Advances in High Energy Physics

Volume 2018, Article ID 4078657, 21 pages

https://doi.org/10.1155/2018/4078657

## Neutrino Mass, Coupling Unification, Verifiable Proton Decay, Vacuum Stability, and WIMP Dark Matter in SU(5)

Centre of Excellence in Theoretical and Mathematical Sciences, Siksha ‘O’Anusandhan (Deemed to be University), Khandagiri Square, Bhubaneswar 751030, Odisha, India

Correspondence should be addressed to M. K. Parida; ni.ca.aos@adirapanim

Received 5 April 2018; Accepted 24 May 2018; Published 6 August 2018

Academic Editor: Farinaldo Queiroz

Copyright © 2018 Biswonath Sahoo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

Nonsupersymmetric minimal SU(5) with Higgs representations and and standard fermions in is well known for its failure in unification of gauge couplings and lack of predicting neutrino masses. Like standard model, it is also affected by the instability of the Higgs scalar potential. We note that extending the Higgs sector by and not only leads to the popular type-II seesaw ansatz for neutrino masses with a lower bound on the triplet mass GeV, but also achieves precision unification of gauge couplings without proliferation of nonstandard light Higgs scalars or fermions near the TeV scale. Consistent with recent LUX-2016 lower bound, the model easily accommodates a singlet scalar WIMP dark matter near the TeV scale which resolves the vacuum stability issue even after inclusion of heavy triplet threshold effect. We estimate proton lifetime predictions for including uncertainties due to input parameters and threshold effects due to superheavy Higgs scalars and superheavy gauge bosons. The predicted lifetime is noted to be verifiable at Super Kamiokande and Hyper Kamiokande experiments.

#### 1. Introduction

Standard model (SM) of strong and electroweak interactions has been established by numerous experimental tests, yet evidences on neutrino mass [1–5], the phenomena of dark matter [6–25], and baryon asymmetry of the universe (BAU) [8, 26–29] call for beyond standard model (BSM) physics. It is well known that grand unified theories (GUTs) [30–37] are capable of addressing a number of limitations of the SM effectively. There are interesting theories on neutrino mass generation mechanisms [38–45] based upon various seesaw mechanisms such as type-I, type-II, type-III [46–62], linear [63, 64], and inverse [65–75]. Interesting models for Dirac neutrino mass origin of the neutrino oscillation data have been also proposed [76, 77]. In the absence of experimental evidence of supersymmetry so far, nonsupersymmetric (non-SUSY) GUTs are being extensively exploited by reconciling to the underlying gauge hierarchy problem through fine-tuning [78, 79]. Higher rank GUTs like SO(10) and can not define a unique symmetry breaking path to the SM gauge theory because of large number of possibilities with one and more intermediate symmetry breakings consistent with electroweak precision data on , and [80–82]. On the other hand, the rank-4 minimal SU(5) [32] with Higgs representations and defines only one unique symmetry breaking path to the standard modelType-I seesaw [46–52] needs nonstandard heavy right-handed neutrino, linear and inverse seesaw both need nonstandard fermions and scalars, and type-III seesaw [38–45, 58–62] needs only nonstandard fermionic extension for their implementation. Out of these popular seesaw mechanisms, type-II seesaw mechanism is the one which needs a heavy nonstandard triplet scalar [52–57, 59]. With a second triplet scalar, it is also capable of predicting baryon asymmetry of the universe [57] which is one of the main motivations behind this investigation. This neutrino mass generation mechanism, gauge coupling unification, dark matter, and vacuum stability are the focus of the present work.

Like the minimal SM, with its fermions per generation and the standard Higgs doublet , the minimal SU(5) with Higgs representations and predicts neutrinos to be massless subject to a tiny eV contribution due to nonrenormalizable Planck scale effect which is nearly orders smaller than the requirement of neutrino oscillation data. As the particle spectrum below the GUT symmetry breaking scale is identically equal to the SM spectrum, like SM, the minimal GUT fails to unify gauge couplings [83–87]. Also it predicts instability of the Higgs quartic coupling at mass scales GeV [88–90] after which the coupling continues to be increasingly negative at least up to the unification scale.

A number of interesting models have been suggested for coupling unification by populating the grand desert and for enhancing proton lifetime predictions [60–62, 91–98]. In these models a number of fermion or scalar masses below the GUT scale have been utilised to achieve unification. Interesting possibility of type-III seesaw [60–62] with experimentally verifiable dilepton production [99] at LHC has been also investigated.

The other shortcoming of minimal non-SUSY SU(5) is its inability to predict dark matter which appears to belong to two distinct categories: (i) the weakly interacting massive particle (WIMP) dark matter of bounded mass TeV and (ii) the decaying dark matter which has been suggested to be a possible source of PeV energy IceCube neutrinos.

In this work we implement a novel mechanism for coupling unification and neutrino masses together. When SU(5) is extended by the addition of its Higgs representations and , it achieves two objectives: (i) neutrino mass and mixing generation through type-II seesaw mechanism and (ii) precision gauge coupling unification with experimentally accessible proton lifetime.

But this does not cure the vacuum instability problem persisting in the model as well as the need for WIMP dark matter prediction. Out of these two, as we note in this work, when the dark matter prediction is successfully inducted into the model, the other problem on vacuum stability is automatically resolved.

In contrast to the popular belief on low proton lifetime prediction of the minimal SU(5) [35], we estimate new precise and enhanced predictions of this model including threshold effects [100–108] of heavy particles near the GUT scale. Predicted lifetimes are found to be within the accessible ranges of Superkamiokande and Hyperkamiokande experimental search programmes [109].

This paper is organised in the following manner. In Section 2 we discuss neutrino mass generation mechanism in extended SU(5). Section 3 deals with the problem of gauge coupling unification. In Section 4 we make proton lifetime prediction including possible uncertainties. Embedding WIMP scalar DM in SU(5) is discussed in Section 5 with a brief outline on the current experimental status. Resolution of vacuum stability issue is explained in Section 6. We summarise and conclude in Section 7. Renormalization group equations for gauge and Higgs quartic couplings are discussed in the Appendix.

#### 2. Neutrino Mass Through Type-II Seesaw in SU(5)

As noted in Section 1, in contrast to many possible alternative symmetry breaking paths to SM from non-SUSY SO(10) and [80–82], SU(5) predicts only one symmetry breaking path which enhances its verifiable predictive capability. Fifteen SM fermions are placed in two different SU(5) representations:Lack of RH in these representations gives vanishing Dirac neutrino mass and vanishing Majorana neutrino mass at renormalizable level. Planck scale induced small Majorana masses can be generated through nonrenormalizable interaction

leading to eV which is too low to explain neutrino oscillation data. Mechanism of Dirac neutrino mass generation has been discussed [76, 77] matching the neutrino oscillation data. Using extensions of the minimal GUT type-III seesaw origin of neutrino mass has been discussed where the nonstandard fermionic triplet mediates the seesaw. This model can be experimentally tested by the production of like-sign dilepton signals at LHC.

Type-II seesaw mechanism for neutrino mass [53–57] does not need any nonstandard fermion but needs only the nonstandard left-handed Higgs scalar triplet with which directly couples with the a dilepton pair. It also directly couples to standard Higgs doublet . As such the standard Higgs VEV can be transmitted as a small induced VEV generating Majorana mass term for the light neutrinos. As this is contained in the symmetric SU(5) scalar representation , the scalar sector of the minimal GUT needs to include in addition to and .

The Yukawa Lagrangiancombined with the relevant part of the Higgs potentialgives rise to the type-II seesaw contribution. In our notation ( generation index) and which are the lepton and scalar doublet of . Here , ( are the Pauli spin matrices) and, similarly, the scalar triplet in the adjoint representation of is expressed as . The Majorana type Yukawa coupling is a matrix in flavor space and is the charge conjugation matrix. Thenwhere different components are given byA diagrammatic representation for type-II seesaw generation of neutrino mass is shown in Figure 1. From the Feynman diagram shown in Figure 1 the induced VEV of the scalar triplet is leading to the type-II seesaw formulaIt is necessary to explain the origin of the breaking scale that occurs in (4), (5), and (8) as well as the Feynman diagram of Figure 1. SU(5) invariance permits the triplet coupling leading to SM invariant coupling . Therefore, in one approach, may be treated as explicitly lepton number violating parameter. Alternatively, it is also possible to attribute a spontaneous lepton number violating origin to this parameter. Since the SM model gauge theory has to remain unbroken down to the electroweak scale, the lepton number violating scale can be generated by the VEV of a Higgs scalar that transforms as a singlet under SM. Such a singlet carrying occurs in the Higgs representation [36, 110]. The part of the SU(5) invariant potential that generates this scale isleading to . The symmetric origin of becomes more transparent if one treats SU(5) as the remnant of or higher rank GUTs like SO(10) and . If unification constraint as discussed below is ignored, the order of magnitude of can be anywhere in the range . But as we will find in the subsequent sections, gauge coupling unification in the present SU(5) framework imposes the lower bound GeV.