Hadron colliders as the “neutralino factory”: Search for a slow decay of the lightest neutralino at the CERN LHC

The prospects are examined for the detection of a slow decay of the lightest neutralino (or any other long-lived particles) at the CERN LHC and at the Very Large Hadron Collider (VLHC). We first point out that such hadron colliders will become the “neutralino factory” producing ${10}^6–{10}^9\mathrm{n}\mathrm{e}\mathrm{u}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{s}/\mathrm{y}\mathrm{r},$ if gluinos and/or squarks actually exist below $O\left(1\right)\mathrm{}$ TeV. The lightest neutralino $\left({\tilde{\chi }}_1^0\right),$ usually assumed to be stable, will be unstable if lighter superparticles such as the gravitino $\left(\tilde{G}\right)$ or axino $\left(ã\right)$ exist, or $R$-parity is not conserved. The decay signal would, however, be missed in usual collider experiments, particularly when the decay mostly occurs outside the detector. In order to search for such a slow decay of ${\tilde{\chi }}_1^0,$ we propose a dedicated experiment where the collision products are dumped by a thick shield, which is followed by a long decay tunnel. The decay product of ${\tilde{\chi }}_1^0$ can be detected by a detector located at the end of the tunnel. The slow arrival time and the large off angle (to the direction of the interaction point) of the decay product will provide a clear signature of slowly decaying ${\tilde{\chi }}_1^0$’s. One can explore the decay length $\left(c\tau \right)$ in a wide range, i.e., 0.2 m to $1\times {10}^5\mathrm{km}$ for $m_{{\tilde{\chi }}_1^0}=25\mathrm{}\mathrm{GeV}$ and 1 m to 2 km for $m_{{\tilde{\chi }}_1^0}=200\mathrm{}\mathrm{GeV}$ at the LHC. This corresponds to the range of the SUSY breaking scale $\sqrt{F}=2\mathrm{}\times {10}^5$ to $2\times {10}^7\mathrm{GeV}$ in case of the ${\tilde{\chi }}_1^0\to \gamma \tilde{G}$ decay predicted in gauge-mediated SUSY breaking models. At VLHC, one can extend the explorable range of $m_{{\tilde{\chi }}_1^0}$ up to $\sim 1000\mathrm{GeV},$ and that of $\sqrt{F}$ up to $\sim 1\times {10}^8\mathrm{GeV}.$ In the case of the ${\tilde{\chi }}_1^0\to \gamma ã$ decay, the Peccei-Quinn symmetry breaking scale $F_a$ can be explored up to $\sim 5\times {10}^{11}\mathrm{GeV}.$ The mass of the decaying particle can be determined by using the correlation between the energy and the arrival time of the decay product. With the setup we propose, one can also search for (i) other decay modes of ${\tilde{\chi }}_1^0$ such as the $R$-parity violating one, (ii) slow decays of any other long-lived neutral or charged particles, and (iii) heavy stable charged particles.