Producing fully-charmed tetraquarks via charm quark fragmentation in colliders

Abstract

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 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 αs expansion. The LDMEs are approximated using the T4c 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-T4c fragmentation function, we predict the T4c production rate at high transverse momentum pT regime in colliders. Both the differential distribution over pT and the integrated cross sections are predicted at the LHC. The cross sections for T4c states production can reach several femtobarns to several hundreds femtobarns, suggesting a substantial potential for T4c event production at the LHC. Additionally, we estimate for the photoproduction of T4c in electron-proton (ep) collisions. It is observed that the cross sections for these processes are moderate at the HERA and EIC, and relatively small at the EicC. Given the luminosities of these colliders, the prospect of detecting these fully-charmed tetraquarks at ep colliders is somewhat challenging.