Towards reconciling the holographic and lattice descriptions of radially excited hadrons

TL;DR

This paper proposes a new phenomenological test to reconcile holographic AdS/QCD models with lattice QCD results for radially excited hadrons, showing the Soft Wall model aligns better with lattice observations.

Contribution

It introduces a consistency test for bottom-up holographic models, comparing KK spectra with lattice QCD, and demonstrates the Soft Wall model passes this test.

Findings

Soft Wall model passes the consistency test

Hard Wall model does not pass the test

Reconciliation of holographic and lattice descriptions is possible

Abstract

Within the framework of AdS/QCD models, the spectra of radially excited hadrons are identified with towers of Kaluza-Klein (KK) states in a putative dual theory. The infinite number of KK states is indispensable to provide correct high energy asymptotics of correlation functions in QCD. It is known, however, that the KK modes of dual theory must be qualitatively different from real hadrons. And what is more important, the radially excited states appear in lattice calculations not as "excitations" of some ground state, but rather as independent states coupled to higher dimensional QCD operators - the larger is a basis of interpolating operators, the larger set of states can be resolved. A question arises whether it is possible to reconcile the holographic and lattice descriptions of radially excited hadrons? We propose a new phenomenological "consistency test" for bottom-up holographic models: If the KK spectrum of massive 5D fields corresponding to higher dimensional operators in QCD coincides with the conventional radial KK spectrum, then the holographic KK states can be identified with real excited mesons in the large-Nc limit of QCD - as in the lattice QCD, they become a superposition of several states interpolated by operators of different canonical dimensions. We demonstrate that the Soft Wall holographic model passes this test while the Hard Wall model does not.