Spin and Orbital Structure of ff̄ in Scalar and Pseudoscalar Decays

We construct the coordinate-space wave function of a fermion–antifermion pair produced in two-body decays of a spin-zero parent. Starting from the S-matrix amplitude we derive a momentum-space wave function and its Fourier transform. For a scalar ( 0⁺ ) coupling we obtain a pure $$L = 1$$ partial wave whose spin factors select definite orbital projections m for specific spin orientations of f and f̄ . For a pseudoscalar ( 0⁻ ) coupling the result is a pure $$L = 0$$ wave with the usual singlet spin structure. We show explicitly why the back-to-back momenta of the final particles do not contradict nonzero orbital angular momentum: L is a property of the relative coordinate. We also discuss why OAM phases are generally invisible in standard HEP measurements that project onto momentum eigenstates, and point to spin-resolved angular correlations as the observable remnants.