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2022

Proton Stability: From the Standard Model to Beyond Grand Unification

Wang, Juven, Wan, Zheyan, You, Yi-Zhuang

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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)$_{\bf B - L}$ symmetry, there is also a compatible discrete baryon plus lepton $\mathbb{Z}_{2N_f, \bf B + L}$ symmetry.
The $\mathbb{Z}_{2N_f, \bf B + L}$ is discrete due to the ABJ anomaly under the BPST SU(2) instanton.
Although both U(1)$_{\bf B - L}$ and $\mathbb{Z}_{2N_f, \bf B + L}$ 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.

Proton Stability: From the Standard Model to Beyond Grand Unification · Around

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