Mixed gauge and anomaly mediation from new physics at 10 TeV

In the context of anomaly-mediated supersymmetry breaking, it is natural forvectorlike fields and singlets to have supersymmetry breaking masses of order10 TeV, and therefore act as messengers of supersymmetry breaking. We show thatthis can give rise to phenomenologically viable spectra compatible withperturbative gauge coupling unification. The minimal model interpolatescontinuously between pure anomaly mediation and gauge mediation with amessenger scale of order 10 TeV. It is also possible to have non-minimal modelswith more degenerate specta, with some squarks lighter than sleptons. Thesemodels reduce to the MSSM at low energies and incorporate a natural solution ofthe mu problem. The minimal model has four continuous parameters and onediscrete parameter (the number of messengers). The LEP Higgs mass bound can besatisfied in the minimal model by tuning parameters at the GUT scale to onepart in 50.Comment: 17 pages, 4 figure