American Journal for Young Scientists · ISSN 3068-9015
SU(3) Weight Diagrams and Gell-Mann–Okubo Mass Relations for Tetraquark and Pentaquark Multiplets
Authors: Varun Rajkumar
Published: September 16, 2026
Category: Physics
Abstract
This paper examines how SU(3) flavor symmetry can be used to classify tetraquarks and pentaquarks and relate the masses of particles within the same multiplet. Young tableaux are used to determine the possible SU(3) representations, and weight diagrams are constructed to show the allowed states in terms of isospin and hypercharge. The tetraquark, pentaquark, and antipentaquark flavor decompositions are derived, including octet, decuplet, 27-plet, and 35-plet representations. The Gell-Mann–Okubo mass relations are then used to connect the masses of states within these multiplets. For hidden-charm tetraquarks, treating the Zc(3900) and Zcs(4000) as members of the same flavor octet gives a predicted mass of approximately 4022 MeV for the missing isoscalar partner. For observed hidden-charm pentaquarks, the available experimental states are not yet sufficient to make a similar mass prediction. These results show how flavor symmetry can help organize exotic hadrons and guide searches for new particles.