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

Abstract

A complete theoretical analysis of the C- conserving semileptonic decays $$\eta ^{(\prime )}\rightarrow \pi ^0l^+l^-$$ η ( ′ ) → π 0 l + l - and $$\eta ^\prime \rightarrow \eta l^+l^-$$ η ′ → η l + l - ($$l=e$$ l = e or $$\mu $$ μ ) is carried out within the framework of the Vector Meson Dominance (VMD) model. An existing phenomenological model is used to parametrise the VMD coupling constants and the associated numerical values are obtained from an optimisation fit to $$V\rightarrow P\gamma $$ V → P γ and $$P\rightarrow V\gamma $$ P → V γ radiative decays ($$V=\rho ^0$$ V = ρ 0 , $$\omega $$ ω , $$\phi $$ ϕ and $$P=\pi ^0$$ P = π 0 , $$\eta $$ η , $$\eta ^{\prime }$$ η ′ ). The decay widths and dilepton energy spectra for the two $$\eta \rightarrow \pi ^0l^+l^-$$ η → π 0 l + l - processes obtained using this approach are compared and found to be in good agreement with other results available in the published literature. Theoretical predictions for the four $$\eta ^{\prime }\rightarrow \pi ^0l^+l^-$$ η ′ → π 0 l + l - and $$\eta ^\prime \rightarrow \eta l^+l^-$$ η ′ → η l + l - decay widths and dilepton energy spectra are calculated and presented for the first time in this work.

Theoretical analysis of $\eta^{(\prime)}\to\pi^0l^+l^-$ and $\eta^{\prime}\to\eta l^+l^-$ decays, and new-physics signatures via $CP$ violation

“…The associated numerical values for the parameters of the model are obtained from an optimisation fit to → and → radiative decays, where = 0 , , and = 0 , , (see Ref. [11] for further details).…”

Precision tests of fundamental physics with $\eta$ and $\eta'$ mesons

“…7, forms an irreducible SM background. The corresponding SM branching ratios have been recalculated recently [54], B (𝜂 → 𝜋 0 𝑒 + 𝑒 − ) = 2.1(5) × 10 −9 and B (𝜂 → 𝜋 0 𝜇 + 𝜇 − ) = 1.2(3) × 10 −9 (as well as similar orders of magnitude for 𝜂 ′ → 𝜋 0 ℓ + ℓ − and 𝜂 ′ → 𝜂ℓ + ℓ − ), based on a vector-meson-dominance model for the corresponding two-photon decays [9]. These are to be compared to the current experimental upper limits, B (𝜂 → 𝜋 0 𝑒 + 𝑒 − ) < 7.5 × 10 −6 [55] and B (𝜂 → 𝜋 0 𝜇 + 𝜇 − ) < 5 × 10 −6 [56].…”

Light meson decays at BESIII

“…Precise measurements of their branching fractions (BFs) are important for a wide variety of physics topics. For example, the decay widths of η/η ′ → γγ are related to the quark content of the two mesons [28], the BFs of η/η ′ → 3π decays can provide valuable information on light quark masses [29], the BFs of η/η ′ → π + π − γ decays are related to details of chiral dynamics [30], and the BFs of some rare decays of the η and η ′ can test fundamental QCD symmetries [31] and probe for physics beyond the standard model [32]. As the BFs of the rare decays are obtained via normalization to the dominant decay modes, a precise determination of the BFs of the dominant decay modes of the η and η ′ is essential.…”