Unbroken B-L Symmetry

Abstract: The difference between baryon number B and lepton number L is the only anomaly-free global symmetry of the Standard Model, easily promoted to a local symmetry by introducing three right-handed neutrinos, which automatically make neutrinos massive. The non-observation of any (B-L)-violating processes leads us to scrutinize the case of unbroken gauged B-L; besides Dirac neutrinos, the model contains only three parameters, the gauge coupling strength g', the Stueckelberg mass $M_{Z'}$, and the kinetic mixing angle $\chi$. The new force could manifest itself at any scale, and we collect and derive bounds on g' over the entire testable range $M_{Z'}$ = 0 - $10^{13}$ eV, also of interest for the more popular case of spontaneously broken B-L or other new light forces. We show in particular that successful Big Bang nucleosynthesis provides strong bounds for masses 10 eV < $M_{Z'}$ < 10 GeV due to resonant enhancement of the rate $\bar{f} f \leftrightarrow \bar{\nu}R \nu_R$. The strongest limits typically arise from astrophysics and colliders, probing scales $M{Z'}/g'$ from TeV up to $10^{10}$ GeV.

• The paper analyzes unbroken B-L symmetry as an anomaly-free extension to the Standard Model, showing how it can incorporate right-handed neutrinos and naturally provide Dirac masses for neutrinos.
• It details the properties of the associated Z' gauge boson and surveys applicable experimental and astrophysical constraints across a wide mass range, including collider searches and stellar observations.
• The model is constrained by various experimental and astrophysical data, including Big Bang Nucleosynthesis, but offers a theoretically appealing and minimal framework for explaining neutrino masses.

An Analysis of Unbroken $B-L$ Symmetry within the Standard Model

The concept of $U(1)_{B-L}$ symmetry, which involves the baryon number ($B$) and lepton number ($L$), presents an intriguing extension to the Standard Model (SM) of particle physics. The paper by Heeck addresses this anomaly-free global symmetry, which is the sole such symmetry in the SM and can be elevated to a local gauge symmetry with the inclusion of three right-handed neutrinos. This modification not only integrates neutrino masses into the model in a natural manner but also maintains $B-L$ conservation.

Model Considerations and Details

The unbroken $U(1)_{B-L}$ model introduces a new particle, the gauge boson $Z'$, characterized by three principal parameters: the gauge coupling strength $g'$, the St\"uckelberg mass $M_{Z'}$, and the kinetic mixing angle $\chi$. Crucially, this construction demands no spontaneous symmetry breaking, thereby avoiding the introduction of a Higgs-like mechanism in this context.

Dirac neutrinos emerge naturally within this framework through their interaction with the right-handed neutrinos and the Higgs field, creating a mass matrix characterized by the usual Yukawa terms. The scenario avoids flavor changing neutral currents, a pivotal conclusion reached within this model, suggesting a potential alignment with observed neutrino phenomena without direct conflict with existing experimental data.

Constraints and Phenomenological Impacts

The unbroken $U(1)_{B-L}$ symmetry requires adherence to existing experimental constraints which define the possible scales and strengths of the $Z'$ boson's properties. The paper systematically surveys applicable constraints—spanning a broad mass range from zero to $10^{13}\text{ eV}$—stemming from astrophysical observations, such as stellar evolution limits, and laboratory conditions, including collider searches and beam-dump experiments. These analyses emphasize the utility of existing experimental data to infer allowable regions for the parameters $g'$ and $M_{Z'}$.

Resonant Enhancements and Big Bang Nucleosynthesis

A direct implication of this study is the significant influence of possible $Z'$ interactions during Big Bang nucleosynthesis (BBN). The resonance phenomena capable of enhancing interaction rates between fermions and right-handed neutrinos demand specific constraints—especially in the mass regime $10\text{ eV} < M_{Z'} < 10\text{ GeV}$—arising from ensuring consistent $N_{\text{eff}}$ counts within cosmological models.

Theoretical and Experimental Implications

The pursuit of an unbroken $B-L$ symmetry fosters considerable interest owing to its theoretical elegance and its potential congruity with experimental results, offering a natural backdrop for the massiveness of neutrinos without invoking Majorana particles. This model's intellectual appeal lies not only in its theoretical consistency but also in its compatibility with $B-L$ conserving leptogenesis models.

Looking forward, the ongoing development of colliders and astrophysical measurements will sharpen the constraints and guide potential refinements to the model, specifically in addressing kinetic mixing and minor coupling perturbations. The simplicity and robustness of unbroken $B-L$—paired with its minimal addition to the SM—advance its standing as an inviting candidate for further investigation as part of the ongoing exploration into the field of beyond standard model physics.