Few-body quark dynamics for doubly-heavy baryons and tetraquarks

TL;DR

This paper examines the three- and four-body quark dynamics in double-charm baryons and tetraquarks, highlighting the accuracy of variational and Born-Oppenheimer methods over diquark approximations, and using inequalities to assess stability.

Contribution

It clarifies the appropriate methods for modeling multi-quark systems and evaluates the stability of tetraquarks using inequalities, challenging some common approximations.

Findings

Variational and Born-Oppenheimer approximations closely match exact energies.

Diquark approximation can be misleading for these systems.

Hall-Post inequalities set lower bounds, ruling out stable tetraquarks in certain cases.

Abstract

We discuss the adequate treatment of the 3- and 4-body dynamics for the quark model picture of double-charm baryons and tetraquarks. We stress that the variational and Born-Oppenheimer approximations give energies very close to the exact ones, while the diquark approximation might be rather misleading. The Hall-Post inequalities also provide very useful lower bounds that exclude the possibility of stable tetraquarks for some mass ratios and some color wave functions.