Proton decay prediction from a gauge-Higgs unification scenario in five dimensions

The Higgs boson mass and top quark mass imply that the Higgs quartic coupling vanishes around the scale of ${10}^9–{10}^{13}\mathrm{GeV}$, depending on the precise value of the top quark mass. The vanishing quartic coupling can be naturally addressed if the Higgs field originates from a five-dimensional gauge field and the fifth dimension is compactified at the scale of the vanishing Higgs quartic coupling, which is a scenario based on gauge-Higgs unification. We present a general prediction of the scenario on the proton decay process $p\to {\pi }^0{e}^{+}$. In many gauge-Higgs unification models, the first-generation fermions are localized towards an orbifold fixed point in order to realize the realistic Yukawa couplings. Hence, four-fermion operators responsible for the proton decay can appear with a suppression of the five-dimensional Planck scale (not the four-dimensional Planck scale). Since the five-dimensional Planck scale is connected to the compactification scale, we have a correlation between the proton partial decay width and the top quark mass. We show that the future Hyper-Kamiokande experiment may discover the proton decay if the top quark pole mass is larger than about 172.5 GeV.

Figure 1

RG running of the Higgs quartic coupling in the SM, for three cases where the top quark pole mass is given by $m_t^{\text{pole}}=171.44\mathrm{GeV}$ (upper dashed line), 172.84 GeV (middle solid line) and 174.24 GeV (lower dashed line). The parameters other than the top quark mass are fixed as $m_h=125.09\mathrm{GeV}$, $M_W=80.384\mathrm{GeV}$ and ${\alpha }_S(M_Z)=0.1184$.

Figure 2

The correlation between the top quark pole mass $m_t^{\text{pole}}$ and the inverse of the proton decay partial width $1/\mathrm{\Gamma }(p\to {\pi }^0{e}^{+})$. The factor $(|\beta h_1+\beta h_2+\alpha h_4{|}^2+|\alpha h_3+\beta h_5{|}^2)$ in Eq. (8) is varied from $10|\alpha {|}^2$ to $0.1|\alpha {|}^2$ with $|\alpha |=0.009{\mathrm{GeV}}^3$, and the lower dashed, solid and upper dashed curves correspond to the cases when it equals $10|\alpha {|}^2$, $|\alpha {|}^2$ and $0.1|\alpha {|}^2$, respectively. The $2\sigma$ experimental bound on $1/\mathrm{\Gamma }(p\to {\pi }^0{e}^{+})$ obtained at Super-Kamiokande [11] is shown by the solid horizontal line, and the $2\sigma$ sensitivity expected at Hyper-Kamiokande [12] is shown by the dotted horizontal line. The $2\sigma$ range of the latest result of the top quark mass measurement by the ATLAS Collaboration [2] is shown by the vertical lines, with the solid one corresponding to the central value and the dashed ones to the $2\sigma$ range.