A model for the measured KATRIN differential Tritium spectrum to search for keV sterile neutrinos

KATRIN (Karlsruhe Tritium Neutrino Experiment) aims to measure the neutrino mass by analyzing the endpoint region of a Tritium spectrum using a high-luminosity source and a high-resolution MAC-E filter technique. KATRIN holds the current best limit on the neutrino mass of 0.8 eV, coming from the joint analysis of the first two measurement campaigns. After KATRIN's data taking, a detector upgrade, called TRISTAN, is planned. The choice for this new detector is a matrix of Silicon Drift Detectors (SDDs) made of 9 modules with 166 pixels each. SDDs, able to sustain a high count rate, will allow a high-statistics measurement of the whole Tritium spectrum, and thus the search for new physics, like sterile neutrinos with mass in the keV-range, candidates to be Dark Matter particles. A model for the measured Tritium spectrum is therefore needed. In this work, I will present the status of such a model, together with experimental tests of one of its parts, the detector response.