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 $sqrt{s} = 8 ,{mathrm{TeV}}$, corresponding to an integrated luminosity of $2 ,{mathrm{fb^{-1}}}$. 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 ${B_c(2^{1}S_{0})^+} to {B_c^{+}pi^{+}pi^{-}}$ and ${B_c(2^{3}S_{1})^+} to {B_c^{*+}pi^{+}pi^{-}}$ 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 $[6830, 6890] ,{mathrm{MeV}}/c^{2}$ and $[6795,6890] ,{mathrm{MeV}}/c^{2}$, respectively.
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