Probing slepton mass nonuniversality ate+e−linear colliders

There are many models with nonuniversal soft SUSY breaking sfermion mass parameters at the grand unification scale. Even in the MSUGRA model scalar mass unification might occur at a scale closer to $M_{\mathrm{Planck}},$ and renormalization effects would cause a mass splitting at $M_{\mathrm{GUT}}.$ We identify an experimentally measurable quantity $\Delta$ that correlates strongly with $\delta m^2\equiv m_{e_R}^2{(M}_{\mathrm{GUT}}\left)-m_{e_L}^2{(M}_{\mathrm{GUT}}\right),$ and which can be measured at electron-positron colliders provided both selectrons and the chargino are kinematically accessible. We show that if these sparticle masses can be measured with a precision of 1% at a 500 GeV linear collider, the resulting precision in the determination of $\Delta$ may allow experiments to distinguish between scalar mass unification at the GUT scale from the corresponding unification at $Q\sim M_{\mathrm{Planck}}.$ Experimental determination of $\Delta$ would also provide a distinction between the MSUGRA model and the recently proposed gaugino-mediation model. Moreover, a measurement of $\Delta$ (or a related quantity ${\Delta }^{\prime })$ would allow for a direct determination of $\delta m^2.$