Advances in High Energy Physics

Volume 2019, Article ID 3572862, 19 pages

https://doi.org/10.1155/2019/3572862

## High Scale Type-II Seesaw, Dominant Double Beta Decay within Cosmological Bound and LFV Decays in SU(5)

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

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

Received 2 September 2018; Accepted 17 December 2018; Published 3 February 2019

Guest Editor: Hiroyasu Ejiri

Copyright © 2019 M. K. Parida and Rajesh Satpathy. 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

Very recently novel implementation of type-II seesaw mechanism for neutrino mass has been proposed in grand unified theory with a number of desirable new physical phenomena beyond the standard model. Introducing heavy right-handed neutrinos and extra fermion singlets, in this work we show how the type-I seesaw cancellation mechanism works in this framework. Besides predicting verifiable LFV decays, we further show that the model predicts dominant double beta decay with normal hierarchy or inverted hierarchy of active light neutrino masses in concordance with cosmological bound. In addition a novel right-handed neutrino mass generation mechanism, independent of type-II seesaw predicted mass hierarchy, is suggested in this work.

#### 1. Introduction

Renormalizable standard model (SM) predicts neutrinos to be massless whereas oscillation experiments prove them to be massive [1–5]. All the generational mixings have been found to be much larger than the corresponding quark mixings. Theoretically [6–13] neutrino masses are predicted through various seesaw mechanisms [14–43]. In a minimal left-right symmetric [44–47] grand unified theory (GUT) like [48, 49] where parity (P) violation in weak interaction is explained along with fermion masses [50–55], a number of these seesaw mechanisms can be naturally embedded while unifying the three forces of the SM [56–72]. More recently precision gauge coupling unification has been successfully implemented in direct symmetry breaking of which may have high potential for new physics [73].

The model that predicts the most popular canonical seesaw as well as the type-II seesaw has also the ability to explain baryon asymmetry of the universe via leptogenesis through heavy RH neutrino [74] or Higgs triplet decays [75–77]. But because of underlying quark lepton symmetry [44], the type-I seesaw scale as well as RH masses are so large that the model predicts negligible lepton flavor violating (LFV) decays like , , , and . Similarly direct mediation of large mass of scalar triplet required for type-II seesaw gives negligible contribution to lepton number violating (LNV) and lepton flavor violating (LFV) decays. Ever since the proposal of left-right symmetry, extensive investigations continue in search of experimentally observable double beta decay [78–82] in the channel [83, 84]. Adding new dimension to such lepton number violating (LNV) process, the like-sign dilepton production has been suggested as a possible means of detection of -boson at accelerator energies [85], particularly the LHC [43]. However, no such signals of TeV scale have been detected so far. Even if mass and seesaw scales are large and inaccessible for direct verification, neutrinoless double beta decay () in the channel [20, 86–91] is predicted close to observable limit with yrs provided light neutrino masses predicted by such high scale seesaw mechanisms are quasidegenerate (QD) with each mass eV [78] and their sum eV. But as noted by the recent Planck data such QD type masses violate the cosmological bound [92].The fact that such QD type masses violate the cosmological bound may be unravelling another basic fundamental reason why detection of double beta decay continues to elude experimental observation for several decades. On the other hand, if neutrinos have smaller NH or IH type masses, there is no hope for detection of these LNV events in near future with RH extended SM. In other words, predicting observable double beta decay in the channel with left-handed helicities of both the beta particles has been a formidable problem confronting theoretical and experimental physicists. However, it has been shown that in case of dynamical seesaw mechanism generating Dirac neutrinos the seesaw scale is accessible for direct experimental verification [93].

The path breaking discovery of inverse seesaw [25–31] with one extra singlet fermion per generation not only opened up the neutrino mass generation mechanism for direct experimental tests, but also lifted up lepton flavor violating (LFV) decays [94] from the abysmal depth of experimental inaccessibility of negligible branching ratios () to the illuminating salvation of profound observability (Br.) [95–100] which has been discussed extensively [99, 101–118]. Despite inverse seesaw, observable double beta decay in the channel and the non-QD type neutrino masses remained mutually exclusive until both the RH neutrinos and singlet fermions () were brought into the arena of LFV and LNV conundrum through the much needed extension of the Higgs sector. The King-Kang [119] mechanism cancelled out the ruling supremacy of canonical seesaw which was profoundly exploited in models with the introduction of both the Higgs representations and [13, 84, 120–125] with successful prediction of observable double beta decay in the channel [20, 86]. Very interestingly, even though high scale type-II seesaw can govern light neutrino masses of any hierarchy, possibility of observable LFV and double beta decay prediction in the channel irrespective of light neutrino mass hierarchies has been realized at least theoretically [13, 125].

The purpose of this work is to point out that there are new interesting physics realizations with suitable extension of a non-SUSY GUT model proposed recently [126] where type-II seesaw, precision coupling unification, verifiable proton decay, scalar dark matter, and vacuum stability have been already predicted. However with naturally large type-II seesaw scale GeV, observable double beta decay accessible to ongoing experiments [78–82] is possible in this model too with QD type neutrinos only of common mass with eV like many other high scale seesaw models as noted above. In this work we make additional prediction that dominant double beta decay in the channel can be realized with NH or IH type hierarchy consistent with much lighter neutrino masses eV. Thus, this realization is consistent with cosmological bound of (1). Although such possibilities were realized earlier in with TeV scale or bosons as noted above, in without the presence of left-right symmetry and associated gauge bosons, we have shown here for the first time that the dominant double beta decay is mediated by a sterile neutrino (Majorana fermion singlet) of GeV mass of first generation. The model further predicts LFV decay branching ratios only 4–5 orders smaller than the current experimental limits. An additional interesting part of the present work is the first suggestion of a new mechanism for heavy RH mass generation that permits these masses to have hierarchies independent of conventional type-II seesaw prediction. Thus highlights of the present model are as follows:(i)first implementation of type-I seesaw cancellation mechanism leading to the dominance of type-II seesaw in ;(ii)prediction of verifiable LFV decays only orders smaller than the current experimental limits;(iii)prediction of dominant double beta decay in the channel close to the current experimental limits for light neutrino masses of NH or IH type in concordance with cosmological bound;(iv)suggestion of a new right-handed neutrino mass generation mechanism independent of type-II predicted mass hierarchy;(v)precision gauge coupling unification with verifiable proton decay which is the same as discussed in [126].

This paper is organised in the following manner. In Section 2 we briefly review the model along with gauge coupling unification and predictions of the intermediate scales. In Section 3 we discuss how type-I seesaw formula for active neutrino masses cancels out giving rise to dominance of type-II seesaw and prediction of another type-I seesaw formula for sterile neutrino masses. Fit to neutrino oscillation data is discussed in Section 4. In Section 5 we suggest a new mechanism of RH mass generation. Prediction on LFV decay branching ratios is discussed in Section 6. Lifetime prediction for double beta decay is presented in Section 7. In Section 8 we discuss the results of this work and state our conclusion. Block diagonalization procedure is explained in more detail in Appendix A.

#### 2. A Non-Supersymmetric SU(****5) Model

##### 2.1. Extension of SU(5)

As noted in [127], inclusion of the scalar with mass in the extended non-SUSY achieves precision gauge coupling unification. Then it has been shown in [126] that type-II seesaw ansatz for neutrino mass is realized by inserting the entire Higgs multiplet containing the LH Higgs triplet at the same mass scale .

The scalar singlet has played two crucial interesting roles of stabilising the SM scalar potential as well as serving as WIMP DM candidate. The introduction of at any scale GeV in this model maintains precision coupling unification. In the present model we extend the model further by the inclusion of the following fermions and an additional scalar :(i)three right-handed neutrino singlets , one for each generation, with masses to be fixed by this model phenomenology;(ii)three left-handed Majorana fermion singlets , one for each generation, similar to those introduced in case of inverse seesaw mechanism [25–31];(iii)a Higgs scalar singlet to generate mixings through its VEV.

Being singlets under the SM gauge group, they do not affect precision gauge coupling unification of [126].

##### 2.2. Coupling Unification, GUT Scale, and Proton Lifetime

As already discussed [126, 127] using renormalization group equations for gauge couplings and the set of Higgs scalars of (2), precision unification has been achieved with the PDG values of input parameters [128–130] on , resulting in the following mass scales and the GUT fine-structure constant :

Using threshold effects due to superheavy Higgs scalars [131–138], proton lifetime prediction for turns out to be in the experimentally accessible range [139]:

Extensive investigations with number of GUT extensions have been carried out with proton lifetime predictions consistent with experimental limits [140–149]. But implementation of type-II seesaw dominance due to type-I seesaw cancellation resulting in dominant LFV and LNV decays as discussed below is new especially in the context of non-SUSY .

#### 3. Cancellation of Type-I and Dominance of Type-II Seesaw

Due to introduction of heavy RHs in the present model which were absent in [126], it may be natural to presume a priori that besides type-II seesaw, type-I seesaw may also contribute substantially to light neutrino masses and mixings. But it has been noted that there is a natural mechanism to cancel out type-I seesaw contribution while maintaining dominance of inverse seesaw [84, 119, 120, 122–124] or type-II seesaw or even linear seesaw [13, 125] as the case may be. Briefly we discuss below how this cancellation mechanism operates in the present extended model resulting in type-II seesaw dominance even in the presence of heavy RHs.

The SM invariant Yukawa Lagrangian of the model is Using the VEVs of the Higgs fields and denoting , , a neutral fermion mass matrix has been obtained which, upon block diagonalization, yields mass matrices for each of the light neutrino (), the right-handed neutrino (), and the sterile neutrino () [120, 124, 125]. The block diagonalization of neutral fermion mass matrix was presented in useful format in [32] but without cancellation of type-I seesaw. Later on, this diagonalization procedure has been effectively utilized to study the type-I seesaw cancellation mechanism in models [13, 120, 124, 125].

In this model the left-handed triplet and RH neutrinos being much heavier than the other mass scales with are at first integrated out from the Lagrangian leading towhich, in the basis, gives the mass matrixwhile the heavy RH neutrino mass matrix is the other part of the full neutrino mass matrix. This mass matrix which results from the first step of block diagonalization procedure as discussed above and in the Appendix isDefining

the transformation matrix has been derived as shown in (10) [120, 125] After the second step of block diagonalization, the type-I seesaw contribution cancels out and gives in the basiswhere has been derived in (12) [120, 125]. We have used the bare mass of and VEV of to be vanishing, i.e., , , to get the form suitable for this model building.

In (11) the three matrices are the first of which is the well-known type-II seesaw formula and the second is the emergence of the corresponding type-I seesaw formula for the singlet fermion mass. The third of the above equations represents the heavy RH mass matrix.

In the third step, , , and are further diagonalized by the respective unitary matrices to give their corresponding eigenvalues:The complete mixing matrix [32, 120] diagonalizing the above neutrino mass matrix occurring in (8) and in (A.1) of the Appendix turns out to beas shown in the Appendix. In (18), , , and .

The mass of the singlet fermion is acquired through a type-I seesaw mechanism:where is the mixing mass term in the Yukawa Lagrangian (6).

#### 4. Type-II Seesaw Fit to Oscillation Data

##### 4.1. Neutrino Mass Matrix from Oscillation Data

Using diagonalization of neutrino mass matrix by the PMNS matrix where denote the mass eigen values. For neutrino mixings we use the abbreviated cyclic notations , , where are cyclic permutations of generational numbers . Following the standard parametrisation we denote the PMNS matrix [128–130]where is the Dirac CP phase and are Majorana phases.

Here we present numerical analyses within limit of the neutrino oscillation data in the type-II seesaw framework [126]. As we do not have any experimental information about Majorana phases, they are determined by means of random sampling; i.e., from the set of randomly generated values, each confined within the maximum allowed limit of , only one set of values for is chosen. Very recent analysis of the oscillation data has determined the and limits of Dirac CP phase [1]. The best fit values of in the normally ordered (NO) and invertedly ordered (IO) cases are near and , respectively, which we utilize for the sake of simplicity. A phenomenological model analysis has yielded [150].

Global fit to the oscillation data [1] is summarized below including respective parameter uncertainties at level:We denote the cosmologically constrained parameter, the sum of the three active neutrino masses, as For normally hierarchical (NH), inverted hierarchical (IH), and quasidegenerate (QD) patterns, the experimental values of mass squared differences have been fitted by the following values of light neutrino masses and the respective values of the cosmological parameter .Using oscillation data and best fit values of the mixings, we have also determined the PMNS mixing matrix numerically:

##### 4.2. Determination of Majorana Yukawa Coupling Matrix

Now inverting the relation where is the diagonalized neutrino mass matrix, we determine for three different cases and further determine the corresponding values of the matrix using where we use the predicted value of eV.

**NH**

**IH**

**QD**

Randomly chosen Majorana phases [126] , , and the central value of the Dirac phase have been used in this analysis. Using the well-known definition of the Jarlskog-Greenberg [151, 152] invariant, and keeping at its best fit values, we have estimated the predicted allowed ranges of the CP-violating parameter in both cases: where the variables have been permitted to acquire values within their respective ranges of the oscillation data. Besides these there are nonunitarity contributions which have been discussed extensively in the literature.

##### 4.3. Scaling Transformation of Solutions

In general there could be type-II seesaw models characterizing different seesaw scales and induced VEVs matching the given set of neutrino oscillation data represented by the same neutrino mass matrix. For two such models, Then the matrix in one case is determined up to good approximation in terms of the other from the knowledge of the two seesaw scales.At GeV our solutions are the same as in [126]. In view of this scaling relation, we can determine the values of the Majorana Yukawa matrix in the present case from the estimations of [126]. For example, if we choose GeV in the present case compared to GeV in [126], we rescale the solutions of [126] by a factor to derive solutions in the present case. Thus graphical representations of solutions are similar to those of [126] for GeV which we do not repeat here. The values of magnitudes of at any new scale are obtained by rescaling them by the appropriate scaling factor while the phase angles remain the same as in [126].

##### 4.4. Dirac Neutrino Mass Matrix

The Dirac neutrino mass matrix plays crucial role in predicting LFV and LNV decays. In certain models [50, 51, 125] this is usually determined by fitting the charged fermion masses at the GUT scale and equating it with the up-quark mass matrix. The fact that at the GUT scale follows from the underlying quark lepton symmetry [44] of . In itself, however, there is no such symmetry to predict the structure of in terms of quark matrices. Also in this model we do not attempt any charged fermion mass fit at the GUT scale or above it. Since the Dirac neutrino mass matrix is not predicted by the symmetry itself, for the sake of simplicity and to derive maximal effects on LFV and LNV decays, we assume to be equal to the up-quark mass matrix at the GUT scale. Noting that is singlet fermion, in the context of relevant Yukawa interaction Lagrangianthis assumption is equivalent to alignment of the two Yukawa couplings:This alignment is naturally predicted in or SO [73], but in the present case it is assumed.

We realize this matrix using renormalization group equations for fermion masses and gauge couplings and their numerical solutions [153–155] starting from the PDG values [128–130] of fermion masses at the electroweak scale. Following the bottom-up approach and using the down-quark diagonal basis, the quark masses and the CKM mixings are extrapolated from low energies using renormalization group (RG) equations [153–157]. After assuming the approximate equality at the GUT scale where is the up-quark mass matrix, the top-down approach is exploited to run down this mass matrix using RG equations [153]. Then the value of near TeV scale turns out to be

As already noted above, although on the basis of symmetry alone there may not be any reason for the rigorous validity of (35), in what follows we study the implications of this assumed value of to examine maximum possible impact on LFV and LNV decays discussed in Sections 6 and 7. Another reason is that the present assumption on may be justified in direct breaking to the SM which we plan to pursue in a future work.

#### 5. Right-Handed Neutrino Mass in SU(****5) vs SO(****10)

##### 5.1. RH Mass in SO(10)

The fermions responsible for type-I and type-II seesaw are the LH leptonic doublets and the RH fermionic singlets of three generations. In the left-handed lepton doublet and the right-handed neutrino are in the same spinorial representation . The Higgs representation contains both the left-handed and the right-handed triplets carrying ,where the quantum numbers are under the left-right symmetry group . The common Yukawa coupling in the Yukawa term generates the dilepton-Higgs triplet interactions both in the left-handed and right-handed sectors giving rise to type-I and type-II seesaw mechanisms. The RH neutrino mass is generated through the VEV of the neutral component of the of The type-II seesaw contribution to light neutrino mass iswhere is the corresponding induced VEV of Here is the quartic coupling in the part of the scalar potential Thus with type-II seesaw dominance, the predicted heavy RH neutrino masses in follow the same hierarchical pattern as the active light neutrino masses

##### 5.2. RH Mass in SU(5)

Feynman diagram for type-II seesaw mechanism in the present model is shown in Figure 1.