Measurements of the branching fractions of ₂^0^0^0, ₂^0^0, and ₂^0^0^ and asymmetry parameter of ₂^0^0^0

We present a study of ₂^0^0^0, ₂^0^0, and ₂^0^0^ decays using the Belle and Belle~II data samples, which have integrated luminosities of 980~fb^-1 and 426~fb^-1, respectively. We measure the following relative branching fractions B (₂^0^0^0) / B (₂^0^-^+) = 0. 48 0. 02 (stat) 0. 03 (syst), B (₂^0^0) / B (₂^0^-^+) = 0. 11 0. 01 (stat) 0. 01 (syst), B (₂^0^0^) / B (₂^0^-^+) = 0. 08 0. 02 (stat) 0. 01 (syst) for the first time, where the uncertainties are statistical (stat) and systematic (syst). By multiplying by the branching fraction of the normalization mode, B (₂^0^-^+), we obtain the following absolute branching fraction results (6. 9 0. 3 (stat) 0. 5 (syst) 1. 3 (norm) ) 10^-3, (1. 6 0. 2 (stat) 0. 2 (syst) 0. 3 (norm) ) 10^-3, and (1. 2 0. 3 (stat) 0. 1 (syst) 0. 2 (norm) ) 10^-3, for ₂^0 decays to ^0^0, ^0, and ^0^ final states, respectively. The third errors are from the uncertainty on B (₂^0^-^+). The asymmetry parameter for ₂^0^0^0 is measured to be (₂^0^0^0) = -0. 900. 15 (stat) 0. 23 (syst).