Extended chiral Khuri–Treiman formalism for η → 3 π and the role of the a 0 ( 980 ) , f 0 ( 980 ) resonances

Recent experiments on η→3π 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 KK¯ channel in the final-state ππ interaction as well as in the initial-state ηπ 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 f0(980) and a0(980) in the dispersive integrals. It is shown that the effect of these resonances in the low-energy region of the η→3π decay is not negligible, in particular for the 3π0 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.