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 $p_{\text{T}}<20\mathrm{G}\mathrm{e}\mathrm{V}\text{\hspace{0.17em}⁣}\mathrm{/}c$ 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.