Visible and Invisible Pseudoscalar Meson Decays from Anomaly Sum Rules

TL;DR

This work develops a dispersive Anomaly Sum Rule framework to describe both visible and semi-visible decays of pseudoscalar mesons, tying the $P\to\gamma\gamma^{(*)}$ transition form factors to the nonperturbative gluon matrix element $\langle 0|G\widetilde{G}|\gamma\gamma^{(*)}\rangle$ via the gluon form factor $B(q^2)$. By saturating axial ASRs with low-lying resonances and employing quark–hadron duality through duality intervals $s_3$, $s_8$, and $s_0$, the authors derive interpolations for $s_{3,8,0}(q^2)$ and $B(q^2)$ that fit space-like and Dalitz data, revealing a nontrivial structure of $B(q^2)$, including a minimum near $q^2\approx1$ GeV$^2$ that hints at a pseudoscalar glueball. They extend the analysis to $P\gamma Z^{0}$ transitions, obtaining $F_{P\gamma Z^{0}}(Q^2)$ and predicting neutrino Dalitz decay widths $\Gamma_{P\to\nu\bar{\nu}\gamma}$; mixing between $\pi^0$, $\eta$, and $\eta'$ plays a crucial role, enhancing the $\pi^0$ and $\eta$ channels in ways consistent with modern mixing schemes. The results connect axial anomalies, nonperturbative gluonic dynamics, and measurable meson decays, offering experimental avenues at facilities like HIAF to probe $B(q^2)$ and possible glueball dynamics, with implications for dark-photon background studies.

Abstract

The decays of pseudoscalar mesons to real and virtual photons as well as neutrino-antineutrino pairs are considered in the framework of the dispersive method based on Anomaly Sum Rules. The contribution of singlet channel involving the new non-perturbative gluon form factor of virtual photon $B(q^2)$ is systematically taken into account. The detailed analysis of its dependence on photon virtuality $q^2$ relying on the available data for meson transition fomfactors is performed. It is shown that B has quite a nontrivial structure at $q^2 \sim 1 GeV^2$ which may be a signal of the existence of pseudoscalar glueball with a mass about 1.5-2 GeV. The calculation of the decay to $ν\bar ν$ pairs leads to the compatibility with the result of Arnellos, Marciano and Parsa of 1982, when pion decay is considered neglecting the mixing effects. The account for these effects results, however, in the enhancement of pion branching ratio by a factor of 3, while that for eta decay is larger by several orders of magnitude. It is stressed, that dependence on the pair invariant mass is entirely defined by QCD and coincides with that of the meson transition form factor. The role of obtained results for the physics at HHaS detector at HIAF is discussed.

Figures (27)

• Figure 1: The matrix element $\langle 0 | \frac{\sqrt{3}\alpha_s}{4\pi} G\tilde{G}|\gamma\gamma \rangle$ schematic representation.
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• Figure 6: $A_{QED}$.