[Paper Review] Possibility of Narrow High-Mass Exotic States

Marek Karliner, Harry J. Lipkin|ArXiv.org|Oct 22, 2007

Quantum Chromodynamics and Particle Interactions2 references3 citations

TL;DR

This paper proposes that narrow high-mass exotic states can emerge in tetraquark systems like $Q\bar{Q}q\bar{q}$ due to destructive interference from final-state interactions via loop diagrams, even when phase space is large. The mechanism arises from mixing between two nearly degenerate color-singlet diquark-antidiquark states ($\bar{\mathbf{3}}\mathbf{3}$ and $\mathbf{6}\bar{\mathbf{6}}$), where one eigenstate decouples from the dominant decay mode (e.g., $J/\psi\pi$), resulting in a narrow width despite large phase space.

ABSTRACT

Narrow high-mass states can arise despite large phase space when two nearly degenerate states are coupled to the same dominant decay mode. Mixing via a final-state interaction loop diagram can produce one very broad state and one narrow state. Such a situation is generic in exotic hadrons where a color singlet with given flavor and spin quantum numbers can be constructed with two distinct internal color couplings of quarks. The simplest realization of this idea are the (Q Qbar q qbar) tetraquarks containing two heavy and two light quarks. We discuss possible experimental implications, including recent data from Belle.

Motivation & Objective

• To explain the existence of narrow high-mass exotic states in hadron spectroscopy despite large phase space for decay.
• To address the puzzle of why some $Q\bar{Q}q\bar{q}$ tetraquarks do not decay broadly into $J/\psi\pi$ or $\Upsilon\pi$ modes.
• To demonstrate that mixing between two nearly degenerate color-singlet diquark-antidiquark configurations can suppress decay amplitudes via final-state interaction loops.
• To provide a mechanism for width suppression in exotic hadrons, relevant to observed narrow resonances like the Belle $\psi'\pi^+$ state.

Proposed method

• Uses a two-state mixing model for tetraquark states with nearly degenerate $\bar{\mathbf{3}}\mathbf{3}$ and $\mathbf{6}\bar{\mathbf{6}}$ color couplings.
• Applies perturbation theory to a loop diagram where the intermediate state $[\bar{Q}Q]_1[X]_1$ (e.g., $J/\psi\pi$) mediates mixing between the two tetraquark eigenstates.
• Derives the width suppression condition via destructive interference, with the suppression factor $\epsilon^2 \sim (\delta m / \Gamma)^2$.
• Calculates the mass ratio $\mathcal{R} = M(\bar{\mathbf{3}}\mathbf{3}) / M(\mathbf{6}\bar{\mathbf{6}})$ in a harmonic oscillator model, showing $\mathcal{R} \approx 1.09$ for $c$-quarks and $1.17$ for $b$-quarks.
• Uses the wave function mixing angle $\theta$ to express the physical eigenstates $|[Tet]_S\rangle$ and $|[Tet]_L\rangle$ as superpositions of the color basis states.
• Evaluates decay matrix elements $\alpha = \langle[\bar{Q}Q]_1[X]_1|T|\bar{\mathbf{3}}\mathbf{3}\rangle$ and $\beta = \langle[\bar{Q}Q]_1[X]_1|T|\mathbf{6}\bar{\mathbf{6}}\rangle$ to determine the degree of destructive interference.

Experimental results

Research questions

• RQ1 Can a narrow resonance emerge in a high-mass exotic state even when phase space allows large decay widths?
• RQ2 What mechanism could suppress the dominant decay mode $J/\psi\pi$ in a $Q\bar{Q}q\bar{q}$ tetraquark?
• RQ3 How does mixing between two nearly degenerate color-singlet diquark-antidiquark configurations lead to width suppression?
• RQ4 Is the Belle $\psi'\pi^+$ resonance a candidate for this mixing-induced width suppression mechanism?
• RQ5 Can accidental cancellation in decay amplitudes from different color configurations suppress charmed or bottom pair production?

Key findings

• The mixing mechanism leads to one eigenstate ($|[Tet]_S\rangle$) with a suppressed decay amplitude to $[\bar{Q}Q]_1[X]_1$, resulting in a narrow width due to destructive interference.
• The suppression factor is $\epsilon^2 \sim (\delta m / \Gamma)^2$, where $\delta m$ is the mass splitting and $\Gamma$ is the decay width of the intermediate state.
• For $c$-quark tetraquarks, the mass ratio $\mathcal{R} \approx 1.09$, and for $b$-quarks, $\mathcal{R} \approx 1.17$, indicating sufficient degeneracy for mixing.
• The $\bar{\mathbf{3}}\mathbf{3}$ and $\mathbf{6}\bar{\mathbf{6}}$ states are superpositions of the physical eigenstates with mixing angle $\theta$ determined by the mass matrix diagonalization.
• The Belle $\psi'\pi^+$ resonance may be explained by this mechanism, though additional data on spin, parity, and branching ratios are needed for confirmation.
• Accidental cancellation in decay amplitudes from $\bar{\mathbf{3}}\mathbf{3}$ and $\mathbf{6}\bar{\mathbf{6}}$ states can also suppress $c\bar{c}$ or $b\bar{b}$ pair production.