Isospin violating decay of $\psi(3770)\rightarrow J/\psi + \pi^0$

TL;DR

This paper investigates the isospin-violating decay of $ ext{psi}(3770)$ into $J/ ext{psi} + ext{pi}^0$ using an effective Lagrangian approach, QCD sum rules, and dispersion relations to understand the decay mechanism.

Contribution

It introduces a method to analyze the decay via intermediate $D$ meson loops with minimized uncertainties and extracts relevant form factors from first principles and experimental data.

Findings

Dispersive part dominates the decay process below open charm threshold.

Form factors are successfully extracted from QCD sum rules and experimental data.

The study offers insights into non-$Dar{D}$ decay mechanisms of $ ext{psi}(3770)$.

Abstract

The strong-isospin violation in $\psi(3770)\rightarrow J/\psi + \pi^0$ via intermediate $D$ meson loops is investigated in an effective Lagrangian approach. In this process, there is only one $D$-meson loop contributing to the absorptive part, and the uncertainties due to the introduction of form factors can be minimized. With the help of QCD spectral sum rules (QSSR), we extract the $J/\psi DD^*$ form factor as an implement from the first principle of QCD. The $DD^*\pi^0$ form factor can be well determined from the experimental data for $D\rightarrow\pi l\nu$. The exploration of the dispersion relation suggests the dominance of the dispersive part via the intermediate $D$ meson loops even below the open charm threshold. This investigation could provide further insights into the puzzling question on the mechanisms for $\psi(3770)\to$ non-$D\bar{D}$ transitions.