Study of $B_c(1P)^+$ states in the $B_c^+ \gamma$ mass spectrum

The study of a wide peaking structure in the B c + γ mass spectrum is reported using a data sample of proton-proton collisions collected by the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9 fb − 1 . The observed structure is consistent with the lowest excited P -wave B c + states and exhibits a statistical significance exceeding 7 standard deviations relative to the background-only hypothesis. A two-peak model serves as an effective description of the data, with various theory-constrained models further explored to provide physical interpretation. Based on the predictions for the B c ( 1 P ) + spectrum, the relative production cross section of the overall B c ( 1 P ) + states with respect to the B c + ground state with the transverse momentum p T and rapidity y of B c + mesons in the regions p T < 20 GeV / c and 2.0 < y < 4.5 at s = 13 TeV is measured to be 0.20 ± 0.03 ± 0.02 ± 0.03 , where the uncertainty terms represent statistical, systematic, and uncertainties related to the choice of theoretical models, respectively. The results provide a test of theoretical models and deepen our understanding of quantum chromodynamics.