Proton Stability: From the Standard Model to Beyond Grand Unification

Abstract

A proton is known for its longevity, but what is its lifetime? While many Grand Unified Theories predict the proton decay with a finite lifetime, we show that the Standard Model (SM) and some versions of Ultra Unification (which replace sterile neutrinos with new exotic gapped/gapless sectors, e.g., topological or conformal field theory under global anomaly cancellation constraints) with a discrete baryon plus lepton symmetry permit a stable proton. For the 4d SM with $N_f$ families of 15 or 16 Weyl fermions, in addition to the continuous baryon minus lepton U(1)${}_{\mathbf{B}-\mathbf{L}}$ symmetry, there is also a compatible discrete baryon plus lepton ${\mathbb{Z}}_{2N_f,\mathbf{B}+\mathbf{L}}$ symmetry. The ${\mathbb{Z}}_{2N_f,\mathbf{B}+\mathbf{L}}$ is discrete due to the ABJ anomaly under the BPST SU(2) instanton. Although both U(1)${}_{\mathbf{B}-\mathbf{L}}$ and ${\mathbb{Z}}_{2N_f,\mathbf{B}+\mathbf{L}}$ symmetries are anomaly-free under the dynamical SM gauge field, it is important to check whether they have mixed anomalies with the gravitational background field and higher symmetries (whose charged objects are Wilson electric or 't Hooft magnetic line operators) of SM. We can also replace the U(1)${}_{\mathbf{B}-\mathbf{L}}$ with a discrete variant ${\mathbb{Z}}_{4,X}$ for $X\equiv 5(\mathbf{B}-\mathbf{L})-\frac{2}{3}\tilde{Y}$ of electroweak hypercharge $\tilde{Y}$. We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM's deformation class. We discuss the proton stability of the SM and Ultra Unification in the presence of discrete $\mathbf{B}+\mathbf{L}$ symmetry protection, in particular (U(1)${}_{\mathbf{B}-\mathbf{L}}\times {\mathbb{Z}}_{2N_f,\mathbf{B}+\mathbf{L}})/{\mathbb{Z}}_2^{\mathrm{F}}$ or $({\mathbb{Z}}_{4,X}\times {\mathbb{Z}}_{2N_f,\mathbf{B}+\mathbf{L}})/{\mathbb{Z}}_2^{\mathrm{F}}$ symmetry with the fermion parity ${\mathbb{Z}}_2^{\mathrm{F}}$.

6 pages. Sequel to arXiv:2112.14765. v2: refinement. Related talks: https://www.youtube.com/results?search_query=cobordism+deformation+standard+model+crticiality. The original title "Proton Stability: From the Standard Model to Ultra Unification" is adjusted in PRD

References in corpus (9)

• Generalized Global Symmetries
• Line Operators in the Standard Model
• Cobordism Classes and the Swampland
• Nonperturbative effects in the Standard Model with gauged 1-form symmetry
• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
• Cobordism and Deformation Class of the Standard Model
• Ultra Unification
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
• Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy

Cited by in corpus (9)

• Symmetric Mass Generation
• Cobordism and Deformation Class of the Standard Model
• Categorical Symmetry of the Standard Model from Gravitational Anomaly
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
• Anomalies of non-Abelian finite groups via cobordism
• Fractionally Charged Particles at the Energy Frontier: The SM Gauge Group and One-Form Global Symmetry
• Non-Invertible Peccei-Quinn Symmetry, Natural 2HDM Alignment, and the Visible Axion
• A Note on Proton Stability in the Standard Model
• Boundary topological orders of (4+1)d fermionic ${\mathbb{Z}}_{2N}^{\mathrm{F}}$ SPT states