Comprehensive Calculations on the OZI-forbidden Nonleptonic Decays of Orthoquarkonia $J/\psi(\Upsilon)\to \pi\pi,\rho\pi$

TL;DR

This paper calculates the decay rates of OZI-forbidden nonleptonic decays of $J/ar{ ext{psi}}( ext{Upsilon})$ into $ ext{pi} ext{pi}$ and $ ho ext{pi}$, finding results consistent with data for some processes and highlighting the need for additional mechanisms for others.

Contribution

The study provides leading-twist calculations of OZI-forbidden decay rates, confirming isospin violation effects and highlighting the potential role of higher twist contributions or other mechanisms.

Findings

Decay rates for $J/ar{ ext{psi}}( ext{Upsilon}) o ext{pi} ext{pi}$ match experimental data.

Decay rates for $J/ar{ ext{psi}}( ext{Upsilon}) o ho ext{pi}$ are underestimated by theory.

Higher twist effects or alternative mechanisms may explain the sizable $ ho ext{pi}$ decay rates.

Abstract

In this work, we calculate the decay rates of the OZI-forbidden processes $J/\psi(\Upsilon)\to \pi\pi, \rho\pi$ at the order of the leading-twist distribution amplitude. The process of $J/\psi(\Upsilon)\to \pi^+ \pi^-$ violates isospin conservation and the amplitude is explicitly proportional to the isospin violation factor $m_u-m_d$, our numerical results on their decay rates are consistent with the data. The process $J/\psi(\Upsilon)\to \rho\pi$ violates the hadronic helicity conservation and should be suppressed, as indicated in literature, its decay rate can only be proportional to $m_q^2$ at the order of leading twist. Our theoretical evaluation confirms this statement that the theoretical evaluation on $\Gamma(J/\psi(\Upsilon)\to \rho\pi)$ is almost one order smaller than the data unless the model parameters take certain extreme values. It may imply that the sizable branching ratio of $J/\psi(\Upsilon)\to \rho\pi$ should be explained by either higher twist contributions or other mechanisms.