Theorem on vanishing contributions to $\sin^2\theta_W$ and intermediate mass scale in Grand Unified Theories with trinification symmetry

TL;DR

This paper proves that in certain Grand Unified Theories with trinification symmetry, quantum corrections do not affect the electroweak mixing angle or intermediate mass scale, ensuring their stability.

Contribution

The paper establishes a rigorous theorem showing the vanishing of quantum corrections to key parameters in GUTs with trinification symmetry, verified numerically for supersymmetric and non-supersymmetric models.

Findings

Quantum corrections to $ ext{sin}^2 heta_W$ vanish at all loop orders.

Intermediate mass scale $M_I$ remains unaffected by gravitational and loop corrections.

Results are numerically confirmed in $E_6$-based GUT models.

Abstract

We prove that the values of the electroweak mixing angle $\sin^2\theta_W$ and intermediate mass scale $M_I$ have vanishing contributions due to one-loop, two-loop and gravitational corrections in Grand Unified Theories which accommodate an intermediate trinification symmetry ($G_{333D}$) invoked with spontaneous D-parity mechanism operative at mass scale greater than $M_I$. The proof of theorem is robust and we verify the results numerically using supersymmetric as well as non-supersymmetric version of $E_6$-GUT.