Search for ηc (2S) →ωω and ωφ and measurements of χcJ →ωω and ωφ in ψ (2S) radiative processes

Using (2712±14)×106 ψ(2S) events collected with the BESIII detector at the BEPCII collider, we search for the decays ηc(2S)→ωω and ηc(2S)→ωφ via the process ψ(2S)→γηc(2S). No statistically significant signals are observed. The upper limits of their product branching fractions at the 90% confidence level are determined to be B(ψ(2S)→γηc(2S),ηc(2S)→ωω)<1.04×10-6 and B(ψ(2S)→γηc(2S),ηc(2S)→ωφ)<1.85×10-7, respectively. We also update the branching fractions of χcJ→ωω and χcJ→ωφ via the ψ(2S)→γχcJ transition. Their branching fractions are determined to be B(χc0→ωω)=(10.66±0.11±0.57)×10-4, B(χc1→ωω)=(6.43±0.07±0.31)×10-4, B(χc2→ωω)=(8.75±0.08±0.42)×10-4, B(χc0→ωφ)=(1.18±0.03±0.07)×10-4, B(χc1→ωφ)=(2.04±0.15±0.11)×10-5, and B(χc2→ωφ)=(9.58±1.07±0.76)×10-6, where the first uncertainties are statistical and the second are systematic.