Abstract
In preparation for upcoming nucleon decay searches at Hyper-Kamiokande, it is important to derive a theoretical upper bound on the proton lifetime in a general class of grand unified theory (GUT) models. In this paper, we make an attempt along this direction for non-SUSY SU(5) models, under the mild restrictions that only one or two SM-decomposed multiplets are singularly light, and that the SU(5) gauge theory is asymptotically free and thus there are no too large representations in the model. We derive criteria for SM-decomposed multiplets that potentially enhance the proton lifetime when they are singularly light. We perform a numerical analysis on the proton lifetime and show that some choices of singularly light multiplets can provide a testable upper bound on the proton lifetime.
Highlights
The Hyper-Kamiokande (HK) experiment is expected to start operation in 2026, and after a 10 year exposure of one kton fiducial volume detector, HK can make a 3σ discovery of p → eþ π 0 process for the partial lifetime up to τp 1⁄4 6.3 × 1034 years [1]
The red lines show the current bound at SK, and the 3σ discovery potential at HK with a 10 year exposure of 1-tank
The unlabeled blue lines correspond to cases with a different second lightest multiplet, and it is evident that all these cases are already excluded by SK
Summary
The Hyper-Kamiokande (HK) experiment is expected to start operation in 2026, and after a 10 year exposure of one kton fiducial volume detector, HK can make a 3σ discovery of p → eþ π 0 process for the partial lifetime up to τp 1⁄4 6.3 × 1034 years [1]. MX can be enhanced arbitrarily, and no upper bound on the proton lifetime in dimension-six processes.. In the minimal model with only 24-dimensional GUT breaking Higgs representation, the gauge coupling unification conditions give. Modify the renormalization group equations (RGEs) and possibly enhance M X above the current experimental bound. (To have a singularly light SM-decomposed multiplet(s), a fine-tuning of the scalar potential is mandatory. We will demonstrate in the main body of the paper that it is possible to put a testable upper bound on the proton lifetime for some choices of singularly light SMdecomposed multiplets. This paper is organized as follows: In Sec. II, we revisit the 1-loop gauge coupling unification conditions in nonSUSY SU(5) GUT, and survey SM-decomposed multiplets that potentially enhance the proton lifetime when they are singularly light.
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