# Dynamical supersymmetry for strange quark and $ud$ antidiquark in hadron mass spectrum

## TL;DR

This paper introduces a supersymmetry-like algebraic framework linking strange quarks and ud diquarks, leading to new hadron classifications and mass predictions for tetraquark states.

## Contribution

It proposes a novel symmetry between s quarks and ud diquarks, constructing an algebraic structure that classifies hadrons and predicts tetraquark masses.

## Key findings

- Classifies hadrons into triplets, nonets, and quintets based on the algebra.
- Predicts masses of tetraquarks $ar{ud}sc$ and $ar{ud}sb$ as 2.942 GeV and 6.261 GeV.
- Provides mass relations incorporating symmetry breaking due to quark mass differences.

## Abstract

Speculating that the $ud$ diquark with spin 0 has a similar mass to the constituent $s$ quark, we introduce a symmetry between the $s$ quark and the $\overline{ud}$ diquark. Constructing an algebra for this symmetry, we regard a triplet of the $s$ quarks with spin up and down and the $\overline{ud}$ diquark with spin 0 as a fundamental representation of this algebra. We further build higher representations constructed by direct products of the fundamental representations. We propose assignments of hadrons to the multiples of this algebra. We find in particular that $\{D_{s}, D_{s}^{*}, \Lambda_{c}\}$, $\{\eta_{s}, \phi, \Lambda, f_{0}(1370)\}$ and $\{\Omega_{c}, T_{sc}\}$ form a triplet, a nonet and a quintet, respectively, where $T_{sc}$ is a genuine tetraquark meson composed of $\overline{ud}sc$. We also find a mass relation between them by introducing the symmetry breaking due to the mass difference between the $s$ quark and the $\overline{ud}$ diquark. The masses of possible tetraquarks $\overline{ud}sc$ and $\overline{ud}sb$ are estimated from the symmetry breaking and the masses of $\Omega_{c}$ and $\Omega_{b}$ to be 2.942 GeV and 6.261 GeV, respectively.