Search for supersymmetry with a compressed mass spectrum in events with a soft $\tau$ lepton, a highly energetic jet, and large missing transverse momentum in proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$

The first search for supersymmetry in events with one soft tau lepton, one energetic jet from initial state radiation, and transverse momentum imbalance is presented. These event signatures are consistent with those from supersymmetric models exhibiting co-annihilation between the scalar tau lepton ($\tilde{\tau}$) and the lightest neutralino ($\tilde\chi^{0}_{1}$) that could generate the observed relic density of dark matter. The data correspond to an integrated luminosity of $77.2~\mathrm{fb}^{-1}$ of proton-proton collisions at $\sqrt{s}=13~\mathrm{TeV}$ collected with the CMS detector at the CERN LHC in 2016 and 2017. The results are interpreted considering a supersymmetric scenario with a small mass difference ($\Delta m$) between the chargino ($\tilde{\chi}^{\pm}_{1}$) or the next-to-lightest neutralino ($\tilde{\chi}^{0}_{2}$), and the lightest neutralino. The mass of the $\tilde{\tau}$ is defined as the average of the $\tilde\chi^{\pm}_{1}$/$\tilde\chi^{0}_{2}$ and $\tilde{\chi}^{0}_{1}$ masses. The data are found to be consistent with the standard model background predictions. Upper limits at $95\%$ confidence level are set on the $\tilde{\chi}^{\pm}_{1}$, $\tilde\chi^{0}_{2}$, and $\tilde{\tau}$ production cross sections for $\Delta{m}(\tilde{\chi}^{\pm}_{1}, \tilde\chi^{0}_{1}) = 50~\mathrm{GeV}$, resulting in a lower mass limit of $290~\mathrm{GeV}$ on the mass of the $\tilde\chi^{\pm}_{1}$/$\tilde\chi^{0}_{2}$, which is the most stringent to date.