Resonances and $CP$ violation in $B_s^0$ and $\overline{B}_s^0 \to J/\psi K^+K^-$ decays in the mass region above the $\phi(1020)$

The decays of $B_s^0$ and $\overline{B}_s^0$ mesons into the $J/\psi K^+K^-$ final state are studied in the $K^+K^-$ mass region above the $\phi(1020)$ meson in order to determine the resonant substructure and measure the $CP$-violating phase, $\phi_s$, the decay width, $\Gamma_s$, and the width difference between light and heavy mass eigenstates, $\Delta\Gamma_s$. A decay-time dependent amplitude analysis is employed. The data sample corresponds to an integrated luminosity of $3{\rm fb}^{-1}$ produced in 7 and 8 Tev $pp$ collisions at the LHC, collected by the LHCb experiment. The measurement determines $\phi_s = 119\pm107\pm34 {\rm \, mrad}$. A combination with previous LHCb measurements using similar decays into the $J/\psi \pi^+\pi^-$ and $J/\psi\phi(1020)$ final states gives $\phi_s=1\pm37 {\rm \,mrad}$, consistent with the Standard Model prediction.