Fully charm tetraquark production at hadronic collisions with gluon radiation effects

Abstract

We have performed, for the first time, a 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. By resumming over various gluon radiation effects, we have improved the precision of their hadroproduction cross-section to the order of ${\cal O}(α_s^5)$. Through symmetry analysis, we investigated the possible quark configurations of the fully charm tetraquark and expanded its states in the color symmetry-antisymmetry basis. By combining LHCb data on the total cross section of the exotic hadron X(6900) and CMS measurements of its spin-parity, we extracted the non-perturbative but universal long-distance matrix elements. The rapidity and transverse momentum distributions are also predicted, which await further experimental verification.

Figures (5)

• Figure 1: Typical Feynman diagrams for the gluon-gluon fusion to fully charm tetraquark up to NLO. The thick black lines stand for the massive charm quarks. The Feynman diagrams from the quark-antiquark annihilation or (anti)quark-gluon scattering can be plotted similarly.
• Figure 2: NLO cross-section results for the fully charm tetraquark dependence on the hadron-hadron center-of-mass energy $\sqrt{S}$. $X(6900)$ is assumed to be $2^{++}$ and its $0^{++}$ partner is also plotted. The comparison with three choices of renormalization and factorization scales are given.
• Figure 3: NLO differential cross-sections for the fully charm tetraquark with different quark configurations dependence on the rapidity $y$.
• Figure 4: NLO and Resum(NLO after resummation) differential cross-sections for the fully charm tetraquark with different quark configurations dependence on the transverse momentum $P_\perp$.
• Figure 5: Distribution of the polar angle $\theta^{\prime *}$ between the $J/\psi$ and the fully charm tetraquark momenta. The CMS 25 data is from the very recent measurement by the CMS experiment CMS:2025fpt.