Perspectives of Open Charm Physics at $\bar PANDA$

The $\bar PANDA$ experiment at FAIR (Facility for Antiproton and Ion Research) in Darmstadt (Germany) is designed for $\bar p p$ annihilation studies and it will investigate fundamental questions of hadron and nuclear physics in interactions of antiprotons with nucleons and nuclei. Gluonic excitations and the physics of hadrons with strange and charm quarks will be accessible with unprecedented accuracy, thereby allowing high precision tests of the strong interactions. In particular, the $D_{s0}^*(2317)^+$ and $D_{s1}(2460)^+$ are still of high interest 11 years after their discovery, because they can not be simply understood in term of potential models. The available statistics and resolution of the past experiments did not allow to clarify their nature. Recently LHCb at CERN has made progresses in this respect, but still not at the level of precision required in order to clarify the puzzle of the $cs$-spectrum. $\bar PANDA$ will be able to achieve a factor 20 higher mass resolution than attained at the B-factories, which is expected to be decisive on these and second-order open questions. The technique to evaluate the width from the excitation function of the cross section of the $D_s$ mesons will be presented, and ongoing simulations performed with $PandaRoot$ will be shown.