[Paper Review] Spectroscopy of light tetraquark states

Sasa Prelovsek, T. Draper+5 more|arXiv (Cornell University)|Oct 15, 2009

Physics of Superconductivity and Magnetism1 references3 citations

TL;DR

This lattice QCD study investigates whether the lightest scalar mesons, the σ(600) and κ(800), are tetraquark states by computing the spectrum of 0++ states with isospin I=0, 1/2, 3/2, and 2 using tetraquark interpolators. Using the generalized eigenvalue method with multiple interpolators, the authors find additional light states in the I=0 and I=1/2 channels beyond the expected ππ and Kπ scattering states, suggesting a strong tetraquark component for the σ and κ resonances.

ABSTRACT

We address the question whether the lightest scalar mesons sigma and kappa are tetraquarks, as is strongly supported by many phenomenological studies. We present a search for possible light tetraquark states with J^PC=0^++ and I=0, 1/2, 3/2, 2 on the lattice. The spectrum is determined using the generalized eigenvalue method with a number of tetraquark interpolators at the source and the sink. In all the channels, we unavoidably find lowest scattering states pi(k)pi(-k) or K(k)pi(-k) with back-to-back momentum k=0,2*pi/L,.. . However, we find an additional light state in the I=0 and I=1/2 channels, which may be related to the observed resonances sigma and kappa with a strong tetraquark component. In the exotic repulsive channels I=2 and I=3/2, where no resonance is observed, we find no light state in addition to the scattering states.

Motivation & Objective

• To determine whether the lightest scalar mesons σ and κ have a dominant tetraquark Fock component, as suggested by phenomenological models.
• To investigate the existence of tetraquark states with JPC=0++ and isospin I=0, 1/2, 3/2, 2 in lattice QCD simulations.
• To disentangle genuine tetraquark states from scattering states (ππ, Kπ) in the spectrum using multiple interpolators and the generalized eigenvalue method.
• To test whether the absence of additional light states in exotic channels (I=2, 3/2) correlates with the absence of observed resonances in those channels.

Proposed method

• Employed the generalized eigenvalue method with multiple tetraquark interpolators at both source and sink to extract energy levels in the 0++ sector.
• Used a set of five tetraquark interpolators in I=0 and I=1/2 channels, including diquark-antidiquark and current-current types, with appropriate flavor combinations to project desired isospin quantum numbers.
• Applied narrow Jacobi smearing to quark fields in the dynamical simulation to enhance overlap with low-lying states.
• Performed simulations on two ensembles: one with Nf=2 dynamical Chirally Improved fermions and one quenched with valence overlap fermions, at varying pion masses and fixed spatial volume.
• Fitted the time dependence of correlation functions using a three-parameter form that accounts for finite-volume effects and scattering state contributions, including both inelastic and elastic scattering states.
• Used effective masses derived from the full correlation matrix to identify energy levels, with stability checks across different time-slice choices and submatrix sizes.

Experimental results

Research questions

• RQ1 Does the lattice spectrum in the I=0 channel contain a state lighter than the ππ scattering threshold, beyond the π(0)π(0) and π(2π/L)π(-2π/L) states?
• RQ2 Is there evidence for a light state in the I=1/2 channel beyond the K(0)π(0) and K(2π/L)π(-2π/L) scattering states?
• RQ3 Do the exotic channels I=2 and I=3/2, which lack observed resonances, show any additional light states beyond the expected ππ and Kπ scattering towers?
• RQ4 Can the generalized eigenvalue method with tetraquark interpolators resolve a genuine tetraquark state from scattering backgrounds in the 0++ sector?

Key findings

• An additional light state appears in the I=0 channel, above the π(0)π(0) and π(2π/L)π(-2π/L) scattering states, suggesting a possible tetraquark component for the σ resonance.
• A similar additional light state is observed in the I=1/2 channel, above the K(0)π(0) and K(2π/L)π(-2π/L) scattering states, indicating a possible tetraquark component for the κ resonance.
• In the exotic I=2 and I=3/2 channels, no additional light state is found beyond the expected ππ and Kπ scattering towers, consistent with the absence of observed resonances in these channels.
• The results are stable under variations in the time-slice choice (t0 ∈ [1,4]), submatrix size (4×4 or 3×3), and are consistent across both dynamical and quenched simulations.
• The observed states in I=0 and I=1/2 channels are not artifacts of the generalized eigenvalue method or missing annihilation diagrams, as confirmed by extensive consistency checks.
• The findings support the phenomenological view that the σ and κ mesons have a dominant tetraquark Fock component, though confirmation by independent simulations is required.