Coupled-channel Omnès matrix for the D-wave isoscalar π π / K K ¯ system and its application to J/ψ → π0π0γ, KKγ

In this work, we construct the D -wave isoscalar π π / K K ¯ coupled-channel Omnès matrix, formulated to satisfy unitarity, analyticity, and the appropriate asymptotic behavior. We employ a two-channel K -matrix model containing poles associated with the f 2 (1270) and f 2 ′ ( 1525 ) resonances. The resulting unitary scattering matrix, which reproduces the experimental ππ → ππ and π π → K K ¯ data and PDG information, serves as input to the homogeneous two-channel Muskhelishvili-Omnès equation.