Distinguishing gauge-mediated from unified-supergravity spectra

We show that gauge-mediation and unified-supergravity give sufficiently firm and different predictions for the spectrum of supersymmetric particles to make it possible to discriminate the two scenarios even if the messenger mass is close to the unification scale. 1 According to our present theoretical understanding, the presence of supersymmetric partners of the three generation of fermions has a very different impact on flavour physics, depending on the relative order of few fundamental high-energy scales. If the hardness scale of the supersymmetry-breaking soft terms (‘mediation scale’, MM) is higher than the hardness scale of the standard Yukawa couplings (‘flavour scale’, MF) or of the unification scale MU ≈ 2 · 10 GeV, we expect that the sfermion mass matrices contain new sources of flavour and CP violation, most likely detectable due to the heavyness of the top quark [1]. In this case it is quite possible that the consequent effects, due to virtual sparticles exchanges, will be discovered even before than the sparticles themselves. If instead the supersymmetry-breaking soft terms are mediated at a lower scale where the flavour and unification physics have decoupled, we expect that the only flavour violation present at low energies is described by the supersymmetrized extension of the standard CKM matrix. In this case supersymmetric loops could give non negligible contributions only to ‘standard’ flavour and/or CP violating effects, mainly to the b → sγ and b → sll decays [2] . If this view is correct, the forthcoming experiments about flavour physics should either discover some signal (or combination of signals), thus giving a strong hint in favour of the first scenario, or exclude new flavour and CP violations up to a certain level, making the first scenario less interesting. In any event, it is clearly useful to have an alternative way of discriminating between the two scenarios. If the mediation scale is sufficiently low (MM <∼10 8 GeV) the decay within the detector of the lightest supersymmetric particle (LSP) into a gravitino would give such an incontrovertible signal. No such a clean signal is present in the remaining range of MM. In this paper we want to show that, within reasonably minimal models, the spectrum of the supersymmetric particles typical of the two scenarios is sufficiently different that is possible to recognize which of the two scenarios is actually realized, even if the mediation scale gets close to the unification scale. 2 Both the two scenarios outlined above can be realized in a clean and predictive way. The first case, MM >∼ min(MF,MU), arises naturally if supergravity interactions mediate the soft terms [3]. In this case the hardness scale of the soft terms, MM, is the reduced Planck mass. Low energy physics suggests that the field theory at this high scale has a unified gauge group, G ⊇ SU(5) ⊃ SU(3)c ⊗ SU(2)L ⊗ U(1)Y , so that the sparticle masses are subject to unification relations. Neglecting, for the moment, SU(5)-breaking effects, unified supergravity predicts