describe the two algorithms, with the respective implementations, and report on the results obtained with them at the PADME energy scale (< 1 GeV), both with a GEANT4 based simulation and with an existing 5×5 matrix of BGO crystals tested at the DAΦNE BTF. (paper)