Fragmentation production of fully-charmed tetraquarks at the LHC

Abstract

The $X(6900)$ resonance, recently discovered in the double-$J/\ensuremath{\psi}$ channel at the LHCb experiment, has spurred intensive interest in unraveling the nature of the fully charmed tetraquark state. The aim of this paper is to present a model-independent framework to study the inclusive production of this novel species of exotic hadrons, the resonances composed of four heavy quark (commonly referred to as ${T}_{4c}$), at large ${p}_{T}$ in hadron colliders. Appealing to asymptotic freedom and the fact ${m}_{c}\ensuremath{\gg}{\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}$, we propose that the universal gluon-to-${T}_{4c}$ fragmentation function, can be decomposed into the product of the perturbatively calculable short-distance coefficients and the long-distance nonrelativistic QCD (NRQCD) matrix elements. We compute the short-distance coefficient at lowest order in ${\ensuremath{\alpha}}_{s}$ and velocity expansion. Adopting the phenomenological four-body wave functions at the origin to roughly estimate those not-yet-known NRQCD matrix elements, and applying the standard QCD factorization theorem, we predict the differential production rates for the ${T}_{4c}$ (${0}^{++}$ and ${2}^{++}$) at large ${p}_{T}$ in $pp$ collision, which eagerly awaits the confrontation with the future LHC experiments.