Search for c (2S) and decays and measurements of ₂₉ and in (2S) radiative processes

Using (2712 14) 10^6 (2S) events collected with the BESIII detector at the BEPCII collider, we search for the decays ₂ (2S) and ₂ (2S) via the process (2S) ₂ (2S). Evidence of ₂ (2S) is found with a statistical significance of 3. 2. The branching fraction is measured to be B (₂ (2S) ) = (5. 653. 77 (stat. ) 5. 32 (syst. ) ) 10^-4. No statistically significant signal is observed for the decay ₂ (2S). The upper limit of the branching fraction at the 90\% confidence level is determined to be B ( (2S) ₂ (2S), ₂ (2S) ) <2. 24 10^-7. We also update the branching fractions of ₂₉ and ₂₉ decays via the (2S) ₂₉ transition. The branching fractions are determined to be B (₂₀) = (10. 630. 110. 46) 10^-4, B (₂₁) = (6. 390. 070. 29) 10^-4, B (₂₂) = (8. 500. 080. 38) 10^-4, B (₂₀) = (1. 180. 030. 05) 10^-4, B (₂₁) = (2. 030. 150. 12) 10^-5, and B (₂₂) = (9. 371. 070. 59) 10^-6, where the first uncertainties are statistical and the second are systematic.