Dynamical generation and dynamical reconstruction

TL;DR

This paper proposes a definition of dynamical generation and reconstruction, using a toy model and large N_c arguments, to distinguish between tetraquark, molecular, and quarkonium states, with implications for meson classification.

Contribution

It introduces a formal framework for dynamical generation and reconstruction, applying unitarization methods and large N_c analysis to identify meson structures.

Findings

Bethe-Salpeter analysis can reconstruct quarkonium states from effective Lagrangians.

Retaining only the lowest term in the Lagrangian causes the reconstructed state to fade as a molecular state in large N_c.

Implication that certain mesons above 1 GeV are likely quarkonia, consistent with the constituent quark model.

Abstract

A definition of `dynamical generation', a hotly debated topic at present, is proposed and its implications are discussed. This definition, in turn, leads to a method allowing to distinguish in principle tetraquark and molecular states. The different concept of `dynamical reconstruction' is also introduced and applies to the generation of preexisting mesons (quark-antiquark, glueballs, >...) via unitarization methods applied to low-energy effective Lagrangians. Large $N_{c}$ arguments play an important role in all these investigations. A simple toy model with two scalar fields is introduced to elucidate these concepts. The large $N_{c}$ behavior of the parameters is chosen in order that the two scalar fields behave as quark-antiquark mesons. When the heavier field is integrated out, one is left with an effective Lagrangian with the lighter field only. A unitarization method applied to the latter allows to `reconstruct' the heavier `quarkonium-like' field, which was previously integrated out. It is shown that a Bethe-Salpeter (BS) analysis is capable to reproduce the preformed quark-antiquark state. However, when only the lowest term of the effective Lagrangian is retained, the large $N_{c}$ limit of the reconstructed state is not reproduced: instead of the correct large $N_{c}$ quarkonium limit, it fades out as a molecular state would do. Implications of these results are presented: it is proposed that axial-vector, tensor and (some) scalar mesons just above 1 GeV obtained via the BS approach from the corresponding low-energy, effective Lagrangian in which only the lowest term is kept, are quarkonia states, in agreement with the constituent quark model, although they might fade away as molecular states in the large $N_{c}$ limit.