Search for new decay modes of the ψ₂(3823) and the process e⁺e⁻ → π⁰π⁰ψ₂(3823)

The decays ψ2(3823)→γχc0,1,2, π+π−J/ψ, π0π0J/ψ, ηJ/ψ, and π0J/ψ are searched for using the reaction e+e−→π+π−ψ2(3823) in a 19  fb−1 data sample collected at center-of-mass energies between 4.1 and 4.7 GeV with the BESIII detector. The process ψ2(3823)→γχc1 is observed in a 9  fb−1 data sample in the center-of-mass energy range 4.3–4.7 GeV, which confirms a previous observation but with a higher significance of 11.8σ, and evidence for ψ2(3823)→γχc2 is found with a significance of 3.2σ for the first time. The branching-fraction ratio B(ψ2(3823)→γχc2)B(ψ2(3823)→γχc1) is determined. No significant ψ2(3823) signals are observed for any of the other decay channels. Upper limits of branching-fraction ratios for ψ2(3823)→π+π−J/ψ, π0π0J/ψ, ηJ/ψ, π0J/ψ, γχc0 relative to ψ2(3823)→γχc1 are reported. The process e+e−→π0π0ψ2(3823) is also searched for, and we find evidence for the process with a significance of 4.3σ. The average cross-section ratio σ(e+e−→π0π0ψ2(3823))σ(e+e−→π+π−ψ2(3823)) is also determined.