Exclusive Decays of the Fully Heavy Tetraquarks into Light Mesons

TL;DR

This paper studies the decay of fully heavy tetraquarks into light mesons using NRQCD and QCD factorization, estimating decay widths and exploring unique features of these processes with advanced computational methods.

Contribution

It introduces a systematic approach employing sector decomposition and related techniques to analyze exclusive heavy tetraquark decays into light mesons, highlighting novel features and computational strategies.

Findings

Decay widths estimated as 10^{-9} GeV and 10^{-14} GeV for specific channels.

Branching ratios around 10^{-8}, currently unobservable.

Methodology applicable to similar decay processes and phase-space integrations.

Abstract

In this work, we investigate the exclusive decays of the fully heavy tetraquark states $T_{4c,b}$ into light mesons, specifically $\pi$ 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 $T_{4c} \to \pi^+\pi^-$ and $T_{4b} \to \pi^+\pi^-$ (and similarly for $K^+K^-$), respectively. The branching ratio for $T_{4c} \to \pi^+\pi^-(K^+K^-)$ 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 $J/\psi \to p\bar{p}$. However, unlike the latter process, the decay $T_{4c,b} \to \pi^+\pi^-(K^+K^-)$ 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.