Radiative Symmetry Breaking of the Minimal Left-Right Symmetric Model

TL;DR

The work addresses how a classically conformal, minimal left-right symmetric model can achieve radiative symmetry breaking via Coleman-Weinberg dynamics, generating the LR-breaking scale dynamically from Planck-scale inputs using the Gildener-Weinberg framework. It analyzes the scalar potential with and without the bidoublet, derives flat directions and RG trajectories, and demonstrates that parity can be maximally broken in much of parameter space, yielding a TeV-scale LR sector and a SM-like Higgs with calculable scalon. The study also discusses fermion masses, FCNC constraints, and the implications for collider phenomenology, highlighting a robust link between LR and EW breaking and a potential experimental handle through the mixing angle tan(\vartheta) and W-boson mass ratio. Overall, the results show that conformal LR symmetry breaking can produce a viable, testable scalar spectrum and a dynamical hierarchy between the Planck and electroweak scales, while illustrating the need for extended fermion sectors or symmetry structures to fully address FCNCs.

Abstract

Under the assumption of classical conformal invariance, we study the Coleman-Weinberg symmetry breaking mechanism in the minimal left-right symmetric model. This model is attractive as it provides a natural framework for small neutrino masses and the restoration of parity as a good symmetry of nature. We find that, in a large fraction of the parameter space, the parity symmetry is maximally broken by quantum corrections in the Coleman-Weinberg potential, which are a consequence of the conformal anomaly. As the left-right symmetry breaking scale is connected to the Planck scale through the logarithmic running of the dimensionless couplings of the scalar potential, a large separation of the two scales can be dynamically generated. The symmetry breaking dynamics of the model was studied using a renormalization group analysis. Electroweak symmetry breaking is triggered by the breakdown of left-right symmetry, and the left-right breaking scale is therefore expected in the few TeV range. The phenomenological implications of the symmetry breaking mechanism are discussed.

Figures (1)

• Figure 1: For small intermediate couplings between the doublet and bidoublet sectors, the main correction to RG flow in the $\kappa_+$--$\kappa_1$ plane is coming from the gauge boson contributions. In Fig. \ref{['fig:kappa1']}, the RG evolution towards lower energies without gauge bosons contributions is shown. As discussed in Sec. \ref{['sec:flatdirectionsofdoublet']}, for any starting values with $\kappa_2>0$ the parity conserving GW condition $\kappa_1=0$ is reached eventually and for $\kappa_2<0$ the evolution tends towards the maximally parity-breaking solution $\kappa_+=0$. The effects of the gauge boson contributions are shown in Fig. \ref{['fig:kappa2']}. For simplicity, the gauge couplings have been fixed to the values at $M_Z$, as they become relevant only at low energy scales. Following the stream lines, it can be seen that even for positive starting values of $\kappa_2$, the parity violating minimum might be reached. This region is depicted in Fig. \ref{['fig:kappa3']}. The gauge boson contributions deflect the RG evolution away from the vanishing coupling fixed-point. As the applicability of the GW formalism requires a sufficiently large $\kappa_1$ (see the discussion following Eq. (\ref{['eq:effectivecoupl']})), this shows that the GW treatment is sufficient for a large portion of parameter space.