The observation possibility of $B_c$ excitations at LHC

It is shown that in the decays $B_c(2P)\to B_c^{\ast }{\gamma }^{\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{d}}$, $B_c(3P)\to B_c^{\ast }{\gamma }^{\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{d}}$ and $B_c(2S)\to B_c^{\ast }+{\pi }^{+}{\pi }^{-}$ followed by the decay $B_c^{\ast }\to B_c+{\gamma }^{\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}}$ the loss of the soft photon ${\gamma }^{\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}}$ do not wash out peaks from the initial excitations. The relative yields of $B_c^{\ast }$, 2P-wave, and 3P-wave states of $B_c$ meson at LHC are estimated as function of transverse energy of emitted photon ${\gamma }^{\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{d}}$. It is pointed out, that the decays $B_c(2S) \to B_c(B_c^*)+\pi^+\pi^-$couldprovideanewinformationabouta$\sigma$ resonance nature.