Observation of a new excited charm-strange meson $D_{s1}(2933)^+$ in $B^0\to D^+ D^- K^+ π^-$ decays

Abstract: A new excited charm-strange meson is observed through an amplitude analysis of the full phase space of $$B^0\to D⁺ D^- K⁺ π<sup>-$$ decays. The analysis is based on a proton-proton collision data sample collected by the \lhcb experiment at a center-of-mass energy $\sqrt{s} = 13\,\text{TeV}$, corresponding to an integrated luminosity of $5.4\text{fb}<sup>{-1}$. The statistical significance of the new state exceeds $10$ standard deviations. Its Breit--Wigner mass and width are measured to be $$m_0 = {2933}^{{+6}<em>{-5}(\text{stat})^{+4}</em>{-3}(\text{syst})} \,\text{MeV}$$ and $$Γ<em>0 = {72}^{+18}</em>{-12}(\text{stat})^{{+\phantom{0}7}_{-10}(\text{syst})} \,\text{MeV}$$, respectively, and its spin-parity quantum numbers are determined to be $J^P = 1<sup>+$. This new meson, denoted as $D_{s1}(2933)<sup>+$, is a candidate for a $D_s(2P<sup>{(\prime)}_{1})<sup>+$ state.

• The paper reports the observation of a new D_{s1}(2933)+ state with J^P=1+, markedly improving the fit likelihood in B0 decay analyses.
• It employs a multidimensional amplitude analysis on 5.4 fb⁻¹ of LHCb pp collision data, using boosted decision trees to suppress combinatorial background.
• The extracted parameters—a mass of ~2933 MeV and width of ~72 MeV—provide a vital benchmark for charm-strange spectroscopy and QCD models.

Observation of the $D_{s1}(2933)^+$: An Excited Charm-Strange Meson in $B^0\to D^+ D^- K^+ \pi^-$ Decays

Introduction and Motivation

The spectroscopy of charm-strange mesons ($D_s$) is a critical probe of nonperturbative QCD dynamics, offering stringent tests of quark model predictions, coupled-channel effects, and phenomenology beyond naive constituent models. While the lowest $D_s$ states are well established, several anomalies persist, such as the unexpectedly low masses of the $D_{s0}(2317)$ and $D_{s1}(2460)$, the quark-model tension at $D_{s0}(2590)$, and a sparse mapping of higher excitations in the $D_s$ spectrum. These puzzles motivate direct searches for higher excited $D_s$ states—including the first radial $P$-wave excitations ($B^0\to D^+ D^- K^+ \pi^-$0), many of which remain unobserved or poorly characterized. The analysis presented in "Observation of a new excited charm-strange meson $B^0\to D^+ D^- K^+ \pi^-$1 in $B^0\to D^+ D^- K^+ \pi^-$2 decays" (2604.21257) offers a decisive contribution to this program.

Data Set and Candidate Selection

The study utilizes $B^0\to D^+ D^- K^+ \pi^-$3 collision data from the LHCb detector at $B^0\to D^+ D^- K^+ \pi^-$4, corresponding to $B^0\to D^+ D^- K^+ \pi^-$5 integrated luminosity. The $B^0\to D^+ D^- K^+ \pi^-$6 candidates are fully reconstructed using the $B^0\to D^+ D^- K^+ \pi^-$7 decay modes. Optimized PID, vertex-quality, and kinematic selection criteria are applied, including a gradient-boosted decision tree for combinatorial background suppression. Signal-dominated regions are isolated via an extended unbinned maximum-likelihood fit to the reconstructed $B^0\to D^+ D^- K^+ \pi^-$8 mass spectrum.

Figure 1: (Left) Mass distribution of selected $B^0\to D^+ D^- K^+ \pi^-$9 candidates with the fit overlaid. (Right) Two-dimensional, background-subtracted mass distribution $D_s$0 vs.\ $D_s$1; the red dashed line marks the peak of the known $D_s$2 states.

The right panel of Figure 1 reveals a distinct enhancement in the $D_s$3 spectrum near $D_s$4, above the already-mapped $D_s$5 threshold, strongly suggestive of an unaccounted excited $D_s$6 contribution.

Amplitude Analysis Formalism

The central analysis is a multidimensional amplitude fit over the full five-body kinematic phase space, essential for disentangling overlapping resonances and extracting quantum numbers. Two topologies are considered: (1) cascade decays via excited $D_s$7 states decaying to the three-body $D_s$8, and (2) quasi-two-body modes involving charmonium intermediates decaying to $D_s$9. The fit includes all established resonances and pertinent nonresonant contributions, with lineshapes modeled as Breit-Wigner distributions with mass-dependent widths or via more flexible, model-independent spline interpolations where strong mixing overlaps are present.

Acceptance and efficiency variation across the multi-dimensional Dalitz space is corrected using kernel density estimation techniques on simulated signal MC, ensuring accurate normalization and systematic error control.

Identification and Properties of the $D_s$0

The baseline amplitude model, including all established contributions, fails to account for the significant excess at $D_s$1. Introducing a new $D_s$2 resonance with a Breit-Wigner parametrization into the fit dramatically improves the likelihood, with a statistical significance exceeding 10 standard deviations. The favored quantum numbers are $D_s$3; alternative ($D_s$4, $D_s$5, $D_s$6) options are strongly excluded ($D_s$7).

The resonance parameters are:

$D_s$8

This state is denoted $D_s$9. Its dominant fit fractions are associated with intermediate decays via vector and axial-vector $D_{s0}(2317)$0 and $D_{s0}(2317)$1 states in the $D_{s0}(2317)$2 system. The extracted pole mass and width are precise and robust under alternative fit models and systematic variations.

Figure 2: $D_{s0}(2317)$3 spectra for selected candidates with fit projections: (left) initial model, (right) baseline including the $D_{s0}(2317)$4 state; significant excess at $D_{s0}(2317)$5 is well accommodated only in the baseline fit.

Projections and Kinematic Consistency

Projections of the amplitude fit onto relevant invariant-mass and angular kinematic variables confirm the necessity of the $D_{s0}(2317)$6 inclusion for accurate data modeling. The fit is validated across multiple subspaces, showing agreement for all dominant resonant and nonresonant structures.

Figure 3: Various kinematic projections for $D_{s0}(2317)$7 candidates in the signal region, with baseline fit overlays; all dominant resonant structures, including the $D_{s0}(2317)$8, are accommodated.

Implications for Charm-Strange Spectroscopy

The observation of $D_{s0}(2317)$9 provides critical data for the mapping of the $D_{s1}(2460)$0 (first radial $D_{s1}(2460)$1-wave) charm-strange multiplet. The mass and width are broadly consistent with recent unquenched quark-model predictions and lattice studies that allow for significant coupled-channel modifications of bare constituent model expectations (cf.\ [Ni et al., 2022; 2023], [Godfrey & Moats 2016], [Yang et al., 2023]). The spin-parity determination and decay patterns are most compatible with assignment as the $D_{s1}(2460)$2.

This result addresses longstanding gaps in the $D_{s1}(2460)$3 spectrum above threshold, and provides input for resolving the apparent $D_{s1}(2460)$4-wave mass anomalies at low energies. It further challenges models positing strong molecular or multiquark-dominated interpretations for higher resonances in light of the successful $D_{s1}(2460)$5/$D_{s1}(2460)$6 description at this mass.

Outlook and Theoretical Perspectives

These measurements have the following theoretical and practical implications:

• Validation of coupled-channel and unquenched quark model calculations: The precise $D_{s1}(2460)$7 state at $D_{s1}(2460)$8 provides an essential calibration point for the coupled-channel dynamics and for lattice QCD computations including open strange thresholds.
• Input to phenomenology of exotic states: Recent LHCb observations of $D_{s1}(2460)$9 tetraquark candidates and open-charm exotica at similar and lower masses now have to be interpreted in the broader context of a well-populated $D_{s0}(2590)$0 spectrum. Overlaps or misidentification due to incomplete conventional spectroscopy can now be corrected.
• Experimental strategies: The success of full multidimensional amplitude analysis in multi-body $D_{s0}(2590)$1 decays strengthens the case for future high-statistics studies of $D_{s0}(2590)$2 excited states using advanced fit techniques, especially as Run 3 and beyond delivers larger datasets.

Conclusion

An amplitude analysis of $D_{s0}(2590)$3 decays reveals a statistically significant new charm-strange meson, $D_{s0}(2590)$4, with $D_{s0}(2590)$5, $D_{s0}(2590)$6, and $D_{s0}(2590)$7. This state fits naturally into the $D_{s0}(2590)$8 excitation of the $D_{s0}(2590)$9 system and provides a crucial input for resolving the structure of charm-strange mesons and for future progress in heavy-hadron spectroscopy and QCD model building (2604.21257).