High-statistics measurement of the η→3π0 decay at the Mainz Microtron

Abstract

The largest, at the moment, statistics of 7 × 10 6 η → 3π 0 decays, based on 6.2 × 10 7 η mesons produced in the γp → ηp reaction, has been accumulated by the A2 Collaboration at the Mainz Microtron, MAMI. It allowed a detailed study of the η → 3π 0 dynamics beyond its conventional parametrization with just the quadratic slope parameter α and enabled, for the first time, a measurement of the second-order term and a better understanding of the cusp structure in the neutral decay. The present data are also compared to recent theoretical calculations that predict a nonlinear dependence along the quadratic distance from the Dalitz-plot center. =-0.0318+/-0.0015) α PDG ( FIG. 2: Comparison of the experimental data [9][10][11][24][25][26][27][28][29][30] (plotted by black points), which were used in the RPP [23] to obtain the averaged value (shown by the vertical lines) for the η → 3π 0 quadratic slope parameter α, to each other and to various calculations [2-4, 16, 17, 19, 21, 22, 31] (colored points). Ref. [2] gives the magnitude of α for the analysis made in Ref.[1], in which its value was not given.

Dispersive construction of two-loop P→πππ(P=K,η) amplitudes

“…In the former case, we have already illustrated this in Ref. [36], and we plan to redo a similar analysis using more recent high-statistics data on the Dalitz-plot distribution of η → πππ [15][16][17][18].…”

“…This limit requires, however, to enlarge the definition of the function L(s) to the region 4M 2 π 0 < s < 4M 2 π , namely to set in this region L(s) = log (1 − σ(s)) − log (1 + σ(s)) , (VI. 18) where we assume the principal branch of the logarithm with a cut on the interval (−∞, 0) along the real axis, and log(x) = log(x + i0) for x < 0. Using the above results for the integrals (VI.2), (VI.3) and (VI.12), it is now a straightforward task to calculate the corresponding S−wave projections of the amplitudes M L 00 , M L x at NLO and, with the help of (V.1), to construct the absorptive part of the function W 00 .…”

“…Our experimental knowledge of the Dalitz-plot structures of the amplitudes for the processes P → πππ has substantially improved during the last decades, for P = K ± [1][2][3][4][5][6][7], P = K L [8], or P = η [9][10][11][12][13][14][15][16][17][18]. This situation is likely to improve further still in the future [19,20].…”

“…[36], devoted to the analysis of the decay of the η meson into three pions. We also plan to update the latter analysis, taking more recent data [15,16,18] into account, but this will be left for a separate work [49]. A rather simple extension of this framework, though, allows dealing with isospin breaking in the pion masses in the case of the decay channels into three neutral pions, which we will treat at a second stage in the present article.…”

Coupled-channel approach in hadron–hadron scattering

“…There is an ongoing experimental effort that has allowed to know with great precision the squared of the η → π + π − π 0 decay amplitude across the entire Dalitz plot [221,222,223,224]. The improvement in the experimental determination of the analogous function for η → 3π 0 has also been remarkable [225,226,227,228,229,230]. To accomplish an equally precise theoretical description of the η → 3π decays from first principles is an interesting prospect in low-energy hadron physics, as several crucial aspects of the standard model enter.…”