Flipped SU(5) GUT phenomenology: proton decay and $$\mathbf {g_\mu - 2}$$

We consider proton decay and $$g_\mu - 2$$ g μ - 2 in flipped SU(5) GUT models. We first study scenarios in which the soft supersymmetry-breaking parameters are constrained to be universal at some high scale $$M_{in}$$ M in above the standard GUT scale where the QCD and electroweak SU(2) couplings unify. In this case the proton lifetime is typically $$ > rsim 10^{36}$$ ≳ 10 36 years, too long to be detected in the foreseeable future, and the supersymmetric contribution to $$g_\mu - 2$$ g μ - 2 is too small to contribute significantly to resolving the discrepancy between the experimental measurement and data-driven calculations within the Standard Model. However, we identify a region of the constrained flipped SU(5) parameter space with large couplings between the 10- and 5-dimensional GUT Higgs representations where $$p \rightarrow e^+ \pi ^0$$ p → e + π 0 decay may be detectable in the Hyper-Kamiokande experiment now under construction, though the contribution to $$g_\mu -2$$ g μ - 2 is still small. A substantial contribution to $$g_\mu - 2$$ g μ - 2 is possible, however, if the universality constraints on the soft supersymmetry-breaking masses are relaxed. We find a ‘quadrifecta’ region where observable proton decay co-exists with a (partial) supersymmetric resolution of the $$g_\mu - 2$$ g μ - 2 discrepancy and acceptable values of $$m_h$$ m h and the relic LSP density.

Confronting SO(10) GUTs with proton decay and gravitational waves

Grand Unified Theories (GUT) predict proton decay as well as the formation of cosmic strings which can generate gravitational waves. We determine which non-supersymmetric SO(10) breaking chains provide gauge unification in addition to a gravitational signal from cosmic strings. We calculate the GUT and intermediate scales for these SO(10) breaking chains by solving the renormalisation group equations at the two-loop level. This analysis predicts the GUT scale, hence the proton lifetime, in addition to the scale of cosmic string generation and thus the associated gravitational wave signal. We determine which SO(10) breaking chains survive in the event of the null results of the next generation of gravitational waves and proton decay searches and determine the correlations between proton decay and gravitational waves scales if these observables are measured.

Nonlocal SU(5) GUT

We show that in nonlocal generalization of standard nonsupersymmetric SU(5) GUT, it is possible to solve the problems with the proton lifetime and the Weinberg angle without introduction of additional particles in the spectrum of the theory. Nonlocal scale [Formula: see text] responsible for ultraviolet cutoff coincides (up to some factor) with GUT scale [Formula: see text]. We find that in the simplest nonlocal modification of the SU(5) model, [Formula: see text]GeV. In the general case, the value of [Formula: see text] is an arbitrary and the most interesting option [Formula: see text] could be realized.

Observable proton decay in flipped SU(5)

We explore proton decay in a class of realistic supersymmetric flipped SU(5) models supplemented by a U(1)R symmetry which plays an essential role in implementing hybrid inflation. Two distinct neutrino mass models, based on inverse seesaw and type I seesaw, are identified, with the latter arising from the breaking of U(1)R by nonrenormalizable superpotential terms. Depending on the neutrino mass model an appropriate set of intermediate scale color triplets from the Higgs superfields play a key role in proton decay channels that include p → (e+, μ+) π0, p → (e+, μ+) K0, p →$$ \overline{v}{\pi}^{+} $$ v ¯ π + , and p →$$ \overline{v}{K}^{+} $$ v ¯ K + . We identify regions of the parameter space that yield proton lifetime estimates which are testable at Hyper-Kamiokande and other next generation experiments. We discuss how gauge coupling unification in the presence of intermediate scale particles is realized, and a Z4 symmetry is utilized to show how such intermediate scales can arise in flipped SU(5). Finally, we compare our predictions for proton decay with previous work based on SU(5) and flipped SU(5).

Realizing unification in two different SO(10) models with one intermediate breaking scale

We derive the threshold corrections in $$\text {SO}(10)$$ SO ( 10 ) grand unified models with the intermediate symmetry being flipped $$\,\text {SU}(5)\times \text {U}(1)$$ SU ( 5 ) × U ( 1 ) or $$\,\text {SU}(3)\times \,\text {SU}(2)\times \text {U}(1)\times \text {U}(1)$$ SU ( 3 ) × SU ( 2 ) × U ( 1 ) × U ( 1 ) , with the masses of the scalar fields set by the survival hypothesis. These models do not achieve gauge coupling unification if the matching conditions do not take threshold corrections into account. We present results showing the required size of threshold corrections for any value of the intermediate and unification scales. In particular, our results demonstrate that both of these models are disfavored since they require large threshold corrections to allow for unification with a predicted proton lifetime above current experimental bounds.

Threshold effects in SO(10) models with one intermediate breaking scale

Despite the successes of the Standard Model of particle physics, it is known to suffer from a number of deficiencies. Several of these can be addressed within non-supersymmetric theories of grand unification based on $$\text {SO}(10)$$ SO ( 10 ) . However, achieving gauge coupling unification in such theories is known to require additional physics below the unification scale, such as symmetry breaking in multiple steps. Many such models are disfavored due to bounds on the proton lifetime. Corrections arising from threshold effects can, however, modify these conclusions. We analyze all seven relevant breaking chains with one intermediate symmetry breaking scale, assuming the “survival hypothesis” for the scalar masses. Two are allowed by proton lifetime and two are disfavored by a failure to unify the gauge couplings. The remaining three unify at a too low scale, but can be salvaged by various amounts of threshold corrections. We parametrize this and thereby rank the models by the size of the threshold corrections required to save them.

Proton decay and the quantum structure of space–time

Virtual black holes in noncommutative space–time are investigated using coordinate coherent state formalism such that the event horizon of a black hole is manipulated by smearing it with a Gaussian of width [Formula: see text], where θ is the noncommutativity parameter. Proton lifetime, the main associated phenomenology of the noncommutative virtual black holes, has been studied, first in four-dimensional space–time and then generalized to D dimensions. The lifetime depends on θ and the number of space–time dimensions such that it emphasizes on the measurement of proton lifetime as a potential probe for the microstructure of space–time.

Conformal GUT inflation, proton lifetime and non-thermal leptogenesis

In this paper, we generalize Coleman–Weinberg (CW) inflation in grand unified theories (GUTs) such as $$\text {SU}(5)$$SU(5) and $$\text {SO}(10)$$SO(10) by means of considering two complex singlet fields with conformal invariance. In this framework, inflation emerges from a spontaneously broken conformal symmetry. The GUT symmetry implies a potential with a CW form, as a consequence of radiative corrections. The conformal symmetry flattens the above VEV branch of the CW potential to a Starobinsky plateau. As a result, we obtain $$n_{s}\sim 1-\frac{2}{N}$$ns∼1-2N and $$r\sim \frac{12}{N^2}$$r∼12N2 for $$N\sim $$N∼ 50–60 e-foldings. Furthermore, this framework allow us to estimate the proton lifetime as $$\tau _{p}\lesssim 10^{40}$$τp≲1040 years, whose decay is mediated by the superheavy gauge bosons. Moreover, we implement a type I seesaw mechanism by weakly coupling the complex singlet, which carries two units of lepton number, to the three generations of singlet right handed neutrinos (RHNs). The spontaneous symmetry breaking of global lepton number amounts to the generation of neutrino masses. We also consider non-thermal leptogenesis in which the inflaton dominantly decays into heavy RHNs that sources the observed baryon asymmetry. We constrain the couplings of the inflaton field to the RHNs, which gives the reheating temperature as $$10^{6}\text { GeV}\lesssim T_{R}<10^{9}$$106GeV≲TR<109 GeV.