# The effect of higher dimensional QCD operators on the spectroscopy of bottom-up holographic models

## TL;DR

This paper investigates how higher dimensional QCD operators influence the spectrum of excited hadrons in bottom-up holographic models, revealing significant degeneracies and state proliferation.

## Contribution

It introduces the consideration of higher dimensional QCD operators in holographic models, showing their impact on hadron spectra and establishing a one-to-one mapping between meson states and QCD operators.

## Key findings

- Higher dimensional operators cause degeneracy of excited states in the Soft Wall model.
- In the Hard Wall model, they lead to a proliferation of excited states.
- The model predicts a direct correspondence between meson states and specific QCD operators.

## Abstract

Within the bottom-up holographic approach to QCD, the highly excited hadrons are identified with the bulk normal modes in the fifth "holographic" dimension. We show that additional states in the same mass range can appear also from taking into consideration the 5D fields dual to higher dimensional QCD operators. The possible effects of these operators were not taken into account in almost all phenomenological applications. Using the scalar case as the simplest example, we demonstrate that the additional higher dimensional operators lead to a large degeneracy of highly excited states in the Soft Wall holographic model while in the Hard Wall holographic model, they result in a proliferation of excited states. The considered model can be viewed as the first analytical toy-model predicting a one-to-one mapping of the excited meson states to definite QCD operators to which they prefer to couple.