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Using $pp$ collision data corresponding to an integrated luminosity of$8.5\,\mathrm{fb}^{-1}$ recorded by the LHCb experiment at centre-of-massenergies of $\sqrt{s} = 7$, $8$ and $13\mathrm{\,Te\kern -0.1em V}$, theobservation of an excited $B_c^+$ state in the $B_c^+\pi^+\pi^-$ invariant-massspectrum is reported. The observed peak has a mass of $6841.2 \pm 0.6 {\,\rm(stat)\,} \pm 0.1 {\,\rm (syst)\,} \pm 0.8\,(B_c^+) \mathrm{\,MeV}/c^2$, wherethe last uncertainty is due to the limited knowledge of the $B_c^+$ mass. It isconsistent with expectations of the $B_c^{*}(2^{3}S_{1})^+$ state reconstructedwithout the low-energy photon from the $B_c^{*}(1^{3}S_{1})^+ \to B_c^+ \gamma$decay following $B_c^{*}(2^{3}S_{1})^+ \to B_c^{*}(1^{3}S_{1})^+ \pi^+ \pi^-$.A second state is seen with a global (local) statistical significance of$2.2\,\sigma$ ($3.2\,\sigma$) and a mass of $6872.1 \pm 1.3 {\,\rm (stat)\,}\pm 0.1 {\,\rm (syst)\,} \pm 0.8\,(B_c^+) \mathrm{\,MeV}/c^2$, and isconsistent with the $B_c(2^{1}S_{0})^+$ state. These mass measurements are themost precise to date.

Observation of an excited $B_c^+$ state