Extended chiral Khuri–Treiman formalism for

Abstract

Recent experiments on $$\eta \rightarrow 3\pi$$ decays have provided an extremely precise knowledge of the amplitudes across the Dalitz region which represent stringent constraints on theoretical descriptions. We reconsider an approach in which the low-energy chiral expansion is assumed to be optimally convergent in an unphysical region surrounding the Adler zero, and the amplitude in the physical region is uniquely deduced by an analyticity-based extrapolation using the Khuri–Treiman dispersive formalism. We present an extension of the usual formalism which implements the leading inelastic effects from the $$K\bar{K}$$ channel in the final-state $$\pi \pi$$ interaction as well as in the initial-state $$\eta \pi$$ interaction. The constructed amplitude has an enlarged region of validity and accounts in a realistic way for the influence of the two light scalar resonances $$f_0(980)$$ and $$a_0(980)$$ in the dispersive integrals. It is shown that the effect of these resonances in the low-energy region of the $$\eta \rightarrow 3\pi$$ decay is not negligible, in particular for the $$3\pi ^0$$ mode, and improves the description of the energy variation across the Dalitz plot. Some remarks are made on the scale dependence and the value of the double quark mass ratio Q