Coupled-channel interpretation of the LHCb double-$J/\psi$ spectrum and hints of a new state near the $J/\psi J/\psi$ threshold

TL;DR

This paper analyzes LHCb double-$J/psi$ spectrum data using coupled-channel models, suggesting the possible existence of a new near-threshold state $X(6200)$ with specific quantum numbers, and proposes experimental tests for its confirmation.

Contribution

It introduces two coupled-channel approaches to interpret the $J/psi$-pair spectrum and predicts a new near-threshold state, providing a framework for future experimental validation.

Findings

Data can be described by coupled-channel models with or without energy dependence.

Hints of a new near-threshold state $X(6200)$ with specific quantum numbers.

Potential existence of other double-quarkonium molecules like $ ext{ } ext{ }$.

Abstract

Recently, the LHCb Collaboration reported pronounced structures in the invariant mass spectrum of $J/\psi$-pairs produced in proton-proton collisions at the Large Hadron Collider. In this Letter, we argue that the data can be very well described within two variants of a coupled-channel approach employing $T$-matrices consistent with unitarity: (i) with just two channels, $J/\psi J/\psi$ and $\psi(2S)J/\psi$, as long as energy-dependent interactions in these channels are allowed, or (ii) with three channels $J/\psi J/\psi$, $\psi(2S)J/\psi$ and $\psi(3770)J/\psi$ with just constant contact interactions. Both formulations hint at the existence of a near-threshold state in the $J/\psi J/\psi$ system with the quantum numbers $J^{PC}=0^{++}$ or $2^{++}$, which we refer to as $X(6200)$. We suggest experimental tests to check the existence of this state and discuss what additional channels need to be studied experimentally to allow for distinctive tests between the two mechanisms proposed. If the molecular nature of the $X(6200)$, as hinted by the three-channel approach, is confirmed, many other double-quarkonium states should exist driven by the same binding mechanism. In particular, there should be an $\eta_c\eta_c$ molecule with a similar binding energy.