[Paper Review] Flavored tetraquark spectroscopy

Andrea L. Guerrieri, Mauro Papinutto+3 more|arXiv (Cornell University)|Nov 9, 2014

Quantum Chromodynamics and Particle Interactions5 references3 citations

TL;DR

This paper proposes a lattice QCD study of flavored tetraquarks—exotic mesons with open charm and light quark content—using interpolating operators that avoid overlap with ordinary mesons. Despite no new resonances found in preliminary simulations, the method successfully isolates known D and D* meson thresholds, validating the approach for future searches of exotic states like doubly charged tetraquarks.

ABSTRACT

The recent confirmation of the charged charmonium like resonance Z(4430) by the LHCb experiment strongly suggests the existence of QCD multi quarks bound states. Some preliminary results about hypothetical flavored tetraquark mesons are reported. Such states are particularly amenable to Lattice QCD studies as their interpolating operators do not overlap with those of ordinary hidden-charm mesons.

Motivation & Objective

• To establish a field-theoretic framework for pure tetraquark states with open flavor quantum numbers, avoiding contamination from ordinary mesons.
• To develop interpolating operators for tetraquarks with specific quantum numbers (J^P = 1^+, I=0 or 1), particularly focusing on [cc][q̄₁q̄₂] configurations.
• To perform a preliminary lattice QCD simulation using a basis of operators to probe the spectrum of these exotic states.
• To assess the feasibility of detecting exotic tetraquarks by comparing extracted energy levels with two-meson thresholds.
• To evaluate the numerical challenges in detecting resonances due to noise in correlation functions involving spin-1 mesons.

Proposed method

• Constructs tetraquark interpolating operators using diquark-antidiquark structures: [cc] with [q̄₁q̄₂], where [cc] is a spin-1, color-anti-fundamental diquark.
• Uses both point-like and stochastic sources to invert quark propagators, enabling correlation functions with different operator types.
• Applies generalized eigenvalue problem (GEVP) techniques to extract energy levels from correlation matrices, using effective mass analysis.
• Implements smearing for quark fields to improve overlap with low-lying states, enhancing signal-to-noise ratio.
• Calculates two-meson thresholds (e.g., DD*, D(1)D*(−1)) in lattice units to compare with extracted spectrum.
• Uses mass splittings from GEVP eigenvalues to reconstruct excited state spectra, minimizing noise correlation with ground state.

Experimental results

Research questions

• RQ1 Can a lattice QCD framework be constructed to unambiguously probe pure tetraquark states without contamination from ordinary mesonic states?
• RQ2 Do the predicted flavored tetraquark states, such as the doubly charged T^{++}, appear as bound or resonant states in the spectrum?
• RQ3 How do the numerical challenges—especially noise in spin-1 meson correlation functions—affect the detection of exotic states?
• RQ4 Can the Lüscher method be applied to extract scattering phase shifts in channels involving D* mesons, given the small elastic window?
• RQ5 Is the D D scattering channel a viable alternative for identifying scalar tetraquark resonances?

Key findings

• No new energy levels beyond known D and D* mesons were observed in the J^P = 1^+, I=0 or I=1 sectors.
• The ground state effective mass for the I=0 channel was measured at am = 1.163(5), consistent with the DD* threshold at 1.166(4).
• The D(1)D*(−1) state was extracted without including its corresponding operator, indicating strong overlap from point-like propagator correlations.
• The spectrum from the smaller operator basis (O₁, O₂, O₃) showed better accuracy than the larger basis (O₂–O₅), likely due to reduced noise in off-diagonal correlators.
• The I=1 channel spectrum was noisier and could not be reliably extracted, suggesting higher numerical challenges for isospin-1 states.
• The two-meson thresholds were computed in lattice units: DD* = 1.166(4), D(1)D*(−1) = 1.230(4), D*D* = 1.254(7), and D*(1)D*(−1) = 1.314(6), providing reference points for resonance searches.