Determination of the quadratic slope parameter in eta -\u3e 3 pi(0) decay

We have determined the quadratic slope parameter α for η→3π0 to be α = -0.031(4) from a 99% pure sample of 106η→3π0 decays produced in the reaction π-p→nη close to the η threshold using the Crystal Ball detector at the AGS. The result is four times more precise than the present world data and disagrees with current chiral perturbation theory calculations by about four standard deviations

Determination of the quadratic slope parameter in eta -\u3e 3 pi(0) decay

We have determined the quadratic slope parameter α for η→3π0 to be α = -0.031(4) from a 99% pure sample of 106η→3π0 decays produced in the reaction π-p→nη close to the η threshold using the Crystal Ball detector at the AGS. The result is four times more precise than the present world data and disagrees with current chiral perturbation theory calculations by about four standard deviations

Extended chiral Khuri–Treiman formalism for

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