Targets for R&D on Nb$_3$Sn conductor for High Energy Physics

High Energy Physics has been consistently pushing the performance of technical superconductors, for the benefit of high field magnet technology. So far the workhorse for particle accelerators has been Nb-Ti, but the practical performance limit has been attained with the LHC. Calls for higher beam luminosity (e.g. HL-LHC), and higher beam energy (e.g. FCC), demand a transition from Nb-Ti to Nb$_{3}$Sn, presently the only practical candidate material offering the required high field performance. This paper provides a summary of desirable properties and performance targets for Nb$_{3}$Sn to satisfy the challenging magnet specifications for upgrades of existing and future HEP accelerators.