Producing Fully-Charmed Tetraquarks via Charm Quark Fragmentation in Colliders

Within the framework of nonrelativistic QCD (NRQCD), we calculate the fragmentation function for a charm quark into an $S$-wave fully-charmed tetraquark, denoted as $T_{4c}$. The charm-to-$T_{4c}$ fragmentation function is expressed as a sum of products of the perturbatively calculable short-distance coefficients and the nonperturbative long-distance matrix elements (LDMEs). The short-distance coefficients are ascertained through the perturbative matching procedure at lowest order in $\alpha_{s}$ expansion. The LDMEs are approximated using the $T_{4c}$ four-body wave functions at the origin, which have been evaluated by various phenomenological potential models in literature. Incorporating the celebrated QCD factorization and the charm-to-$T_{4c}$ fragmentation function, we predict the $T_{4c}$ production rate at high transverse momentum $p_T$ regime in colliders. %After implementing appropriate kinematic constraints, Both the differential distribution over $p_T$ and the integrated cross sections are predicted at the \texttt{LHC}. The cross sections for $T_{4c}$ states production can reach several femtobarns to several hundreds femtobarns, suggesting a substantial potential for $T_{4c}$ event production at the \texttt{LHC}. Additionally, we estimate for the photoproduction of $T_{4c}$ in electron-proton ($ep$) collisions. It is observed that the cross sections for these processes are moderate at the \texttt{HERA} and \texttt{EIC}, and relatively small at the \texttt{EicC}. Given the luminosities of these colliders, the prospect of detecting these fully-charmed tetraquarks at $ep$ colliders is somewhat challenging.