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 an experimental signature of one soft, hadronically decaying $\tau$ lepton, one energetic jet from initial-state radiation, and large transverse momentum imbalance is presented. These event signatures are consistent with direct or indirect production of scalar $\tau$ leptons ($\tilde{\tau }$) in supersymmetric models that exhibit coannihilation between the $\tilde{\tau }$ and the lightest neutralino (${\tilde{\chi }}_1^0$), and that could generate the observed relic density of dark matter. The data correspond to an integrated luminosity of 77.2 fb${}^{-1}$ of proton-proton collisions at $\sqrt{s}=$ 13 TeV collected with the CMS detector at the LHC in 2016 and 2017. The results are interpreted in a supersymmetric scenario with a small mass difference ($\Delta m$) between the chargino (${\tilde{\chi }}_1^{\pm }$) or next-to-lightest neutralino (${\tilde{\chi }}_2^0$), and the ${\tilde{\chi }}_1^0$. The mass of the $\tilde{\tau }$ is assumed to be the average of the ${\tilde{\chi }}_1^{\pm }$ and ${\tilde{\chi }}_1^0$ masses. The data are consistent with standard model background predictions. Upper limits at 95% confidence level are set on the sum of the ${\tilde{\chi }}_1^{\pm }$, ${\tilde{\chi }}_2^0$, and $\tilde{\tau }$ production cross sections for $\Delta m({\tilde{\chi }}_1^{\pm },{\tilde{\chi }}_1^0)=$ 50 GeV, resulting in a lower limit of 290 GeV on the mass of the ${\tilde{\chi }}_1^{\pm }$, which is the most stringent to date and surpasses the bounds from the LEP experiments.