Pion-pion scattering and the K→3π decay amplitudes

Abstract

We revisit the recently proposed method for the determination of the ππ scattering length combination a 0 − a 2 , based on the study of the π 0 π 0 spectrum in K + → π + π 0 π 0 . In view of a precision measurement, we discuss here the effects due to smaller absorptive contributions to the K + → π + π 0 π 0 and K + → π + π + π − amplitudes. We outline a method of analysis that can lead to a precision determination of a 0 − a 2 and is based on very general properties of the S matrix. The discussion of final-state rescattering and cusp effects is also extended to the two K L → 3π coupled channels. Thanks to the present work, the theoretical error on the a 0 − a 2 combination extracted from the K + → π + π 0 π 0 spectrum is reduced to about 5%. A further reduction requires the evaluation of the effects arising from radiative corrections.

Measurement of the η→3π0 Dalitz plot distribution with the WASA detector at COSY

“…A similar effect was observed in the K L → 3π 0 decay [25] and it should be present also in the η → 3π 0 and η ′ → π 0 π 0 η decays. There are important consequences of this phenomenon for the analysis of the η → 3π 0 decay [26,27,28,17,29]. The amplitude is no longer a function only of the z variable but has to explicitly depend on the Mandelstam variables.…”

Results from NA48/2 on pi-pi scattering lengths measurements in K+- to pi+ pi- e+- v and K+- to pi0 pi0 pi+- decays

“…The observed cusp in the M 2 00 distribution (Figure 4 right) was interpreted as strong rescattering from the K ± → π + π − π ± decay and has been evaluated at one-and two-loop orders [7,8,18]. At one loop, the M 0 unperturbed amplitude is to be supplemented by the rescattering amplitude M 1 , imaginary above threshold.…”

“…S-wave ππ scattering lengths are then extracted with an improved precision using recent theoretical work [6] including isospin symmetry breaking effects. The slopes of the K 3π Dalitz Plot are extracted together with the S-wave ππ scattering lengths and rely also on refined theoretical calculations [7,8]. Both results are compared to previous K e4 measurements, to values obtained from a pionium life time experiment [9] and to the precise predictions from Chiral Perturbation Theory.…”

Isospin violation, light quark masses, and all that

“…Refs. [23,24]) since it allows for a precise extraction of the pion-pion scattering lengths [25][26][27]. The cusp effect is driven by the rescattering from two neutral pions through an intermediate charged pion pair and should thus also be visible in other processes like η → 3π 0 (as discussed before) or η → ηπ 0 π 0 .…”