Lattice calculation of the and s-wave scattering length

Yu Meng; Chuan Liu; Xin-Yu Tuo; Haobo Yan; Zhaolong Zhang

doi:10.1140/epjc/s10052-025-14192-z

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 458
https://doi.org/10.1140/epjc/s10052-025-14192-z

Regular Article - Theoretical Physics

Lattice calculation of the $η_{c} η_{c}$ $\eta _c\eta _c$ and $J / ψ J / ψ$ $J/\psi J/\psi$ s-wave scattering length

Yu Meng¹^a, Chuan Liu²^,3^,4^b, Xin-Yu Tuo⁵, Haobo Yan² and Zhaolong Zhang²

¹ School of Physics, Zhengzhou University, 450001, Zhengzhou, China
² School of Physics, Peking University, 100871, Beijing, China
³ Center for High Energy Physics, Peking University, 100871, Beijing, China
⁴ Collaborative Innovation Center of Quantum Matter, 100871, Beijing, China
⁵ Physics Department, Brookhaven National Laboratory, 11973, Upton, NY, USA

^a yu_meng@zzu.edu.cn
^b liuchuan@pku.edu.cn

Received: 12 December 2024
Accepted: 14 April 2025
Published online: 25 April 2025

Abstract

We calculate the s-wave scattering length in the $0^{+}$ $$0^+$$ sector of $η_{c} η_{c}$ $\eta _c\eta _c$ and the $2^{+}$ $$2^+$$ sector of $J / ψ J / ψ$ $J/\psi J/\psi$ using three $N_{f} = 2$ $$N_f=2$$ twisted mass gauge ensembles with the pion mass $300 - 365$ $$300{-}365$$ MeV and lattice spacing $a = 0.0667, 0.085, 0.098$ $$a=0.0667,0.085,0.098$$ fm, respectively. The scattering lengths are extracted using the conventional Lüscher finite size method. We observe sizable discretization effects and the results after a continuum extrapolation are $a_{η_{c} η_{c}}^{0^{+}} = - 0.104 (09)$ $a^{0^+}_{\eta _c\eta _c}=-0.104(09)$ fm and $a_{J / ψ J / ψ}^{2^{+}} = - 0.165 (16)$ $a^{2^+}_{J/\psi J/\psi }=-0.165(16)$ fm. The slight difference of light quark mass is ignored in this study. Our results indicate that the interaction between the two respective charmonia are repulsive in nature in both cases.

© The Author(s) 2025

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