Study of $B_{c}(1P)^{+}$ states in the $B_{c}^{+} \gamma$ mass spectrum

The study of a wide peaking structure in the $B_{c}^{+} \gamma$ 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 $13~\text{TeV}$, corresponding to an integrated luminosity of $9~\text{fb}^{-1}$. The observed structure is consistent with the lowest excited $P$-wave $B_{c}^{+}$ states and exhibits a statistical significance exceeding seven 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 $B_{c}(1P)^{+}$ spectrum, the relative production cross-section of the overall $B_{c}(1P)^{+}$ states with respect to the $B_{c}^{+}$ ground state with the transverse momentum $p_{\text{T}}$ and rapidity $y$ of $B_{c}^{+}$ mesons in the regions $p_{\text{T}}<20~\mathrm{Ge\kern -0.1em V\!/}c$ and $2.0<y<4.5$ at $\sqrt{s}=13~\text{TeV}$ is measured to be $0.20 \pm 0.03 \pm 0.02 \pm 0.03$, 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.