[Paper Review] Diquark-antidiquark states with hidden or open charm

Luciano Maiani, F. Piccinini+2 more|ArXiv.org|Mar 2, 2006

Quantum Mechanics and Non-Hermitian Physics2 references3 citations

TL;DR

This paper proposes that charmed mesons with hidden or open charm, including the X(3872) and Y(4260), are tetraquark states composed of diquark-antidiquark pairs, using a constituent quark model with spin-dependent interactions and diquark masses derived from known hadron spectra. The model successfully explains the narrow width and decay patterns of X(3872) as a 1++ state and predicts the Y(4260) as a 1-- orbital excitation of a [cs][c̄s̄] state with a mass of 4330±70 MeV.

ABSTRACT

Some features and predictions of a recently proposed model based on diquark-antidiquark bound states are illustrated. Its ability in accomodating newly discovered charmed resonances around 4 GeV is discussed.

Motivation & Objective

• To explain the anomalous properties of newly discovered charmed resonances, such as X(3872) and Y(4260), which do not fit well within the conventional charmonium picture.
• To investigate whether these states can be understood as molecular-like tetraquark states composed of diquark-antidiquark pairs.
• To explore the role of spin-spin interactions and orbital excitations in generating a rich spectrum of JPC states with hidden or open charm.
• To account for isospin breaking effects in the X(3872) state, which explains its decay into both J/ψρ and J/ψω final states.
• To predict the existence and decay modes of yet-unobserved states, such as the 2++ state at ~3940 MeV and the DsD̄s decay channel of Y(4260).

Proposed method

• Construct a Hamiltonian based on constituent quark model with spin-spin interactions, using diquark masses derived from known meson and baryon masses.
• Diagonalize the Hamiltonian in a basis of definite diquark and antidiquark spin quantum numbers to obtain eigenstates with definite JPC quantum numbers.
• Use the spin-spin coupling coefficients (κij) from one-gluon exchange and baryon mass splittings to estimate interactions between heavy and light quarks.
• Model the [cq][c̄q̄′] system with both hidden charm (q′=u,d) and open charm with strangeness (q′=s), allowing for different JPC states.
• Include isospin breaking via mixing between |cu⟩ and |cd⟩ states, parameterized by a mixing angle θ derived from experimental decay rate ratios.
• Predict orbital excitations by introducing relative orbital angular momentum (L=1) in the [cs][c̄s̄] system, consistent with the Y(4260) observation.

Experimental results

Research questions

• RQ1 Can the X(3872) resonance be explained as a 1++ diquark-antidiquark tetraquark state with suppressed D-D̄ decay due to unnatural parity?
• RQ2 What is the role of isospin breaking in the mixing of ud and cd diquark components in the X(3872), and how does it affect its decay branching ratios?
• RQ3 Can the Y(4260) resonance be interpreted as a 1-- orbital excitation of a [cs][c̄s̄] diquark-antidiquark state with L=1?
• RQ4 What are the predicted masses and decay modes of other unobserved diquark-antidiquark states with hidden or open charm?
• RQ5 How do the spin and flavor structure of diquarks lead to a spectrum of JPC states that matches experimental observations?

Key findings

• The 1++ state in the [cq][c̄q̄′] system is identified as the X(3872), with a predicted mass consistent with experiment and a narrow width due to suppression of D-D̄ decay.
• The X(3872) is predicted to decay into both J/ψρ and J/ψω final states due to isospin breaking, with a mixing angle θ ≈ 20° derived from Belle's measured decay rate ratio.
• The 2++ state in the [cq][c̄q̄′] system is predicted at 3940 MeV, consistent with the X(3940) state observed by Belle in the J/ψω channel.
• The Y(4260) resonance is interpreted as a 1-- orbital excitation of a [cs][c̄s̄] state with L=1, predicted to have a mass of 4330±70 MeV, in good agreement with the experimental value.
• The model predicts that Y(4260) should decay into DsD̄s, a channel that remains to be observed experimentally.
• The Ds(2317) and Ds(2457) resonances are identified as the 0+ and 1+ states in the [cs][c̄q̄′] sector, respectively, with decay modes matching experimental observations.