In this work, the search for excited $B_c^+(2S)$ states, through their decay to $B_c^+\pi^+\pi^-$, is presented.
For the first time, signals consistent with the $B_c^+(2S)$ and $B_c^{+\,*}(2S)$ states are observed in proton-proton collisions at $\sqrt(s) = 13~\textrm{TeV}$, in an event sample corresponding to an integrated luminosity of $143~\textrm{fb}^{-1}$, collected by the CMS experiment during the 2015-2018 LHC running periods. These excited $\bar b c$ states are observed in the $B_c^+\pi^+\pi^-$ invariant mass spectrum, with the ground state $B_c^+$ reconstructed through its decay to $J/\psi \pi^+$. The two states are reconstructed as two well-resolved peaks, separated in mass by $29.1 \pm 1.5(\textrm{stat}) \pm 0.7(\textrm{syst})~\textrm{MeV}$. The observation of two peaks, rather than one, is established with a significance exceeding five standard deviations. The mass of the $B_c^+(2S)$ meson is measured to be $6871.0 \pm 1.2 (\textrm{stat}) \pm 0.8 (\textrm{syst}) \pm 0.8 (B_c^+)~\textrm{MeV}$, where the last term corresponds to the uncertainty in the world-average $B_c^+$ mass.