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The $\overline{B_s^0} \rightarrow \chi_{c2} K^+ K^- $ decay mode is observedand its branching fraction relative to the corresponding $\chi_{c1}$ decaymode, in a $\pm 15 \textrm{MeV}/c^2$ window around the $\phi$ mass, is found tobe $\frac{\mathcal{B}(\overline{B_s^0} \rightarrow \chi_{c2} K^+ K^-) }{\mathcal{B}(\overline{B_s^0} \rightarrow \chi_{c1} K^+ K^-)} = (17.1 \pm 3.1\pm 0.4 \pm 0.9)\%,$ where the first uncertainty is statistical, the secondsystematic and the third due to the knowledge of the branching fractions ofradiative $\chi_c$ decays. The decay mode $\overline{B_s^0} \rightarrow\chi_{c1} K^+ K^- $ allows the $ B_s^0$ mass to be measured as $m(B_s^0) =5366.83 \pm 0.25 \pm 0.27 \, \textrm{MeV}/c^2,$ where the first uncertainty isstatistical and the second systematic. A combination of this result with otherLHCb determinations of the $B_s^0$ mass is made.

Observation of the decay $\overline{B_s^0} \rightarrow \chi_{c2} K^+ K^- $ in the $\varphi$ mass region