Decoding spin-parity quantum numbers and decay widths of double $J/ψ$ exotic states

TL;DR

This work addresses how to determine the spin-parity and decay widths of fully charmed tetraquark states decaying to double $J/ obreak{/ obreak}psi$ by computing helicity amplitudes in two complementary frameworks: a quark-model potential approach and a heavy-diquark EFT approach. It develops the full angular-distribution formalism for cascade decays, enabling extraction of helicity amplitudes from angular observables via the Jacob-Wick construction, and investigates quantum entanglement (concurrence) of the final $J/ obreak{/ obreak}psi$ pairs as a diagnostic of the underlying structure. The results favor a $J^{PC}=2^{++}$ assignment for the observed structures, while spin-0 decays exhibit higher entanglement, constraining the allowed helicity amplitudes. The study provides explicit angular-distribution templates and entanglement-based bounds to guide experimental fits and future searches for fully charmed tetraquark states, with open-charm and $ ext{two-photon}$ channels highlighted as complementary probes.

Abstract

We derive helicity amplitudes for the fully charmed tetraquark states decays into vector meson pair under two types of models, where the one is from quark model and the other one is from diquark model. The decay angular distributions have been given by the cascade decays $T_{4c}\to J/ψ(D_{(s)}^*)+J/ψ(\bar{D}_{(s)}^*)$ along with $J/ψ\to μ^++μ^-$ or $D_{(s)}^*\to D_{(s)}+π$, showing that spin-0 and spin-2 states can be distinguished. We also find that the spin-0 state decay to $J/ψ$-pair exhibits a higher degree of quantum entanglement than that in spin-2 state decays. These findings will assist in experimentally differentiating various spin-parity states, determining decay widths and unveiling undiscovered hadronic states within existing structures, thereby shedding light on the internal properties of double $J/ψ$ exotic states.

Figures (11)

• Figure 1: Typical Feynman diagrams for fully charmed tetraquark decays.
• Figure 2: The illustration of helicity angles in fully charmed tetraquark decays into double $J/\psi$.
• Figure 3: The Comparison of $\theta_1$ distributions for various tetraquarks into double $J/\psi(\to \mu^++\mu^-)$ within different models between the experiment and the theory. The experimental data with error bars are taken from the CMS measurement CMS:2025fpt.
• Figure 4: The Comparison of $\Phi$ distributions for various tetraquarks into double $J/\psi(\to \mu^++\mu^-)$ within different models between the experiment and the theory. The experimental data with error bars are taken from the CMS measurement CMS:2025fpt.
• Figure 5: The concurrence of fully charmed tetraquark into double $J/\psi$ under two different theoretical models.