# Hadronic Superpartners from Superconformal and Supersymmetric Algebra

## TL;DR

This paper develops a supersymmetric QCD framework embedded in AdS space to relate various hadron spectra, including light and heavy hadrons, revealing underlying symmetries and aiding in the identification of new charmonium states.

## Contribution

It introduces an effective supersymmetric light-front Hamiltonian for hadrons that accounts for spin interactions and connects mesons, baryons, and tetraquarks across different quark masses.

## Key findings

- Hadron spectra follow linear Regge trajectories with identical slopes.
- Supersymmetry relates mesons, baryons, and tetraquarks even with heavy quark masses.
- The framework helps identify structures of new charmonium states.

## Abstract

Through the embedding of superconformal quantum mechanics into AdS space, it is possible to construct an effective supersymmetric QCD light-front Hamiltonian for hadrons, which includes a spin-spin interaction between the hadronic constituents. A specific breaking of conformal symmetry determines a unique effective quark-confining potential for light hadrons, as well as remarkable connections between the meson, baryon, and tetraquark spectra. The pion is massless in the chiral limit and has no supersymmetric partner. The excitation spectra of relativistic light-quark meson, baryon and tetraquark bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. Although conformal symmetry is strongly broken by the heavy quark mass, the basic underlying supersymmetric mechanism, which transforms mesons to baryons (and baryons to tetraquarks) into each other, still holds and gives remarkable connections across the entire spectrum of light, heavy-light and double-heavy hadrons. Here we show that all the observed hadrons can be related through this effective supersymmetric QCD, and that it can be used to identify the structure of the new charmonium states.