Dynamical generation and dynamical reconstruction

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.

14 pages, 3 figures

References in corpus (27)

• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• Mass and width of the lowest resonance in QCD
• A low-lying scalar meson nonet in a unitarized meson model
• The Physics of Glueballs
• A Theory of Scalar Mesons
• Vector meson-vector meson interaction in a hidden gauge unitary approach
• The ρρinteraction in the hidden gauge formalism and the f_0(1370) and f_2(1270) resonances
• Scalar Glueball, Scalar Quarkonia, and their Mixing
• Global aspects of the scalar meson puzzle
• Mixing of scalar tetraquark and quarkonia states in a chiral approach
• Scalar Mesons a0(1450) and sigma(600) from Lattice QCD
• Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length
• On the spectral functions of scalar mesons
• Strong and electromagnetic decays of the light scalar mesons interpreted as tetraquark states
• Role of the tetraquark in the chiral phase transition
• QCD Coulomb gauge approach to hybrid mesons
• Information on the structure of the a1 from tau decay
• Nature of the axial-vector mesons from their Nc behavior within the chiral unitary approach
• Phenomenological Lagrangian approach to the electromagnetic deuteron form factors
• Baryonium, tetra-quark state and glue-ball in large N_c QCD
• Decays of sigma, kappa, a0(980) and fo(980)
• Towards an understanding of the light scalar mesons
• Tau decay and the structure of the a1
• On the scalar nonet in the extended Nambu Jona-Lasinio model
• How Universal is the Coupling in the Sigma Model?
• Chiral Unitary Dynamics of Hadrons and Hadrons in a Nuclear Medium
• Chiral Partners in a Chirally Broken World

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• The Glueball in a Chiral Linear Sigma Model with Vector Mesons
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• Non-exponential decay in quantum field theory and in quantum mechanics: the case of two (or more) decay channels
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• Phenomenology of a pseudoscalar glueball and charmed mesons
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