Proton decay testing low energy supersymmetry with precision gauge unification

Abstract

We show that gauge coupling unification in supersymmetry (SUSY) models can make a nontrivial interconnection between collider and proton decay experiments. Under the assumption of precise gauge coupling unification in the Minimal Supersymmeric Standard Model, with negligible grand unified theories threshold corrections, the low energy SUSY spectrum and the unification scale are intertwined, and the lower bound on the proton lifetime can be translated into upper bounds on SUSY masses. We find that the current limit on τðP → π 0 e þ Þ already excludes gluinos heavier than ∼70 (120 and 200) TeV if their mass ratio to winos, R ≡ M 3 /M 2 , is ∼1 (3 and 7), respectively. Next generation nucleon decay experiments are expected to bring these upper bounds down to ∼5 (10 and 15) TeV for R ∼ 1 (3 and 7). DOI: 10.1103/PhysRevD.97.035027 Proton decay would be the key evidence for grand unified theories (GUTs) [1]. Among possible decay channels, a special role is played by the p → π 0 e þ mode for which the dominant contribution may come from the D ¼ 6 operators depending almost exclusively on the X, Y boson mass and the unified gauge coupling. Unification of the gauge couplings in the minimal supersymmeric Standard Model (MSSM) as a link between the supersymmetric spectrum and the GUT spectrum and a window to the GUT physics has been studied intensively. Most such works have focused on constraining the GUT spectrum making simple assumptions on the low energy supersymmetry (SUSY) spectrum. In this study, we take the opposite approach, very similar to the one proposed in the early Ref.[2] with similar motivation.Following several studies [3,4], we assume that the unification of the gauge couplings is precise within the MSSM without threshold corrections of GUT scale particles. In fact, such a situation can be realized in a class of extra dimensional GUT models, proposed as a solution to the doublet-triplet splitting problem. In such a scenario, the relevant superheavy particles are in general mass degenerate around the compactification scale, leading to small threshold corrections. In particular, in a 6-D orbifold GUT model that breaks the GUT symmetry nonlocal by Wilson lines, the threshold correction exactly vanishes when the size of two extra dimensions are the same [5,6]. On the other hand, the GUT threshold corrections in conventional models depend on the mass ratios between superheavy particles forming incomplete multiplets (such as the colored Higgs and the X, Y bosons in the minimal SU(5)). If those superheavy particles have hierarchical mass spectra, the threshold corrections can become large enough to spoil "the success of gauge coupling unification in the MSSM" [5,8]. We stress again that all conclusions derived in this paper are subject to the assumption of the precision gauge coupling unification within the MSSM.Under the assumption of precise gauge coupling unification (GCU), we show that the low energy SUSY spectrum and the unification scale are intertwined, and the lower bound on the proton lifetime τ p→π 0...

A new approach to gauge coupling unification and proton decay

“…The general solutions can be written as ln 25 6 , 4). Substituting these numbers the solutions become [28]…”

“…where we used b i = ( 25 6 , 4). Substituting these numbers the solutions become [28] T S = M −28 3 M 32 2 µ 12 m 3 A X T 1 19 ,…”

Detectable dimension-6 proton decay in SUSY SO(10) GUT at Hyper-Kamiokande

“…Therefore, it is worth pursuing the possibility that p → π 0 e + will be observed at HK. In fact, as the LHC results imply that the SUSY particles have mass above multi-TeV scale, some people revisit the unification conditions in the context of the high-scale SUSY scenario [12,13,14,15]. As the wino and gluino are heavier, the unification scale becomes lower, and it can reach the discovery range of HK for ∼10-100 TeV wino and gluino masses.…”