Production of meson molecules in ultra-peripheral heavy ion collisons

TL;DR

This paper calculates the production cross section of a lightest exotic charmonium meson molecule in ultra-peripheral heavy ion collisions, providing a theoretical prediction for experimental searches.

Contribution

It introduces a formalism for explicitly treating exotic meson molecules as bound states in ultra-peripheral collisions, focusing on the $D^+ D^-$ molecular state.

Findings

Cross section for $Pb-Pb$ collisions at 5.02 TeV is about 3 microbarns.

Method projects free meson pairs onto bound states at the amplitude level.

Provides a theoretical framework for detecting exotic meson molecules in heavy ion collisions.

Abstract

In this work we present a calculation of exotic charmonium production in ultra-peripheral collisions, in which the exotic state is explicitly treated as a meson molecule. Our formalism is general but we focus on the lightest possible exotic charmonium state: a $D^+ D^-$ molecular bound state. It was proposed some time ago and it has been object of experimental searches. Here we study the production of the open charm pair in the process $\gamma \gamma \to D^+ D^-$. Then we use a prescription to project the free pair $ |D^+ D^- \rangle$ onto a bound state at the amplitude level and compute the cross section of the process $\gamma \gamma \to B$ (where $B$ is the bound state). Finally, we convolute this last cross section with the equivalent photon distributions coming from the projectile and target in an ultra-peripheral collision and find the $A A \to A A B$ cross section, which, for $Pb-Pb$ collisions at $\sqrt{s_{NN}} = 5.02$ TeV, is of the order of $3 \, \mu \mbox{b}$.