Exclusive Decays of the Fully Heavy Tetraquarks into Light Mesons

TL;DR

The paper addresses exclusive decays of fully heavy tetraquarks $T_{4c}$ and $T_{4b}$ into light mesons within a two-scale framework that combines NRQCD factorization for the heavy sector with collinear factorization for the light final states. The authors derive a master amplitude formula, perform perturbative matching to obtain explicit LO hard kernels $T^{(J)}_{\bar{3}\otimes3}$, $T^{(J)}_{6\otimes\bar{6}}$, and incorporate a pion LCDA $\Phi_π(x,μ_F)$ expanded in Gegenbauer moments $a_n(μ_F)$ that evolve via ERBL, enabling convolutions with LDME to predict decay widths. They tackle the technical challenge of $i\varepsilon$-prescriptions in the denominators by employing sector decomposition aided by the Cheng-Wu theorem, and present numerical results showing $\Gamma(T_{4c}\to\pi^+\pi^-/K^+K^-) \sim 10^{-9}$ GeV and $\Gamma(T_{4b}\to\pi^+\pi^-/K^+K^-) \sim 10^{-14}$ GeV, corresponding to branching ratios of order $10^{-8}$ for $T_{4c}$, thereby confirming these decays are currently unobservable. The results are sensitive to the nonperturbative LDME inputs and the factorization scale, and the work lays a path to extend the method to other channels such as $T_{4c,b}\to p\bar p$ and to broader phase-space integrals. Overall, the paper provides a concrete factorization-based framework for predicting exclusive fully heavy tetraquark decays and introduces practical numerical techniques for challenging multi-variable integrals.

Abstract

In this work, we investigate the exclusive decays of the fully heavy tetraquark states $T_{4c,b}$ into light mesons, specifically $π$ and $K$, using the framework of Non-Relativistic QCD (NRQCD) and collinear QCD factorization for hard exclusive processes. We estimate the decay widths to be $10^{-9}$ GeV and $10^{-14}$ GeV for the decays $T_{4c} \to π^+π^-$ and $T_{4b} \to π^+π^-$ (and similarly for $K^+K^-$), respectively. The branching ratio for $T_{4c} \to π^+π^-(K^+K^-)$ is on the order of $10^{-8}$, making it currently unobservable in existing experiments. The factorization of $T_{4c,b}$ into light hadrons shares similarities with the decay $J/ψ\to p\bar{p}$. However, unlike the latter process, the decay $T_{4c,b} \to π^+π^-(K^+K^-)$ exhibits unique features that arise only in processes involving multiple incoming or outgoing particles. One such feature is the necessity of maintaining the $i\varepsilon$-prescription for the denominators or propagators due to the divergences in the kinematic region of interest. Employing the sector decomposition method, along with the aid of the Cheng-Wu theorem and the {\tt QHull} program, we present a systematic approach to handle the convolutions and phase-space integrations. This method can also be extended to similar processes, such as $T_{4c,b} \to p\bar{p}$, as well as to phase-space integrations where each denominator is a linear combination of integration variables.

Figures (3)

• Figure 1: A typical Feynman diagram for $T_{4c} \to {\pi^+\pi^-}$.
• Figure 2: Decay widths for $T_{4c} \to \pi^+\pi^-$ and $T_{4c} \to K^+K^-$ as a function of the renormalization/factorization scale $\mu$. The input LDMEs for $T_{4c}$ are taken from Model ILu:2020cns and Model IIliu:2020eha, while the input non-perturbative parameters $a_n(\mu_F)$ for $\pi$ and $K$ are taken from the RQCDRQCD:2019osh and LPCLatticeParton:2022zqc Collaborations.
• Figure 3: Visualization for the triangularization.