Not Even Decoupling Can Save Minimal Supersymmetric SU(5)

TL;DR

This work shows that the minimal SUSY SU(5) grand unified theory is incompatible with the Super-Kamiokande bound on proton decay via p rrow K^+ \\bar{\\nu}, by tying the color-triplet mass M_{H_C} to precise gauge-coupling unification and experimental inputs through RGEs. It demonstrates that decoupling the first two generations of sfermions does not salvage the model, since the dominant contributions come from third-generation sparticles, particularly higgsinos, leading to proton lifetimes far below experimental limits. The paper also surveys viable routes to suppress dimension-five decay or to alter the high-scale spectrum (e.g., via additional Higgs multiplets, extra dimensions, PQ symmetry, or missing-partner constructions) and discusses how dimension-six proton decay from X,Y gauge-boson exchange can still probe or constrain flipped SU(5) and related theories. Overall, the minimal framework is excluded, but the authors highlight several extensions that could remain viable and emphasize that upcoming experiments targeting dimension-six channels could provide crucial tests of GUT scenarios.

Abstract

We make explicit the statement that Minimal Supersymmetric SU(5) has been excluded by the Super-Kamiokande search for the process $p \to K^{+} \overlineν$. This exclusion is made by first placing limits on the colored Higgs triplet mass, by forcing the gauge couplings to unify. We also show that taking the superpartners of the first two generations to be very heavy in order to avoid flavor changing neutral currents, the so-called ``decoupling'' idea, is insufficient to resurrect the Minimal SUSY SU(5). We comment on various mechanisms to further suppress proton decay in SUSY SU(5). Finally, we address the contributions to proton decay from gauge boson exchange in the Minimal SUSY SU(5) and flipped SU(5) models.

Figures (4)

• Figure 1: The dimension five operator results from the exchange of the colored Higgs triplet. The super-particles are then removed from the initial state by chargino exchange. Wino exchange is shown here, but there is an analogous diagram which involves higgsino exchange.
• Figure 2: Plot showing 68% and 90% contours allowed by the renormalization group analysis for the color Higgs triplet mass, $M_{H_{C}}$, and the GUT scale, $M_{GUT} \equiv (M_{\Sigma} M_{V}^{2})^{1/3}$.
• Figure 3: A contour plot of the proton partial lifetime, $\tau(p \to K^{+} \bar{ \nu})$, in the case where the $1^{st}$ and $2^{nd}$ generation scalars are taken to be 10 TeV. The third generation scalars are taken to have masses order 1 TeV, except for the stops, which are given soft masses of 800 GeV and 400 GeV. We fix tan $\beta$ to be 2.1. Note that the lifetime is approximately proportional to $\mu$, and essentially independent of $M_{2}$. The shaded region is excluded by chargino searches at LEP II. Lifetimes for other values of $M_{H_{C}}$ can be found by noting that the lifetime goes as $M_{H_{C}}^{2}$.
• Figure 4: A plot of proton partial lifetime, $\tau(p \to K^{+} \bar{\nu})$, vs. $\tan \beta$. Top squark masses are 400 GeV and 800 GeV, while all other $3^{rd}$ generation sparticles have masses are set to 1 TeV. All other variables are fixed as stated. It is seen that the lifetime peaks for values of tan $\beta$ slightly greater than 2 in this case. Lifetimes for other values of $M_{H_{C}}$ can be found by noting that the lifetime goes as $M_{H_{C}}^{2}$.