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 T4c. The charm-to-T4c fragmentation function can be expressed as a sum of products of the perturbatively calculable short-distance coefficients and the nonperturbative long-distance matrix elements. The short-distance coefficients are ascertained through the perturbative matching procedure at lowest order in αₛ and v expansion. Incorporating the celebrated QCD factorization and the charm-to-T4c fragmentation function, we are able to predict the T4c production rate at high transverse momentum pT in colliders. In phenomenology, we approximate the NRQCD matrix elements with phenomenological four-body wave functions at the origin. After applying appropriate kinematic constraints, both the differential distribution over pT and the integrated cross sections are predicted at the LHC. The cross section can reach approximately $100$ fb, indicating the potential for a significant number of T4c events to be produced at the LHC. Additionally, we provide predictions for the photoproduction of T4c in electron-proton ($ep$) collisions. However, it is observed that the cross sections for these processes are relatively small at the HERA, EIC as well as EicC. Given these findings, the prospect of detecting these fully heavy tetraquarks at $ep$ colliders appears to be rather challenging.