The absence of spin-3/2 or higher fundamental particles in the Standard Model of particle physics can be attributed to a combination of theoretical and experimental reasons. Here are a few key factors:
Gauge Symmetry: The Standard Model is based on the principle of local gauge symmetry, particularly the symmetry group known as the SU(3) × SU(2) × U(1). This symmetry framework successfully describes the fundamental particles and their interactions observed in experiments. However, incorporating particles with higher spins would require extending the gauge symmetry and introducing new fields and interactions, which would significantly complicate the theory.
Unitarity and Renormalizability: Theories with higher spin fields tend to face challenges in maintaining unitarity and renormalizability. Unitarity ensures that probabilities are conserved, while renormalizability ensures the cancellation of divergent quantities in calculations. Higher spin fields introduce new types of interactions that can lead to non-unitary or non-renormalizable theories, making them less favorable from a theoretical standpoint.
Experimental Constraints: Experimental observations have not provided compelling evidence for fundamental particles with spin-3/2 or higher. The particle spectrum of the Standard Model, confirmed by experiments such as those at the Large Hadron Collider (LHC), currently consists of particles with spins 0, 1/2, and 1. These include the Higgs boson (spin-0), quarks (spin-1/2), and gauge bosons like photons and W and Z bosons (spin-1).
Supersymmetry: One proposed extension of the Standard Model that does introduce higher-spin particles is supersymmetry (SUSY). Supersymmetry posits a symmetry between fermions and bosons, resulting in a doubling of the particle spectrum. In SUSY, spin-3/2 particles called gravitinos can appear. However, while SUSY is an attractive theoretical framework for various reasons, experimental evidence supporting its predictions has not yet been observed.
It's important to note that the absence of spin-3/2 or higher particles in the Standard Model is a feature of the model as it stands. However, the Standard Model is not considered a complete theory and is believed to be an effective description at energies currently probed by experiments. Beyond the Standard Model, theories such as string theory and grand unified theories have been proposed that may accommodate higher-spin particles and offer a more comprehensive framework for particle physics.