Probing Heavy-Quark Spin Symmetry in Double $J/ψ$ Hadroproduction

We perform the first complete $\mathcal{O}(\alpha_s^5)$ analysis of the prompt hadroproduction of $J/\psi$ pairs with large transverse momenta $p_T^{\psi\psi}$ in the nonrelativistic-QCD factorization framework, including all possible Fock state combinations $c\bar{c}(m)+c\bar{c}(n)$, with $m,n={}^3S_1^{[1,8]},{}^1S_0^{[8]},{}^3P_J^{[1,8]}$. We observe that CMS and ATLAS data constrain a specific linear combination of the long-distance matrix elements (LDMEs) $\langle\mathcal{O}^{J/\psi}({}^1S_0^{[8]})\rangle$ and $\langle\mathcal{O}^{J/\psi}({}^3P_0^{[8]})\rangle$. In conjunction with two other combinations fixed by single prompt $J/\psi$ hadroproduction, we gain a new LDME set, which turns out to be largely compatible with the world data of prompt $J/\psi$ yield and polarization and to probe heavy-quark spin symmetry, by which agreement is established with LHCb data of prompt $\eta_c$ yield. Our $\mathcal{O}(\alpha_s^5)$ predictions also nicely agree with CMS and ATLAS data in the lowest bins of $J/\psi$ pair invariant mass $m^{\psi\psi}$, beyond leading-order kinematics.