Explaining the Many Threshold Structures in the Heavy-Quark Hadron Spectrum

TL;DR

This paper develops a nonrelativistic effective field theory to explain the numerous near-threshold peaks observed in heavy-quark hadron spectra, attributing them to threshold cusps and attractive interactions, and predicts their occurrence at various heavy-hadron thresholds.

Contribution

It introduces a theoretical framework for understanding threshold structures in heavy-quark hadron spectra and predicts the conditions under which these structures appear, enhancing interpretation of experimental data.

Findings

Threshold cusps appear as peaks only with attractive interactions.

The width of the cusp is inversely proportional to the reduced mass.

Threshold structures are expected at all relevant heavy-hadron pair thresholds.

Abstract

Tremendous progress has been made experimentally in the hadron spectrum containing heavy quarks in the last two decades. It is surprising that many resonant structures are around thresholds of a pair of heavy hadrons. There should be a threshold cusp at any $S$-wave threshold. By constructing a nonrelativistic effective field theory with open channels, we discuss the generalities of threshold behavior, and offer an explanation of the abundance of near-threshold peaks in the heavy quarkonium regime. We show that the threshold cusp can show up as a peak only for channels with attractive interaction, and the width of the cusp is inversely proportional to the reduced mass relevant for the threshold. We argue that there should be threshold structures at any threshold of a pair of heavy-quark and heavy-antiquark hadrons, which have attractive interaction at threshold, in the invariant mass distribution of a heavy quarkonium and light hadrons that couple to that open-flavor hadron pair. The structure becomes more pronounced if there is a near-threshold pole. Predictions of the possible pairs are also given for the ground state heavy hadrons. Precisely measuring the threshold structures will play an important role in revealing the heavy-hadron interactions, and thus understanding the puzzling hidden-charm and hidden-bottom structures.