Fully charm tetraquark production at hadronic collisions with gluon radiation effects

We report the first complete next-to-leading order QCD calculation for processes involving fully charm tetraquark states, revealing that the renormalization constant of the color-singlet four charm quark operator is exactly unity at this order. We have investigated the possible quark configurations of the fully charm tetraquarks and expanded their states in the color symmetry-antisymmetry basis. By applying the transverse momentum dependent factorization formalism, large logarithms induced by soft and collinear gluon radiations are resummed to all orders in the expansion of the strong interaction coupling at the accuracy of next-to-leading logarithm. By combining LHCb data on the total cross section of the exotic hadron $X(6900)$ and CMS measurements of its spin-parity, we extracted its nonperturbative but universal long-distance matrix element. The rapidity and transverse momentum distributions of the $X(6900)$ and its spin-zero partners are also predicted, which await further experimental verification.