Supergravity at Colliders

TL;DR

The paper investigates collider-based probes of supergravity by assuming a gravitino LSP and a charged slepton NSP, showing that the NSP lifetime, once the gravitino mass is inferred kinematically, provides a direct test of the supergravity prediction tied to the Planck scale. It further demonstrates that the 3-body decay \\tilde{\\tau} -> \\tau \\psi_{3/2} \\gamma$ encodes the gravitino’s spin-3/2 through distinctive angular-energy distributions and photon polarizations, enabling discrimination from spin-1/2 scenarios with sufficient event statistics. Cosmological constraints from reheating and BBN are discussed, outlining how overproduction and late NSP decays constrain parameter space but can be alleviated by entropy production or low $T_R$. Collectively, these results outline a feasible program to test spontaneously broken local supersymmetry at colliders and to connect collider observables with the gravitino’s role in cosmology and dark matter.

Abstract

We consider supersymmetric theories where the gravitino is the lightest superparticle (LSP). Assuming that the long-lived next-to-lightest superparticle (NSP) is a charged slepton, we investigate two complementary ways to prove the existence of supergravity in nature. The first is based on the NSP lifetime which in supergravity depends only on the Planck scale and the NSP and gravitino masses. With the gravitino mass inferred from kinematics, the measurement of the NSP lifetime will test an unequivocal prediction of supergravity. The second way makes use of the 3-body NSP decay. The angular and energy distributions and the polarizations of the final state photon and lepton carry the information on the spin of the gravitino and on its couplings to matter and radiation.

Figures (4)

• Figure 1: Diagrams contributing to $\widetilde{\tau}\to\tau+\psi_{3/2}+\gamma$ at tree level. We do not take into account the diagram with a neutralino intermediate state. It turns out that (a) is the crucial ingredient to prove the spin-3/2 nature of the gravitino.
• Figure 2: (a) shows the kinematical configuration of the 3-body decay. (b) illustrates the characteristic spin-3/2 process: if photon and $\tau$-lepton move in opposite directions and the spins add up to $3/2$, the invisible particle also has spin $3/2$.
• Figure 3: Contour plots of the differential decay rates for (a) gravitino $\psi_{3/2}$ and (b) neutralino $\lambda$. $m_{\widetilde{\tau}}=150\,\mathrm{GeV}$ and $m_{X}=75\,\mathrm{GeV}$ ($X=\psi_{3/2},\lambda$). The boundaries of the different gray shaded regions (from bottom to top) correspond to $\Delta(E_\gamma ,\cos\theta)[\mathrm{GeV}^{-1}] =10^{-3}, 2\times10^{-3}, 3\times10^{-3}, 4\times10^{-3}, 5\times10^{-3}$. Darker shading implies larger rate.
• Figure 4: Angular asymmetries for gravitino $\psi_{3/2}$ (solid curve), goldstino $\chi$ (dashed curve) and neutralino $\lambda$ (dotted curve). We use $m_{\widetilde{\tau}}=150\,\mathrm{GeV}$ and cut the photon energy below $10\%$ of the maximal photon energy (cf. App. \ref{['app:Details']}). Note that the asymmetries only depend on the ratio $r=m_X^2/m_{\widetilde{\tau}}^2$ ($X=\psi_{3/2}, \chi,\lambda$).