- The paper introduces alternative neutrino mass mechanisms by employing Dirac and inverse seesaw frameworks using B−L gauge symmetry.
- It details a novel anomaly-free model with unique B−L charge assignments that employs heavy Dirac fermions to achieve light neutrino masses.
- The study leverages S3 flavour symmetry to attain realistic leptonic mixing angles and explore potential dark matter candidates.
Dirac or Inverse Seesaw Neutrino Masses with B − L Gauge and S3 Flavour Symmetries
This paper addresses the extensions of the Standard Model (SM) through a B − L gauge symmetry to explore alternative mechanisms for neutrino mass generation. Typically, the B − L symmetry has been applied to enhance Majorana seesaw mechanisms for neutrino masses. However, this paper proposes a novel anomaly-free extension of the SM that allows for Dirac and inverse seesaw neutrino masses using B − L gauge symmetry coupled with S3 flavour symmetry.
Main Discussion
The paper begins by highlighting the anomaly-free condition of the SM when extended with an additional U(1) gauge group. The B − L gauge symmetry, which assigns a charge related to baryon number minus lepton number, often utilizes three singlet right-handed neutrinos to cancel gauge anomalies. This adjustment, linked to existing models, results in a robust Majorana seesaw mechanism with spontaneous symmetry breaking induced by a scalar field carrying a B − L charge of two.
The authors introduce a different solution for neutrino masses under B − L symmetry, proposing Dirac or inverse seesaw masses. They assign right-handed neutrinos different B − L charges of +5, −4, −4, maintaining the anomaly-free condition. The associated scalar fields under B − L symmetry exhibit unique charges, notably +3, facilitating Dirac seesaw and inverse seesaw mechanisms—neither resulting in Majorana mass terms nor breaking lepton number conservation, thus keeping lepton number as a global symmetry.
Anomaly-Free Assignments and Seesaw Mechanism
The paper meticulously works through neutrino mass matrix formulations for Dirac and inverse seesaw scenarios. The Dirac seesaw mechanism described involves intermediate heavy Dirac fermions, leading to light neutrino masses considerably smaller than conventional Majorana seesaw, attributed to the effective mass matrix formulation. Conversely, the inverse seesaw mechanism utilizes two complex scalar fields resulting in a different mass hierarchy and the possibility of having one massless neutrino.
Implications for Flavour Symmetry
Utilizing S3 flavour symmetry, the paper extends the theoretical formulation into the leptonic sector, particularly focusing on the μ−τ sector. The S3 symmetry, a non-Abelian discrete group, aids the understanding of neutrino oscillation data through maximal mixing scenarios. Specific coupling constants and vacuum expectation values (VEVs) lead to a phenomenologically viable model consistent with experimental observations.
Implications and Future Developments
Overall, this paper contributes to the theoretical landscape by offering alternative mechanisms for neutrino mass generation within the framework of B − L gauge symmetry, proposing viable candidates for dark matter, and achieving realistic mixing angles in the leptonic sector. The theoretical implications suggest possibilities for new physics beyond the SM, including novel approaches to flavour symmetry and dark matter candidates.
Further developments might involve extension into the quark sector or exploration of additional scalar fields under the S3 symmetry for enriched symplectic structures that could resolve current limitations in flavour physics. The elucidation of S3 symmetry's implications across sectors might yield insights into particle interactions at fundamental levels.
In conclusion, the paper presents a rigorous academic discourse on extending B − L gauge symmetry and incorporating S3 flavour symmetry, thus providing new pathways for understanding neutrino properties while maintaining consistency with empirical observations.