Theoretical analysis of the doubly radiative decays η(′)→π0γγ and

R. Escribano

¹

,

Sergi Gonzàlez-Solís

²

,

Renata Jora

³

et al.

Abstract

The scalar and vector meson exchange contributions to the doubly radiative decays η ð0Þ → π 0 γγ and η 0 → ηγγ are analyzed within the linear sigma model and vector meson dominance frameworks, respectively. Predictions for the diphoton invariant mass spectra and the associated integrated branching ratios are given and compared with current available experimental data. While a satisfactory description of the shape of the η → π 0 γγ and η 0 → π 0 γγ decay spectra is obtained, thus supporting the validity of the approach, the corresponding branching ratios cannot be reproduced simultaneously. A first theoretical prediction for the recently measured η 0 → ηγγ by the BESIII Collaboration is also presented.

Light meson decays at BESIII

“…was found to be 1.33 × 10 −4 . This result seems in tension with theoretical prediction [12], but more data are needed in order to draw a final conclusion. Dalitz plot analysis of ω → π + π − π 0 provides further constraints to the calculation of electromagnetic transition form factor of ω → π 0 γ * , it is useful to test prediction from dispersive theory [15], and to estimate the so-called crossed-channel effect [16].…”

“…Within the framework of the linear σ model and VDM model, the branching fractions of η → γγπ 0 and η → γγη are predicted to be 3.8×10 −3 and 2.0×10 −4 [12], respectively. Using 1.31×10 9 J/ψ , BESIII determined for the first time the branching fraction B(η → γγπ 0 ) = (32.0 ± 0.7 ± 2.3) × 10 −4 [13] and extracted the non resonant branching fraction (6.16 ± 0.64 ± 0.67) × 10 −4 , which confirmed the theoretical prediction and indicated that this decay was dominated by the VDM processes (ω and ρ contributions dominate).…”

A theoretical analysis of the semileptonic decays $$\eta ^{(\prime )}\rightarrow \pi ^0l^+l^-$$ and $$\eta ^\prime \rightarrow \eta l^+l^-$$

“…[9] an estimation for the electron mode, Γ (η → π 0 e + e − )| box ≥ 1.2 ± 0.2 μeV, which is in accordance with our result, and an estimate for the muon mode, Γ (η → π 0 μ + μ − )| box ≥ 4.3 ± 0.7 μeV, which in this case is incompatible with our calculation. 12 Additionally, Ng et al also presented in Ref.…”

“…Alternatively, one could have used the theoretical prediction from Ref. [12] Γ (η → π 0 γ γ )| th = 0.17±0.01 eV to obtain Γ (η → π 0 e + e − )/Γ (η → π 0 γ γ ) = (1.6± 0.4) × 10 −5 . 10 The discrepancy with Smith's relative branching ratio might be explained, though, by the effect of p-wave terms that he neglected after admitting that they are not necessarily small.…”

“…Physically, it may be explained to some extent by the fact that the diphoton invariant spectra for the three η ( ) → π 0 γ γ and η → ηγ γ peak at low m 2 γ γ (cf., e.g., Ref. [12] and references therein). On the other hand, the dilepton energy spectra for the muon modes, shown in Fig.…”