The SUSY reach of Higgs Factories in the most challenging scenario: scalar $τ$-leptons with lowest cross section and small mass differences
The direct pair-production of the $\tildeτ$, is one of the most interesting channels to search for SUSY in: the $\tildeτ$ is likely to be the lightest of the scalar leptons, and the signature of $\tildeτ$ pair production is one of the experimentally most difficult ones, making it the ``worst'' possible scenario for SUSY searches. The current limit on $\tildeτ$ production in the general MSSM comes from LEP. Limits obtained at LHC do extend to higher masses, but they are only valid under strong assumptions. Future $e^+e^-$ colliders will be powerful for SUSY searches, offering advantages with respect to previous $e^+e^-$ colliders as well as to hadron machines. In order to quantify their capabilities, the ``worst-case'' scenario for $\tildeτ$ searches has been studied, taking into account the effect of the $\tildeτ$ mixing on both $\tildeτ$ production cross section and on detection efficiency. To evaluate the latter, the ILD detector concept, originally developed for the International Linear Collider (ILC), and the ILC beam conditions at a centre-of-mass energy of $500$\,GeV have been used for detailed simulations, including for the first time the effect of bunch-crossings containing no hard $e^+e^-$ interaction, but only low-$\it{P_{T}}$ hadrons from $γγ$ interactions and $e^+e^-$ pairs from beamstrahlung. Still, the obtained exclusion and discovery reaches extend nearly up to the kinematic limit even in the worst-case scenario. This remains true also when the $\tildeτ$ and the lightest SUSY particle are quite close in mass. The results of the detailed study are extrapolated to centre-of-mass energies, integrated luminosities and beam polarisations of other proposed Higgs factory projects and discussed in view of their respective experimental environments, in particular addressing the case of FCCee.