Extended chiral Khuri–Treiman formalism for η→ 3 π and the role of the a0(980) , f0(980) resonances

Abstract

Recent experiments on η→ 3 π 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→ 3 π decay is not negligible, in particular for the 3 π0 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.