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Dynamical generation of charmoniumlike tetraquarks in an off-shell coupled-channel formalism

Hee-Jin Kim1 and Hyun-Chul Kim2,1,3

Phys. Rev. D 114, 054053 – Published 28 September, 2026

DOI: https://doi.org/10.1103/3k6p-qxd3

Abstract

We investigate the dynamical generation of isoscalar charmoniumlike states with quantum numbers JPC=0++,1++,2++, and 3−− in the mass range of 3.6 to 4.3 GeV. We employ the off-shell coupled-channel formalism, constructing kernel amplitudes from effective Lagrangians that respect heavy-quark spin-flavor and chiral symmetries. To focus solely on dynamically generated states, we explicitly exclude s-channel pole diagrams and include only t- and u-channel meson exchanges. Solving the integral equations, we identify six poles in the complex energy plane. In the scalar (0++) sector, we find a bound state below the DD¯ threshold and a resonance at sR=(3861−i23)  MeV. For the axial-vector (1++) sector, the experimentally observed χc1(3872) is reproduced as a bound state near the DD¯* threshold, alongside a broader resonance at (3961−i32)  MeV, which is a plausible candidate for the X(3940). Furthermore, we find a narrow tensor (2++) pole at (4005−i6)  MeV and a ψ3-like (3−−) pole at (4030−i33)  MeV. The present results demonstrate that coupled-channel dynamics, particularly involving the D*D¯* channel, play a crucial role in the formation of these charmoniumlike exotic states.

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