Search for Η_c (2s) →ωω and Ωφ and Measurements of Χ_cj → Ωω and Ωφ in Ψ(2s) Radiative Processes

Using (2712 +/- 14) x 10(6) psi(2S) events collected with the BESIII detector at the BEPCII collider, we search for the decays eta(c) (2S) -> omega omega and eta(c) (2S) -> omega phi via the process psi(2S) -> gamma eta(c)(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(psi(2S) -> gamma eta(c)(2S), eta(c) (2S) -> omega omega) < 1.04 x 10(-6) and B(psi(2S) -> gamma eta(c)(2S),eta(c) (2S) -> omega phi) < 1.85 x 10(-7), respectively. We also update the branching fractions of chi(cJ) -> omega omega and chi(cJ) -> omega phi via the psi(2S) ->gamma chi(cJ) transition. Their branching fractions are determined to be B(chi(co) -> omega omega) = (10.66 +/- 0.11 +/- 0.57)x10(-4), B(chi(c1) -> omega omega) = (6.43 +/- 0.07 +/- 0.31)x10(-4), B(chi(c2) -> omega omega) = (8.75 +/- 0.08 +/- 0.42)x10(-4), B(chi(c0) -> omega phi) = (1.18 +/- 0.03 +/- 0.07) x 10(-4), B(chi(c1) -> omega phi) = (2.04 +/- 0.15 +/- 0.11) x 10(-5), and B(chi(c2) -> omega phi) = (9.58 +/- 1.07 +/- 0.76) x 10(-6), where the first uncertainties are statistical and the second are systematic.