Proton lifetime upper bound in non-SUSY SU(5) GUT

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.

Figure 1

Proton partial lifetime for $p\to {\pi }^0{e}^{+}$ process, ${\tau }_p$, in the case when $(\mathbf{6},\mathbf{3},1/3)$ is the leading lightest SM-decomposed multiplet. The horizontal axis is the mass of the leading lightest multiplet, which is $(\mathbf{6},\mathbf{3},1/3)$ in this figure. ${\alpha }_s^{(5)}(M_Z)=0.1181+3·0.0011$ (left), $0.1181-3·0.0011$ (right). The red lines show the current bound at SK (solid), and the $3\sigma$ discovery potential at HK with a 10 year exposure of 1-tank (dashed). The blue line labeled as $(\mathbf{10},\mathbf{1},-1)$ shows the proton partial lifetime when $(\mathbf{10},\mathbf{1},-1)$ is the second lightest multiplet. 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.

Figure 2

Proton partial lifetime, ${\tau }_p$, in the case when $(\mathbf{8},\mathbf{3},0)$ is the leading lightest SM-decomposed multiplet. The horizontal axis is the mass of the leading lightest multiplet, which is $(\mathbf{8},\mathbf{3},0)$ in this figure. ${\alpha }_s^{(5)}(M_Z)=0.1181+3·0.0011$ (left), $0.1181-3·0.0011$ (right). The red lines show the current bound at SK (solid), and the $3\sigma$ discovery potential at HK with a 10 year exposure of 1-tank (dashed). Each blue line with a label shows the proton partial lifetime when the second lightest multiplet is as indicated by the label. 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. Interestingly, if the second lightest multiplet is $(\mathbf{6},\mathbf{1},-2/3)$, $(\mathbf{6},\mathbf{1},1/3)$, or $(\mathbf{6},\mathbf{2},-1/6)$, the model can evade the current bound and predicts a proton lifetime within the coverage of HK.

Figure 3

Proton partial lifetime, ${\tau }_p$, in the case when $(\mathbf{6},\mathbf{3},1/3)$ is the second lightest SM-decomposed multiplet. The horizontal axis is again the mass of the leading lightest multiplet. ${\alpha }_s^{(5)}(M_Z)=0.1181+3·0.0011$ (left), $0.1181-3·0.0011$ (right). The red lines show the current bound at SK (solid), and the $3\sigma$ discovery potential at HK with a 10 year exposure of 1-tank (dashed). Each blue line with a label shows the proton partial lifetime when the leading lightest multiplet is as indicated by the label. 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. Interestingly, if the leading lightest multiplet is $(\mathbf{8},\mathbf{1},1)$ or $(\mathbf{6},\mathbf{2},5/6)$, the model can evade the current bound and predicts a proton lifetime within the coverage of HK.

Figure 4

Proton partial lifetime, ${\tau }_p$, in the case when $(\mathbf{8},\mathbf{3},0)$ is the second lightest SM-decomposed multiplet. The horizontal axis is again the mass of the leading lightest multiplet. ${\alpha }_s^{(5)}(M_Z)=0.1181+3·0.0011$ (left), $0.1181-3·0.0011$ (right). The red lines show the current bound at SK (solid), and the $3\sigma$ discovery potential at HK with a 10 year exposure of 1-tank (dashed). Each blue line with a label shows the proton partial lifetime when the leading lightest multiplet is as indicated by the label. 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. Interestingly, if the leading lightest multiplet is $(\mathbf{6},\mathbf{2},5/6)$, the model can evade the current bound and predicts a proton lifetime within the coverage of HK.

Figure 5

Proton partial lifetime, ${\tau }_p$, in the case when the two light SM-decomposed multiplets do not include $(\mathbf{6},\mathbf{3},1/3)$ or $(\mathbf{8},\mathbf{3},0)$. The horizontal axis is the mass of the leading lightest multiplet. ${\alpha }_s^{(5)}(M_Z)=0.1181+3·0.0011$ (left), $0.1181-3·0.0011$ (right). The red lines show the current bound at SK (solid), and the $3\sigma$ discovery potential at HK with a 10 year exposure of 1-tank (dashed). Each blue line with a label shows the proton partial lifetime when the leading and second lightest multiplets are as indicated by the label. 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.