Parametrization of the energy resolution of a hadronic sampling calorimeter involving radiation length

Abstract

The stochastic term of the energy resolution (a_stoc) in a hadronic sampling calorimeter scales with absorber thickness (t) as √t, while shower containment is governed by the material's radiation length (X₀). We propose a new parametrization using absorber (z_t) and readout (z_s) radiation lengths. Using the ATLAS Hadronic End-Cap (HEC) geometry, we simulated 5000 electron (e) and 5000 pion (π⁻) beams with energies from 20–150 GeV, across various absorber/readout material combinations. For each beam energy, we extracted the spectral peak (E₀) and root-mean-square (σ), and fit the resolution first with the conventional a_stoc model, then with our proposed parametrization. For electrons, results show that a_stoc scales as (z_t + z_s)^−1/2, with a distinct dependence on absorber material. However, this relation does not fully capture the resolution behavior for π⁻ beams.