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

TL;DR

This work presents the first observation of orbitally excited B_c states in the B_c^+ γ mass spectrum, using pp collisions collected by LHCb at √s = 7, 8, and 13 TeV corresponding to ~9 fb^−1. A two-peak, theory-independent fit reveals a structure consistent with B_c(1P)^+ states, with peak masses around M1 ≈ 6705 MeV/$c^2$ and M2 ≈ 6752 MeV/$c^2$ after accounting for detector resolution; a six-peak, theory-constrained model anchored in lattice QCD and NRQCD also describes the data, yielding a production ratio R = 0.20 ± 0.03 (stat) ± 0.03 (theory). The photon-energy calibration using χ_c decays and cross-checks with D_s1(2460)^+ underpin the mass-scale accuracy, while the systematic uncertainty analysis supports a robust measurement of B_c(1P)^+ production relative to B_c^+ in the specified kinematic region. The results test QCD predictions for a unique two-heavy-quark system and lay groundwork for future resolution of individual 1P states via photon-conversion techniques.

Abstract

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 $13~\text{TeV}$, 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.

Figures (7)

• Figure 1: Distribution of $M(B_{c}^{+}\gamma)-M(B_{c}^{+})$ for the selected $B_{c}^{+}$ candidates. The distribution of $B_{c}^{+}$ candidates from the high-mass sideband region is also shown for comparison.
• Figure 2: Distribution of $M(J/\psi\gamma) - M(J/\psi)$ for selected $\chi_c$ candidates with converted photons, in the region $E_\gamma \in [5.9, 7.2]~\mathrm{Ge V}$ and $n_{\text{tracks}} \in [125, 181]$. Fit results are also shown. Contributions from $\chi_{c0}, \chi_{c1}$, and $\chi_{c2}$ decays are shown with different line colors, while the gray vertical line indicates the known $\chi_{c1}$ mass PDG2024.
• Figure 3: Distribution of $M(D_{s}^{+}\gamma) - M(D_{s}^{+})$ for the selected $D_{s1}(2460)^{+}$ candidates with converted photons. Fit results are also shown. The gray vertical line indicates the known $D_{s1}(2460)^{+}$ mass PDG2024.
• Figure 4: Mass distribution of the selected $B_{c}^{+}$ candidates reconstructed from the $B_{c}^{+} \rightarrow\xspace J/\psi \pi^+$ decay. The fit results are also shown.
• Figure 5: Distribution of the mass difference $M(B_{c}^{+}\gamma)-M(B_{c}^{+})$ with the result of the lattice QCD fit model also shown. The contributions of the six signal peaks from four $B_{c}(1P)^{+}$ states are shown, where both the location and the relative contributions are fixed to the central values predicted by C.T.H. Davies et al.Davies:1996gi. The inset illustrates a zoomed signal region in logarithmic scale.