Longitudinal dynamics for mesons on the light cone

Abstract

We survey a set of proposed light-front models for confinement in the valence quark sector of the mesons and portray similarities as well as differences. We present the spectroscopies for the light mesons that result from a selection of longitudinal confinement forms. We note that the Sturm-Liouville theory provides a unifying framework for many elements of this comparison.

Meson masses and decay constants in holographic QCD consistent with ChPT and HQET

“…In particular, it is not correct that these symmetry breaking terms be generated by the longitudinal part of Hamiltonian (potential) as was proposed in Refs. [9]- [13]. Another important point is that the full Hamiltonian cannot be fully universal and must be specific for each type of mesons.…”

“…I;L (z, x). The latter was discussed in the series of papers [9]- [13]. In particular, it was proposed that the longitudinal interaction potential generates explicitly breaking of chiral symmetry.…”

“…Recently, in Refs. [9]- [13], our ideas were further developed by the construction of the so-called longitudinal potential, which produces longitudinal wave functions of hadrons. We feel that we can improve the construction of such potentials, by requiring a more exact correspondence with chiral perturbation theory (ChPT) [14,15], which is the low-energy limit of quantum chromodynamics (QCD).…”

“…Notice that this is not a case in the formalisms proposed in Refs. [9]- [13]. There are a few conditions that should be imposed.…”

“…Another point, which requires to reconsider the formalisms developed in Refs. [9]- [13], is the condition that the dependence on quark condensate in a Lagrangian/Hamiltonian should vanish in the chiral limit (i.e., when current quark masses vanish, m i → 0).…”