The cusp effect in eta' --> eta pi pi decays

Abstract

Strong final-state interactions create a pronounced cusp in η ′ → ηπ 0 π 0 decays. We adapt and generalize the non-relativistic effective field theory framework developed for the extraction of ππ scattering lengths from K → 3π decays to this case. The cusp effect is predicted to have an effect of more than 8% on the decay spectrum below the π + π − threshold.

Rescattering effects in η → 3π decays

“…In this work we will use the modified non-relativistic effective field theory (NREFT) framework to analyze the final-state interactions in η → 3π. This framework provides a useful tool to investigate low-energy scattering and decay processes: it has found applications in detailed studies of cusp effects in K → 3π [29][30][31] and η → 3π [32] as well as η ′ → ηππ [33] decays, and has recently been extended to describe near-threshold pion photo-and electroproduction on the nucleon [34,35] (for an overview on cusp effects in meson decays, see Ref. [36]).…”

Photoproduction of neutral pions

“…Along the lines of previous work which analyzed the cusps in K → 3π and η ′ → ηππ decays [2][3][4], we construct a nonrelativistic theory which provides a rigorous framework to describe the structure of the cusp order by order in a perturbative expansion in terms of small momenta and effective range parameters of pion-nucleon scattering as well as threshold parameters of the photoproduction reaction [5]. By construction, the theory correctly reproduces the low-energy singularities in the Mandelstam plane.…”

Pion photoproduction in a nonrelativistic theory

“…The covariant formulation of nonrelativistic field theories introduced in Refs. [10][11][12] is used here since it incorporates the correct relativistic dispersion law for the particles. The nonrelativistic proton, neutron and pion fields are denoted by ψ, χ and π k , respectively.…”