Rescattering effects in η → 3π decays

Abstract

The isospin-breaking decay η → 3π is an ideal tool to extract information on light quark mass ratios from experiment. For a precise determination, however, a detailed description of the Dalitz plot distribution is necessary. In that respect, in particular the slope parameter α of the neutral decay channel causes some concern, since the one-loop prediction from chiral perturbation theory misses the experimental value substantially. We use the modified non-relativistic effective field-theory, a dedicated framework to analyze final-state interactions beyond one loop including isospin-breaking corrections, to extract charged and neutral Dalitz plot parameters. Matching to chiral perturbation theory at next-to-leading order, we find α = −0.025 ± 0.005, in marginal agreement with experimental findings. We derive a relation between charged and neutral decay parameters that points towards a significant tension between the most recent KLOE measurements of these observables.

Measurement of theη→π+π−π0Dalitz plot distribution

“…The discrepancies are more than five standard deviations for the NNLO parameter a and b values. Also, model independent relations between neutral and charged Dalitz plot parameters show tensions [30].…”

“…and decay K → 3π [28] decays and subsequently was applied to η → 3π decays [29,30]. A more model dependent analysis providing uniform treatment of all three pseudoscalar η and η ′ decay modes, including η → 3π was pursued in Ref.…”

Dispersive analysis ofω/ϕ→3π,πγ*

“…For example, the decay η → 3π [30][31][32][33][34][35], is of interest because it is sensitive to isospin breaking, which in QCD originates from the mass difference between the up and down quarks. Dispersive analysis of ω decay was performed in [36] and more recently in [37].…”

Analysis Tools for Next-Generation Hadron Spectroscopy Experiments

“…For a real decay process, the solution of the integral equations is further complicated by the analytic properties of the amplitude, which require a careful choice of the integration contour in the complex plane. For an application of these methods to η, ω, φ → 3π decays see [126][127][128][129][130].…”