Towers of hybrid mesons

TL;DR

This paper models hybrid mesons as quark-antiquark pairs with excited gluon fields, providing analytical solutions and predicting mass towers that aid experimental searches for heavy hybrid mesons.

Contribution

It introduces an analytical solution for the Schrödinger equation with an excited string potential in hybrid mesons, predicting linear mass towers for heavy quarkonia.

Findings

Predicted mass towers for hybrid charmonia and bottomonia.

Masses follow a linear function of a harmonic oscillator band number.

Provides a potential guide for experimental detection of heavy hybrid mesons.

Abstract

A hybrid meson is a quark-antiquark pair in which, contrary to ordinary mesons, the gluon field is in an excited state. In the framework of constituent models, the interaction potential is assumed to be the energy of an excited string. An approximate, but accurate, analytical solution of the Schr\"{o}dinger equation with such a potential is presented. When applied to hybrid charmonia and bottomonia, towers of states are predicted in which the masses are a linear function of a harmonic oscillator band number for the quark-antiquark pair. Such a formula could be a reliable guide for the experimental detection of heavy hybrid mesons.