Lagrangian alternative to QCD string

TL;DR

This paper introduces an effective field theory approach to describe radially excited hadrons in QCD, replacing the traditional string model with scalar field interactions and exploring topological solutions.

Contribution

It proposes a novel effective field model with a periodic potential to explain hadron excitations, offering an alternative to string and AdS/QCD models.

Findings

Radially excited hadrons emerge as excitations over multiple vacua.

Quantum corrections split excited modes into nearly degenerate states.

Existence of classical topological configurations like domain walls and monopoles.

Abstract

The spectrum of radially excited hadrons provides much information about the confinement forces in QCD. The confinement is realized most naturally in terms of the QCD string whose quantization gives rise to the radially excited modes. We propose an alternative framework for the description of the excited spectrum. Namely we put forward some effective field models in which the hadrons acquire masses due to interaction with a scalar field modeling the non-perturbative gluon vacuum. The effective potential for this field is periodic with an infinite number of non-equivalent vacua. The radially excited hadrons emerge as elementary excitations over different vacua. We construct explicit examples for such effective theories in the meson sector. An interesting byproduct of the considered models is the existence of a classical field configuration in each vacuum. Depending on the model, it can represent a domain wall, Nielsen-Olesen vortex or 't Hooft-Polyakov monopole. In the pure scalar sector, it is shown that the first quantum correction leads to splitting of the radially excited modes into two nearly degenerate states. Such a phenomenon has some phenomenological support. The presented approach may be also viewed as an alternative framework to the bottom-up AdS/QCD models where the radial excitations appear on the classical level as well.