A Mesonic Analog of the Deuteron

TL;DR

This paper investigates a mesonic analog of the deuteron using the LAMP model, revealing a transition from a molecular state to a four-quark bound state without pion exchange contribution.

Contribution

It introduces a novel application of the LAMP model to meson interactions, demonstrating a transition from molecular to four-quark states at short distances.

Findings

Bound state appears due to absence of Pauli repulsion.

Transition from molecular to four-quark state at ~0.45 fm.

Pion exchange does not contribute to binding.

Abstract

Using the LAMP model for nuclear quark structure, we calculate the binding energy and quark structure of a $B$ meson merging with a $D$ meson. The larger-than-nucleon masses of the two heavy quarks allow for a more reliable application of the Born-Oppenheimer-like approximation of the LAMP. With the absence of quark-level Pauli Exclusion Principle repulsive effects, the appearance of a bound state is unsurprising. Our variational calculation shows that the molecular, deuteron-like state structure changes rather abruptly, as the separation between the two mesons decreases, at a separation of about 0.45 fm, into a four-quark bound state, although one maintaining an internal structure rather than that of a four-quark bag. Unlike the deuteron, pion exchange does not provide any contribution to the $\approx 150$ MeV binding.