Abstract
In light of recent experimental results, we revisit the dispersive analysis of the omega rightarrow 3pi decay amplitude and of the omega pi ^0 transition form factor. Within the framework of the Khuri–Treiman equations, we show that the omega rightarrow 3pi Dalitz-plot parameters obtained with a once-subtracted amplitude are in agreement with the latest experimental determination by BESIII. Furthermore, we show that at low energies the omega pi ^0 transition form factor obtained from our determination of the omega rightarrow 3pi amplitude is consistent with the data from MAMI and NA60 experiments.
Highlights
Because of Bose symmetry only odd angular momentum is allowed in each of the π π channels, and the final state is dominated by the J = I = 1 isobars, i.e. the ρ meson
The analysis presented in this paper could be relevant to understand the hadronic contributions to the anomalous magnetic moment of the muon
In the calculation of the helicity partial wave amplitudes for γ ∗γ ∗ → π π [52,53,54], which are responsible for the twopion contribution to hadronic lightby-light (HLbL), the most important left-hand cut beyond the pion pole is almost exclusively attributed to the ω exchange
Summary
We start by introducing the kinematical definitions for the ω( pV ) → π 0( p0) π +( p+) π −( p−) process. Defined by the real phase shift δ(s) For the latter we take the solution of the Roy equations of Ref. Due to the three-particle cut, which become physically accessible in the decay amplitude, this subtraction constant is complex and is determined by two parameters, its modulus and phase, b = |b| eiφb. (2.22a) where b is not constrained to satisfy Eq (2.19), and the functions Fa(s) and Fb(s) are given by These functions only need to be calculated once, since they are independent of the numerical values of a and b, which become fit parameters, as will be discussed in Sect. By introducing one subtraction we reduce the sensitivity to the unknown high energy behavior of the phase shift and/or to the inelastic contributions, which are embedded in the subtraction constant. In order to obtain α, β, and γ for a given theoretical amplitude Fth(z, φ) we minimize [21]
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