Search for excited $B_c^{+}$ states

A search is performed in the invariant mass spectrum of the $B_c^{+}{\pi }^{+}{\pi }^{-}$ system for the excited $B_c^{+}$ states $B_c(2^1{S}_0{)}^{+}$ and $B_c(2^3{S}_1{)}^{+}$ using a data sample of $pp$ collisions collected by the LHCb experiment at the centre-of-mass energy of $\sqrt{s}=8\mathrm{T}\mathrm{e}\mathrm{V}$, corresponding to an integrated luminosity of $2\mathrm{f}{\mathrm{b}}^{-1}$. No evidence is seen for either state. Upper limits on the ratios of the production cross-sections of the $B_c(2^1{S}_0{)}^{+}$ and $B_c(2^3{S}_1{)}^{+}$ states times the branching fractions of $B_c(2^1{S}_0{)}^{+}\to B_c^{+}{\pi }^{+}{\pi }^{-}$ and ${B_c(2^{3}S_{1})^+} \to {B_c^{*+}\pi^{+}\pi^{-}}$overtheproductioncross-sectionofthe$B_c^{+}$ state are given as a function of their masses. They are found to be between 0.02 and 0.14 at $95\mathrm{\%}$ confidence level for $B_c(2^1{S}_0{)}^{+}$ and $B_c(2^3{S}_1{)}^{+}$ in the mass ranges $[6830,6890]\mathrm{M}\mathrm{e}\mathrm{V}\mathrm{/}{c}^2$ and $[6795,6890]\mathrm{M}\mathrm{e}\mathrm{V}\mathrm{/}{c}^2$, respectively.