Classically Conformal B-L extended Standard Model (0902.4050v3)

Abstract: Under a hypothesis of classically conformal theories, we investigate the minimal B-L extended Standard Model, which naturally provides the seesaw mechanism for explaining tiny neutrino masses. In this setup, the radiative gauge symmetry breaking is successfully realized in a very simple way: The B-L gauge symmetry is broken through the conformal anomaly induced by quantum corrections in the Coleman-Weinberg potential. Associated with this B-L symmetry breaking, the Higgs mass parameter is dynamically generated, by which the electroweak symmetry breaking is triggered. We find that a wide range of parameter space can satisfy both the theoretical and experimental requirements.

• The paper introduces a classically conformal B‑L extension that addresses the gauge hierarchy problem and generates neutrino masses through the seesaw mechanism.
• It employs the Coleman-Weinberg mechanism for radiative symmetry breaking, predicting a Higgs mass between 130 and 170 GeV and a B‑L breaking scale above a few TeV.
• The model offers testable predictions, including a detectable Z’ boson and additional Higgs states, thereby linking theoretical solutions with experimental prospects.

Classically Conformal $B-L$ Extended Standard Model

The paper under review explores the extension of the Standard Model (SM) of particle physics by integrating a $B-L$ (Baryon minus Lepton number) gauge symmetry under the framework of classically conformal theories. The key emphasis is on resolving significant issues within the SM, like the gauge hierarchy problem and the explanation of tiny neutrino masses through the seesaw mechanism.

Research Overview

The authors propose a minimal extension to the SM, incorporating a $B-L$ symmetry that offers a novel solution to pivotal challenges such as the gauge hierarchy problem. This problem arises due to the quadratic divergences in quantum corrections to the Higgs boson's self-energy, demanding precise cancellations which are unnatural at higher scales such as the Planck scale.

Classical conformal symmetry, as argued by Bardeen, along with its minimal violation by quantum anomalies, can potentially eliminate these divergences if appropriately integrated with new physics. The model considered extends the SM by introducing right-handed neutrinos and a scalar singlet $\Phi$, resulting in dynamics that allow for radiative symmetry breaking via the Coleman-Weinberg potential. In this paradigm, the $B-L$ gauge symmetry is initially exact at the classical level but is subsequently broken through quantum corrections, inducing electroweak symmetry breaking. This mechanism not only generates a mass for the Higgs but also aligns well with observed phenomenology across a broad parameter space.

Numerical Results and Model Implications

A variety of computational results assert the consistency of this model with current experimental observations:

• The calculated Higgs mass is bounded between approximately 130 and 170 GeV, compatible with experimental constraints.
• The $B-L$ breaking scale, denoted as $M$, must be greater than a few TeV to comply with experimental bounds, particularly the constraints on $Z'$ boson searches.
• The Coleman-Weinberg mechanism necessitates $\alpha_\lambda(0)$ to be negative to maintain stable electroweak symmetry breaking, given current fermionic parameters such as the large top Yukawa coupling.

The extended model not only effectively addresses the hierarchy problem but also naturally incorporates neutrino masses through the seesaw mechanism. Moreover, it potentially resolves dark matter problems by introducing a stable singlet scalar.

Theoretical and Practical Implications

From a theoretical perspective, adopting a $B-L$ extension potentially bridges the gap between the electroweak and Planck scales without necessitating additional tuning of model parameters. Practically, if the $B-L$ breaking scale is low enough to be within detectability of collider experiments (such as the Large Hadron Collider), this model opens avenues for verifying the existence of the expected new particles, like the $Z'$ boson and additional Higgs states.

Conclusions and Prospects for Further Research

The work suggests that minimal $B-L$ extensions provide a fruitful ground for addressing unresolved issues within the SM, without introducing multiple unforeseen complexities. Continuing focus on models like these should be coupled with vigilant data from particle experiments to validate the predicted phenomena. Future work could advance in precision tests of Higgs and $Z'$ physics, explore deeper the implications for cosmology and baryogenesis, and examine potential dark matter candidates within this framework. Integrating high-precision cosmological data or studying further extensions could yield more insights into the early universe and its underlying symmetries.