Gravitino and Goldstino at Colliders∗

We consider theories with spontaneously broken global or local supersymmetry where the pseudo-goldstino or the gravitino is the lightest superparticle (LSP). Assuming that the long-lived next-to-lightest superparticle (NSP) is a charged slepton, we study several supergravity predictions: the NSP lifetime, angular and energy distributions in 3-body NSP decays. The characteristic couplings of the gravitino, or goldstino, can be tested even for very small masses. ∗Contribution to the LHC / LC study group report, eds. G. Weiglein et al. Introduction The discovery of supersymmetry at the Tevatron, the LHC or a future Linear Collider would raise the question how supersymmetry is realized in nature. Clearly, supersymmetry is broken. Spontaneously broken global supersymmetry would predict the existence of a spin-1/2 goldstino (χ) whereas the theoretically favoured case of local supersymmetry requires a massive spin-3/2 gravitino (ψ3/2). In a recent paper [1] we have studied how a massive gravitino, if it is the lightest superparticle (LSP), may be discovered in decays of τ̃ , the scalar τ lepton, which is naturally the next-to-lightest superparticle (NSP). The determination of gravitino mass and spin appears feasible for gravitino masses in the range from about 1GeV to 100GeV. As we shall discuss in this note, evidence for the characteristic couplings of a pseudogoldstino, which corresponds to the spin-1/2 part of the gravitino, can be obtained even for masses much smaller than 1GeV. The gravitino mass depends on the mechanism of supersymmetry breaking. It can be of the same order as other superparticle masses, like in gaugino mediation [2] or gravity mediation [3]. But it might also be much smaller as in gauge mediation scenarios [4]. As LSP, the gravitino is an attractive dark matter candidate [5]. The τ̃ NSP has generally a long lifetime because of the small, Planck scale suppressed coupling to the gravitino LSP. The production of charged long-lived heavy particles at colliders is an exciting possibility [6]. They can be directly produced in pairs or in cascade decays of heavier superparticles. In the context of models with gauge mediated supersymmetry breaking the production of slepton NSPs has previously studied for the Tevatron [7], for the LHC [8] and for a Linear Collider [9]. The dominant τ̃ NSP decay channel is τ̃ → τ +missing energy. In the following we shall study how to identify the gravitino or goldstino as carrier of the missing energy. First, one will measure the NSP lifetime. Since the gravitino couplings are fixed by symmetry, the NSP lifetime is predicted by supergravity given the gravitino mass, which can be inferred from kinematics. Second, one can make use of the 3-body NSP decay τ̃ → τ + γ+X where X = ψ3/2 or X = χ. The angular and energy distributions and the polarizations of the final state photon and lepton carry the information on the spin and couplings of gravitino or goldstino. For gravitino masses in the range from about 10 keV to 100GeV, the NSP is essentially stable for collider experiments, and one has to accumulate the NSPs to study their decay. Sufficiently slow, strongly ionizing sleptons will be stopped within the detector. One may also be able to collect faster sleptons in a storage ring. For gravitino masses less than O(10 keV) the τ̃ can decay inside the detector, which may be advantageous