S- and D-wave vector charmonia

TL;DR

This paper reexamines the decay constants of vector charmonia, decomposes their Bethe-Salpeter amplitudes by orbital angular momentum, and confirms Psi(3770) and Psi(4160) as D-wave states.

Contribution

It introduces a detailed decomposition of Bethe-Salpeter amplitudes in terms of orbital angular momentum for vector charmonia, confirming the D-wave nature of specific states.

Findings

Psi(3770) identified as D-wave state

Psi(4160) identified as D-wave state

Decay constants support D-wave classification

Abstract

We revisit earlier calculations of leptonic decay constants of vector charmonia and present and illustrate our decomposition of the corresponding covariant Bethe-Salpeter amplitudes in terms of orbital angular momentum as interpreted in the meson's rest frame. Our results confirm our previous conclusions drawn from the magnitudes of vector-meson leptonic decay constants, identifying the Psi(3770) and Psi(4160) as D-wave states in our setup.