Electromagnetic and hadronic decay of fully heavy tetraquark

In this study, we compute the electromagnetic and hadronic decay widths of the S-wave fully heavy tetraquark $T_{4Q}$ ($Q=c$ or $b$) at lowest order in $\alpha_s$ and $v$, in the framework of nonrelativistic QCD. The short-distance coefficients are determined through the standard procedure of matching. The nonperturbative long-distance matrix elements are related to the phenomenological four-body Schr\"odinger wave functions at the origin, whose values are taken from literature. The branching fractions are predicted to be around $10^{-4}$ and $10^{-7}-10^{-6}$ for the $T_{4c}$ hadronic decay and electromagnetic decay, respectively. Combing our results with the $T_{4c}$ production cross sections at the LHC, we also predict the event numbers for various decay channels. With integrated luminosity $\mathcal{L}=100 \,{\rm fb}^{-1}$, it is expected that the event numbers can reach $10^3$ for $T_{4c}\to \gamma\gamma$, and $10^6$ for $T_{4c}\to {\rm LH}$, at the LHC. The detecting prospect is promising. In addition, the decay widths of $T_{4b}$ are estimated based on simple dimensional analysis as well as velocity scaling rule.