Search for excited $B_{c}^{+}$ states

A search is performed in the invariant mass spectrum of the B$_{c}^{+}$ π$^{+}$π$^{−}$ 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 $ TeV, corresponding to an integrated luminosity of 2 fb$^{−1}$. 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$_{0}$)$^{+}$ → B$_{c}^{+}$ π$^{+}$π$^{−}$ and B$_{c}$ (2$^{3}$S$_{1}$)$^{+}$ → B$_{c}^{*}^{+}$π$^{+}$π$^{−}$ over the production cross-section of the B$_{c}^{+}$ state are given as a function of their masses. They are found to be between 0.02 and 0.14 at 95% confidence level for B$_{c}$ (2$^{1}$S$_{0}$)$^{+}$ and B$_{c}$ (2$^{3}$S$_{1}$)$^{+}$ in the mass ranges [6830, 6890] MeV/c$^{2}$ and [6795, 6890] MeV/c$^{2}$, respectively.