Effect of charmed meson loops on charmonium transitions

TL;DR

This paper systematically investigates how intermediate charmed meson loops influence charmonium transitions involving pion or eta emission, revealing enhancement in certain S-wave and P-wave transitions and suppression in mixed states, with implications for effective Lagrangian models.

Contribution

It provides a non-relativistic effective field theory analysis of charmed meson loop effects on various charmonium transitions, highlighting when these loops are enhanced or suppressed compared to tree-level contributions.

Findings

Charmed meson loops are enhanced in S-wave to S-wave and P-wave to P-wave transitions.

Loops are often suppressed in S-wave to P-wave transitions, depending on the case.

The study offers a cross check for numerical evaluations and discusses implications for effective Lagrangian approaches.

Abstract

The effects of intermediate charmed mesons on charmonium transitions with the emission of one pion or eta are studied systematically. Based on a non-relativistic effective field theory we show that charmed meson loops are enhanced compared to the corresponding tree-level contributions for transitions between two S-wave charmonia as well as for transitions between two P-wave charmonia. On the contrary, for the transitions between one S-wave and one P-wave charmonium state, the loops need to be analyzed case by case and often appear to be suppressed. The relation to and possible implications for an effective Lagrangian approach are also discussed. This study at the same time provides a cross check for the numerical evaluations.