Observation of the state in decays
Using 9 fb of LHCb proton-proton collision data, this study presents the first observation of the tetraquark state in the decay channel with a statistical significance exceeding , confirming that existing resonances are insufficient to explain the data.
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Technical Summary: Observation of the state in decays
Problem and Motivation
The nature of exotic hadrons, particularly charged charmonium-like states with minimal quark content , remains a critical testing ground for nonperturbative Quantum Chromodynamics (QCD). The state (historically referred to as ) was first reported by the Belle collaboration and later confirmed by LHCb in the hidden-charm decay channel . While its resonant nature and quantum numbers () were firmly established in this channel, its internal structure—whether a molecular state, a compact tetraquark, or a kinematic effect like a triangle singularity—remains debated. A crucial discriminator between these models is the relative strength of its open-charm versus hidden-charm decays. To date, no open-charm decay mode of the had been observed, leaving a gap in understanding its dynamics. This paper addresses the search for the in the open-charm decay channel .
Methodology
The analysis utilizes proton-proton collision data collected by the LHCb experiment at center-of-mass energies of and $13$ TeV, corresponding to an integrated luminosity of . The study focuses on the reconstruction of candidates, where and the mesons are reconstructed via or final states.
The analysis employs an unbinned maximum-likelihood amplitude analysis (Partial Wave Analysis) using the TF-PWA software. The signal amplitude is constructed as a coherent sum of resonant and nonresonant contributions across three two-body subsystems: , , and .
- System: Known excited resonances (, , , and ) are included. The broad spin-1 components are described using a quasi-model-independent (QMI) method with cubic-spline interpolation to avoid biases inherent in simple Breit-Wigner sums.
- System: Standard resonant contributions are considered.
- System: The primary goal is to test for the presence of the state. A relativistic Breit-Wigner function is introduced to model this contribution.
The fit is performed simultaneously across six independent subsamples (combinations of decay modes and Run 1/Run 2 data). Systematic uncertainties are evaluated by varying signal and background models, efficiency maps, and amplitude descriptions (including alternative K-matrix models and Blatt-Weisskopf radius variations).
Key Results
- Necessity of the Tetraquark: A reference fit including only known resonances fails to describe the data, specifically failing to reproduce a pronounced dip observed in the invariant mass spectrum near $4.4$ GeV. The of this reference fit is $82.1$ for 64 bins.
- Observation of : The inclusion of the state in the subsystem significantly improves the fit quality, reducing the to $72.8$. The change in negative log-likelihood () is $-43.0$ with 2 degrees of freedom, corresponding to a statistical significance of .
- Properties:
- Spin-Parity: The hypothesis is preferred over and assignments by more than .
- Mass and Width: When allowed to vary, the fitted mass is MeV and the width is MeV. These are consistent with previous measurements in the channel within and , respectively.
- Fit Fraction: The fit fraction is . The analysis notes large negative interference effects with the QMI S-wave and nonresonant components, which are necessary to generate the observed dip structure.
- Exclusion of Other States: The inclusion of other exotic candidates such as , , and yields marginal improvements in fit quality (significances of , , and respectively when tested individually, diminishing further when included simultaneously). Upper limits on their fit fractions are established at the 95% confidence level.
- Branching Ratios: The product of branching fractions is measured. The ratio of partial decay widths is determined as .
Significance and Claims
The paper claims the first observation of the state in an open-charm decay channel (). The observation is confirmed at a statistical significance exceeding (specifically after accounting for systematic uncertainties).
The authors state that the measured properties (mass, width, and spin-parity) are consistent with those previously measured in the hidden-charm channel. Crucially, the measured ratio of partial widths to open-charm and hidden-charm final states is near unity. The paper concludes that this result disfavors the dominance of either decay mode and provides "important input for understanding its internal structure," though it explicitly notes that "dedicated theoretical calculations are still lacking" to interpret this specific ratio. The observation confirms that the is a genuine resonance with significant coupling to open-charm final states.
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