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

Very recently a novel implementation of type-II seesaw mechanism for neutrino mass has been proposed in SU(5) grand unified theory with a number of desirable new physical phenomena beyond the standard model.Introducing heavy right-haded neutrinos and extra fermion singlets, in this work we show how the type-I seeaw cancellation mechanism works in this SU(5) 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 mechanism for heavy right-handed neutrino mass generation independent of type-II seesaw predicted mass hierarchy, is suggested in this work.

The SO(10) model that predicts the most popular canonical seesaw as well as the type-II seesaw has also the potential to explain baryon asymmetry of the universe via leptogenesis through heavy RH neutrino [52] or Higgs triplet decays [53]. But because of underlying quark lepton symmetry [41], the type-I seesaw scale as well as RHν masses are so large that the model predicts negligible lepton flavor violating (LFV) decays like µ → eγ , τ → µγ , τ → eγ , and µ → eēe. 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 [54][55][56] in the W R −W R channel [57,58]. Adding new dimension to such lepton number violatin g (LNV) process, the like-sign dilepton production has been suggested as a possible means of detection of W R -boson at accelerator energies [59], particularly the LHC [60]. However, no such signals of TeV scale W R − have been detected so far. Even if W R mass and seesaw scales are large and inaccessible for direct verification, neutrinoless double beta decay (0ν2β) in the W L − W L channel [20,[61][62][63][64][65][66] is predicted close to observable limit with τ ββ ≥ 10 25 yrs provided light neutrino masses predicted by such high-scale seesaw mechanisms are of quasidegenerate (QD) type with masses m ν ≥ O(0.2) eV [54]. But as noted by the recent Planck data such QD type masses violate the cosmological bound [67] Σ ν ≡ 3 i=1m i < 0.23 (eV).. (1) The fact that such QD type ν masses violate the cosmological bound may be unravelling another basic frundamental 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 RHν extended SM. In other words predicting observable double beta decay in the W L − W L channel with left-handed helicities of borh the beta particles has been a formidable problem confronting theoretical and experimentral 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 [68].
The path breaking discovery of inverse seesaw [26][27][28][29][30][31][32] 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 [69] from the abysmal depth of experimental inaccessibility of negligible branching ratios ( Br.(l α → l β γ) ∼ 10 −50 ) to the illuminating salvation of profound observability ( Br. 10 −8 − 10 −16 ) [70] which has been discussed extensively [71][72][73]. Despite inverse seesaw, observable double beta decay in the W L − W L channel and the non-QD type neutrino masses remained mutually exclusive until both the RH neutrinos and singlet fermions (S i ) were brought into the arena of LFV and LNV conundrum through the much needed extension of the Higgs sector. The King-Kang [74] mechanism cancelled out the ruling supremacy of canonical seesaw which was profoundly explioted in SO(10) models with the introduction of both the SO(10) Higgs representations 16 H and 126 † H [13,58,[75][76][77][78][79] with successful prediction of observable double beta decay in the W L − W L channel [20,61]. 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 W L − W L channel irrespective of light neutrino mass hierarchies has been realized at least theoretically [13,79].
The purpose of this work is to point out that there are new interesting physics realisations with suitable extensions of a non-SUSY SU(5) GUT model proposed recently [80] 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 > 10 9.2 GeV observable double beta decay accessible to ongoing experiments [54][55][56] is possible in this model too with QD type neutrinos only of common mass with |m 0 | ≥ 0.2 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 W L − W L channel can be realised with NH or IH type hierarchy consistent with much lighter neutrino masses |m i | << 0.2 eV. Thus this realization is consistent with cosmological bound of eq.(1). Although such possibilities were realized earlier in SO (10) with TeV scale W R or Z bosons as noted above, in SU(5) without any expectation of verifiable left-right symmetry, we have shown here for the first time that the dominant double beta decay is mediated by a sterile neutrino (Majorana fermion singlet) of O(1) GeV mass of first generartion. The model further predicts LFV decay branching ratios only 4 − 5 orders smaller than the current experimental limits. An dditional interesting part of the present work is the first suggestion of a new mechanism for heavy RHν mass generation that permits these masses to have hierarchies independent of conventional type-II seesaw prediction. Some applications of such masses are briefly noted. Thus the highlights of the present model are • First implementation of the mechanism for cancellation of type-I seesaw leading to the dominance of type-II seesaw in SU(5).
• Prediction of verifiable LFV decays only 4 − 5 orders smaller than the current experimental limits.
• Prediction of dominant double beta decay in the W L − W L channel close to the current experimental limits for light neutrino masses of NH or IH type in concordance with cosmological bound.
• Suggestion of a new mechanism for right-handed neutrino mass generation independent of type-II predicted mass hierarchy.
• Precision gauge coupling unification with verifiable proton decay which is the same as discussed in [80].
This paper is organised in the following manner. In Sec.2 we briefly review the SU(5) model along with gauge coupling unification and predictions of the intermediate scales. In Sec.3 we discuss how type-I seesaw formula for active neutrinos cancels out giving rise to dominance of type-II seesaw and prediction of another type-I seesaw formula for sterile neutrino mass. Fit to neutrino oscillation data is discussed in Sec.4. In Sec.5 we present our suggestion for a new mechanism of RHν mass generation. Predictions on LFV branching ratios is discussed in Sec.6. Lifetime prediction for double beta decay is presented in Sec.7. In Sec.8 we discuss the results of this work and state our conclusion.
The scalar singlet χ S (1, 0, 1) has played the crucial interesting role of stabilising the SM scalar potential. The interjaction of 15 H at any scale > 10 9.23 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 scalars. Being singlets under the SM gauge group they do not affect precision mixing unification of ref. [80].
• Three right handed neutrino singlets N i (i = 1, 2, 3), one for each generation, with masses to be fixed by this model phenomenology.
• A Higgs scalar singlet ξ S (1, 0, 1) to generate S − N mixings through its VEV and to ensure vacuum stability of the scalar potential.

CANCELLATION OF TYPE-I AND DOMINANCE OF TYPE-II SEESAW
Due to the introdution of heavy RHνs in the present model which were absent in [80], it may be natural to presume apriori 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 maitaining dominance of inverse seesaw [58,[74][75][76][77][78] or type-II seesaw or even linear seesaw [13,79] as the case may be. Briefly we discuss below how this mechanism operates in the present extended model resulting in type-II seesaw dominance even in the presence of heavy RHνs.
The SM invariant Yukawa Lagrangian of the model is Using the VEVs of the Higgs fields and denoting M = y χ < χ S >= y χ V χ , M D = Y < Φ >,, a 9×9 neutral-fermion mass matrix has been obtained which upon block diagonalisation yields 3 × 3 mass matrices for each of the light neutrino (ν α ) , the right handed neutrino (N α ), and while the 3 × 3 heavy RH neutrino mass matrix M N is the other part of the full 9 × 9 neutrino mass matrix. This 9 × 9 mass matrixM BD which results from the first step of block diagonalization procedure as discussed above and in the appendix is Defining The transfrmation matrix W 1 has been derived as shown in eqn. (10) [75,79] After the second step of block diagonalization, the type-I seesaw contribution cancels out and gives in the (ν, S, N ) basis where W 2 has been derived in eqn. (12) [75,79]. We ahve used the bare mass of S i and VEV of χ L (2, −1/2, 1) to be vanshing i,e µ S = 0, < χ L >= 0 to get the form suiatable for this model building In eq.(11), the three 3 × 3 matrices are the first of these being the well known type-II seesaw formula and the second is the emergence of the corresponding type-I seesaw formula for sterile fermion mass. The third of the above equations represents the heavy RHν mass matrix.
In the third step, m ν , m S , and m N are further diagonalized by the respective unitary matrices to give their corresponding eigenvalues The complete mixing matrix [33,75] diagonalizing the above 9 × 9 neutrino mass matrix given in (??) turns out to be as shown in the appendix. In eqn.
The mass of the singlet fermion is aquired through a type-I seesaw mechanism where M is the N − S mixing mass term in the Yukawa Lagrangian eq.(??).

Neutrino Mass Matrix from Oscillation Data
Using diagonalisation of neutrino mass matrix (m ν ) by the PMNS matrix U PMNS where m i (i = 1, 2, 3) denote the mass eigen vlaues. For neutrino mixings we use the abbreviated cyclic notations t i = sin θ jk , c i = cos θ jk where i, j, k are cyclic permutations of generational numbers 1, 2, 3. In the standard parametrisation we [82][83][84] where δ D is the Dirac CP phase and (α M , β M ) are Majorana phases.
Here we present numerical analyses within 3σ limit of the neutrino oscillation data in the type-II seesaw framework [80]. 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 2π only one set of values for (α M , β M ) is chosen. Very recent analysis of the oscillation data has determined the 3σ and 1σ limits of Dirac CP phase δ D [1], The best fit values of δ D in the normally ordered (NO) and invertedly ordered (IO) cases are near 1.2π and 1.5π, respectively, which we utlise for the sake of simplicity.
Global fit to the oscillation data [1] is summarised below including respective parameter uncertainties at 3σ level We denote the cosmologically constrained parameter, the sum of the three active neutrino masses, The last line clearly shows violation of cosmological bound in the QD case. Using oscillation data and best fit values of the mixings we have also determined the PMNS mixing matrix numerically

Determination of Majorana Yukawa Coupling Matrix
Now inverting the relationm ν = U † P M N S M ν U * P M N S wherem ν is the diagonalised neutrino mass matrix, we determine M ν for three different cases and further determine the corresponding values of the f matrix using and keeping δ D at its best fit values we have estmted the predicted allowed ranges of the CP-Violating parameter in both cases.
where the variables have been permitted to acquire values within their respective 3σ ranges of the oscillation data. Besides these there are non-unitarity contributions which have been discussed extensively in the literature.

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 f − matrix in one case is determined up to good approximation in terms of the other from the knowledge of the two seesaw scales At M ∆ (1) = 10 12 GeV our solutions are the same as in [80]. In view of this scaling relation, we can determine the values of the Majorana Yukawa matrix in the present case from the estimations of [80]. For example, if we choose M ∆ (1) = 10 10 GeV in the present case compared to M ∆ (2) = 10 12 GeV in [80], we rescale the solutions of [80] by a factor 10 −2 to derive solutions in the present case. Thus graphical representations of solutions are similar to those of ref. [80] for M ∆ (2) = 10 12 GeV which we do not repeat here. The values of magnitudes of f ij at any new scale are obtained by rescaling them by the appropriate scaling factor while the phase angles remain the same as in [80].

Dirac Neutrino Mass Matrix
The Dirac neutrino mass matrix M D plays crucial role in predicting LFV and LNV decays.
In certain SO(10) models [45,46,79,99] this is usually determined by fitting the charged fermion masses at the GUT scale and equating it with the upquark mass matrix. The fact that M 0 D M 0 u at the GUT scale follows from the underlying quark lepton symmetry [41] of SO (10). In SU(5) itself, however, there is no such symmetry to dictate the structure of M D in terms of quark matrices. Also in this SU(5) 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 SU(5) symmetry itself, for the sake of simplicity and to derive maximal effects on LFV and LNV decays, we assume M 0 D to be equal to the up-quark mas matrix M 0 u at the GUT scale. Noting that N is SU(5) singlet fermion, in the context of relevant Yukawa interaction Lagrangian this assumption is equivalent to alighment of the two Yukawa couplings This alignment is naturally predicted in SO (10) or SO(18) [51], but in the present SU(5) case it is assumed. We realise this matrix M D using renormalisation group equations for fermion masses and gauge couplings and their numerical solutions [97] starting from the PDG values [82][83][84] 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 renormalisation group (RG) equations [97,98]. After assuming the approximate equality M 0 D M 0 u at the GUT scale where M 0 u is the up-quark mass matrix, the top-down approach is exploited to run down this mass matrix M 0 D using RG equations [97]. GeV .
As already noted above, although on the basis of SU(5) symmetry alone there may not be any reason for the rigorous validity of eq. (35), in what follows we study the implications of this assumed value of M D to examine maximum possible impact on LFV and LNV decays discussed in Sec.6 and Sec.7. Another reason is that the present assumption on M D may be justified in direct SO(10) breaking to the SM which we plan to pursue in a future work [100].

RHν 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 SO(10) the left handed lepton doublet (ν, l) T and the right-handed neutrino N are in the same representation 16 F .
In SO (10) generates the dilepton-Higgs triplet interactios 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 ∆ R The type-II seesaw contribution to light neutrino mass is Here λ 10 is the quartic coupling in the part of the scalar potential Thus with type-II seesaw dominance, the predicted heavy RH neutrino masses in SO (10) follow the same hierarchical pattern as the active light neutrino masses

RHν Mass in SU(5)
Feynman diagram for type-II seesaw mechanism in the present model is shown in Fig.1 In Figure 1: Feynman diagram representing type-II seesaw mechanim for neutrino mass generation in SU (5). Scalar fields φ, σ S and ∆ L represent SM Higgs doublet, singlet, and LH triplet as defined in the text. This diagram defines the trilinear coupling mass µ ∆ = λ σ S .
contrast to SO(10) where the LH leptonic doublet and the RHν are in the single representation 16 F , in SU(5) they are in different fermionic representations In SU(5), while the dilepton Higgs interaction is given by the RH neutrino mass is generated through The fact that N is a singlet under SU(5) forces σ S to be a singlet too . Further this singlet σ S must carry B − L = −2 as its VEV generates the heavy Majorana mass In sharp contrast to SO(10) where the LH triplet ∆ L and the RH triplet ∆ R scalars contained in the same representation 126 † H generate the type-II seesaw and M N the situation in SU(5) is different. Since LH triplet ∆ L (3, −1, 2) mediating type-II seesaw belongs to Higgs representation 15 H ⊂ SU(5) and σ S belongs to a completely different representation which is a singlet 1 ⊂ SU(5), the two relevant Majorana type couplings in general may not be equal Also this assertion is further strengthened if we do not assume SU(5) to be a remnant of SO (10). Then the RH neutrino mass hierarchy can be decoupled from the type-II seesaw prediction. It is interesting to note that in SU (5 where µ ∆ is the trilinear coupling in the potential term The VEV of this singlet σ S can explain the dynamical origin of this trilinear coupling through where λ is the quartic coupling in the potential term where the second line represents the SU (5) Thus the SU(5) model gives similar explanation for quartic coupling as in direct breaking of SO (10). But the predicted hierarchy of RHν masses may not in general follow the same hierarchical pattern as given by SO(10) as shown in eq. (43). This is precisely because the eq.(43) follows because the same diagonalisation matrix U P M N S diagonalises the LH and the RH neutrino mass matrices which is further rooted in the fact that same Majorana coupling f 10 that generates the type-II seesaw mass term also generates M N . But because of the general possibility f N = f , the RHνs may acquire a completely different pattern depending upon the value of f N . Unlike SO(10), these masses are also allowed to be quite different from the type-II seesaw scale.
Even if the value of v σ may be needed to be near M ∆ L , the value of M N is allowed to be considerably lower by finetuning the value of f N . Our LFV and LNV decay phenomenology as discussed below may need M N = 1 − 10 TeV which is realizable using this new technique in SU (5). In contrast SO(10) needs U (1) R × U (1) B−L or SU (2) R × U (1) B−L gauge symmetry and hence new gauge bosons near the TeV scale to generate such RHν masses which should be detected at LHC [58,79]. Thus a new mechanism for RHν mass emerges here by noting the coupling f N = f which has the potential to generate RHν masses in the range 100 − 10 15 GeV. Thus the RHν mass predictions in the two GUTs in the presence of type-II seesaw dominance are Type-II Seesaw Dominated SO(10):- Type-II Seesaw Dominated SU (5):- Here m i , i = 1, 2, 3 represents the three mass eigen values of light neutrinos. It is to be noted that m i is absent in the RHS of eq.(56) in the SU(5) case.

LEPTON FLAVOR VIOLATIONS
In the SM extensions there has been extensive investigation of lepton flavor violating phenemena l α → l β + γ and other processes like µ → eēe including unitarity violations [71][72][73]. In the flavor basis we use the standard charged current Lagrangian In predicting the LFV branching ratios we have used the relevant formulas of [71] while assuming a simplifying diagonal structure for M, which, in comdination with eq.35), gives the elements of the ν − S mixing matrix The S − N mixing matrix Noting that the physical neutrino flavor state ν α is a mixture ofν,Ŝ andN where U ∼ U P M N S and the other two mixings violate unitarity. For large M N M the third term in the RHS of eq.(61 can be dropped leading to the unitarity violation parameter η where There has been extensive discussion on the constraint imposed on this parameter [72,73]. The largest out of these is η τ τ ≤ 0.0027. Theoretically In the completely degenerate case of S − N mixing, The RH neutrinos in the present model being degenerate of masses M N i m S i have much less significant contributtions than the singlet fermions. The predicted branching ratios being only few to four orders less than the current experimental limits [70] are verifiable by ongoing searches, For the sake of comoleteness we present the variation of LFV decay branching ratios as a function of the lightest neutrino mass in Fig. 2. In this approach the LFV decay rate mediated by the W L boson in the loop depends predominantly upon N − S mixing matrix M and the Dirac neutrino mass matrix M D , although subdominantly upon the RHν mass matrix M N . However in the high scale type-II seesaw ansatz in this case LFV decay rate is independent of light neutrino masses. This behavior of LFV decay rates are clearly exhibited in Fig.2 where the three branching ratios have maintained constancy with the variation of m ν .
7 DOMINANT W L − W L -CHANNEL DOUBLE BETA DE-CAY WITHIN COSMOLOGICAL BOUND

Double Beta Decay Mediation by Sterle Neutrinos
As the W R boson has mass > 10 15 GeV and the doubly charged Higgs bosons have masses > 10 9.2 GeV, they have negligible contributions for direct mediations of 0νββ process. Feynman diagrams for 0νββ decay amplitude due to the exchanges of Majorana fermions ν, S, and N are shown in Fig. 3. In Fig.4 we present Feynman diagram for 0νββ decay amplitude due to the sterile neutrino exchange where its mass insertion has been explicitly indicated. Mass  Table 1. We have used the singlet fermion mass seesaw formula of eq.(15) and M N 1 = M N 2 = M N 3 = 4000 GeV. These solutions are displayed in Fig.5.
We use normalisations necassary for different contributions [101,102], due to exchanges of light-neutrinos, sterile neutrinos, and the heavy RH neutrinos in the W L − W L channel. They lead to the inverse half life [75,78,79], Here G 01 = 0.686 × 10 −14 yrs −1 , M 0ν ν = 2.58 − 6.64, and K 0ν = 1.57 × 10 −25 yrs −1 eV −2 . In eq.(67) the three effective mass parametes have been defined as with The quantitym S i is the i-th eigen value of the S− fermion mass matrix m S . The magnitude of neutrino virtuality momentum |p| has been estimated to be in the allowed range |p| = 120 MeV−200 MeV [101,102]. The RHνs being much heavier than the singlet fermions, their contributions have been neglected.

Singlet Fermion Assisted Enhanced Double Beta Decay Rate
We use neutrino oscillation date to estimate M ee ν for NH and IH cases with the values of Dirac phase and Majorana phases as discussed above. We further use the values of M i from Table 1 and Fig. 5 and the Dirac neutrino mass matrix from eq.(35 to estimate M ee S while treating the RHν mass at its assumed degenerate value of M N i = 4TeV(i = 1, 2, 3). The variation of effective parameter m ee as a function of lightest neutrino mass is shown in Fig.6 when m s 1 = 2 GeV.
As noted from the analytic formulas the effective mass parameter in the singlet femion dominated case being inversely proportional to m s 1 , it will proportionately decrease for the larger value of the mediating particle mass. This feature has been shown in Fig.7. We present predictions of double-beta decay half life as a function of the singlet fermion mass in Fig.8. It is clear that while for m s 1 = 2 GeV the half life saturates the current expeerimental limit, for larger masses the halftife increases. Neglecting heavy RHν contribitions but including those due to the lightest sterile neutrino and the IH type light neutrinos our predictions of half life as a function of the lightest sterile neutrino mass is shown in Fig. 9 Predicted lifetimes are seen to decrease with increasing sterile neutrino mass. The sterile neutrino exchange contribution completely dominates over light neutrino exchange contributions for m S 1 = 1.3 − 7 GeV in case of IH but for m S 1 = 1.5 − 20 GeV in case of NH. At m S 1 1.5GeV both types of solutions saturate the current laboratory limits reached by deifferent experimental groups . For double beta decay half-life expectations in standard and non-standard scenarios see ref. [107].

SUMMARY, DISCUSSION AND CONCLUSION
A recently proposed scalar extension of minimal non-SUSY SU(5) GUT has been found to realize precision gauge coupling unification, high scale type-II seesaw ansatz for neutrino masses, and prediction of a WIMP scalar DM candidate that also completes vacuum stability of the scalar potential. But the LFV decays are predicted to have negligible rates inaccessible to ongoing searches in foreseeable future. Like wise experimentally verifiable double beta decay rates measurable by different search experiments are possible only for quasi-degenerate neutrino mass spectrum with large common mass scale |m 0 | ≥ 0.2 that violates the recently measured cosmological bound i m i ≤ 0.1 eV. In order to remove these deficits we have extended this model by the addiion of three RHνs, three extra Majorana fermion singlets S i (i = 1, 2, 3) and a scalar singlet ξ S (1, 0, 1) that generates N − S mixing mass term through its vacuum expectation value. In the original thory of type-I seesaw cancellation mechanism, although the choice of particles is same as N i , S i and ξ S (1, 0, 1), the neutrino mass is given by double seesaw [74]. Further there is no grand unification of gauge couplings or prediction of proton decay in this model [74], and the scalar potential of the model has vacuum instability . In addition the N i are not gauged. The model does not predict dominant contributions to double beta decay through this mechanism with NH or IH type neutrin masses. In non-SUSY SO(10) models of unification of three forces, implementing the cancellation of type-I seesaw [58,75,78], the TeV scale RH neutrinos are gauged but the neutrino masses are controlled by inverse seesaw. But in [13,79] the RHνs are gauged and the neutrino mass formula is linear seesaw or type-II seesaw [13]. In all type-II seesaw dominated SO(10) models, the RHν masses have the same hierarchy as the left-handed neutrino masses:M N 1 : M N 2 : M N 3 :: m 1 : m 2 : m 3 . This happens precisely because the left-handed and the right-handed dilepton Yukawa interactions originate from the same SO(10) invariant term: f 16 F 16 F 126 † . In SU(5), however, as the LH triplet ∆ L (3, −1, 1) generating type-II seesaw and the singlet σ S (1, 0, 1) generating RHνs belong to different scalar representations 15 H ⊂ SU (5) and 1 H ⊂ SU (5), respectively, they can possess different Majorana couplings in their respecive Yukawa interactions:f ll∆ L C and f N σ S N N . Because of this reason the the generated RHν masses through M N = f N σ s no longer follows the predicted type-II hierarchical pattern. Then the allowed fine tuning |f N | << |f | permits M N ∼ O(1 − 10) TeV RH neutrino mass scale even though, unlike SO(10) models, there are no low mss W R or Z bosons at this scale in this SU(5) model. The apprehension of unacceptably large active neutrino mass generation through type-I seesaw mechanism is rendered inoperative through the well established procedure of cancellation mechanism that is also shown to operate profoundly in this SU(5) model. Such RHνs generating N − S mixing mass M O(100 − 1000) GeV now reproduce the well known results on LFV decay branching ratios only 4 − 5 orders lower than the current experimental limit as well as the extensively investigated non-unitarity effects. Through the sterile neutrino canonical seesaw formula emerging from this cancellation mechanism (in the presence of For larger values of m S 1 the predicted decay rate decreases and the sterile neutrino contribution becomes negligible for m s i >> 50 GeV. In the limiting case when all the singlet fermion masses have such large values, the double beta decay rates asymptotically approach the respective standard NH or IH type contributions. The new mechanism of RHν mass generation also allows the second and the third generation sterile neutrino masses to be quasi-degenerate (QD) near 1 − 10 TeV scale while keeping m S 1 ∼ 1 − 10 GeV suitable for dominant double beta decay mediation. There is a possibility that such TeV scale QD masses while maintaining observable predictions on LFV decays can effectively generate baryon asymetry of the universe via resonant leptogenesis [79]. Vacuum stability of the scalar potential can be implemented though the scalar singlet ξ S (1, 0, 1) following the method of [103,104]. A scalar singlet DM can be easily accommodated as discussed in [80]. Irrespective of scalar DM, the model can also accommodate a Majorana fermion singlet dark matter [105] which can emerge from the additional fermionic representation 24 F ⊂ SU (5) .
The predictions of new fermions has an additional advantage over scalars as these masses are protected by leptonic global symmetries [106]. The predictions of such Majorana type sterile neutrinos can be tested by high enegy and high luminousity accelerators through their like-sign dilepton production processes [108]. For example at LHC they can mediate the process pp → W L X → l ± l ± jjX where the jets could manifest as mesons. It would be quite interesting to examine emergence of such SU(5) theory as a remnant of SO(10) or E 6 GUTs.
We conclude that even in the presence of SM as effective gauge theory descending from a suitable SU(5) extension, it is possible to predict experimentally accessible double beta decay rates in the W L − W L channel satisfying the cosmological bound on active neutrino masses as well as verfiable LFV decays. The RHν masses can be considerably different from those constrained by conventional type-I or type-II seesaw frameworks which are instrumental in predicting interesting physical phenomena even if there are no non-standard heavy gauge bosons anywhere below the GUT scale.

ACKNOWLEDGMENT
M. K. P. thanks the Science and Engineering Research Board, Department of Science and Technology, Government of India for grant of research project SB/S2/HEP-011/2013. R.S. thanks Siksha 'O' Anusandhan University for research fellowship.