2023

Ala-Mattinen, Kalle; Heikinheimo, Matti; Tuominen, Kimmo; Kainulainen, Kimmo

We study the origin of the real intermediate state subtraction problem and compare its different solutions. We show that the ambiguity in subtraction schemes arises from the on-shell approximation for the 2-point functions that reduces the Schwinger-Dyson equations to the Boltzmann limit. We also suggest a new subtraction scheme which, unlike the earlier definitions, never leads to negative scattering rates. This scheme also quantifies the validity of the on-shell limit in terms of an effective one-particle weight function 𝑅⁡(Δ), where Δ measures the region around the resonance associated with the real state.