Left-right models with light neutrino mass prediction and dominant neutrinoless double beta decay rate

In TeV scale left-right symmetric models, new dominant predictions to neutrinoless double beta decay and light neutrino masses are in mutual contradiction because of large contribution to the latter through popular seesaw mechanisms. We show that in a class of left-right models with high-scale parity restoration, these results coexist without any contravention with neutrino oscillation data and the relevant formula for light neutrino masses is obtained via gauged inverse seesaw mechanism. The most dominant contribution to the double beta decay is shown to be via $W^-_L- W^-_R$ mediation involving both light and heavy neutrino exchanges, and the model predictions are found to discriminate whether the Dirac neutrino mass is of quark-lepton symmetric origin or without it. We also discuss associated lepton flavor violating decays.

In TeV scale left-right symmetric models, new dominant predictions to neutrinoless double beta decay and light neutrino masses are in mutual contradiction because of large contribution to the latter through popular seesaw mechanisms. We show that in a class of left-right models with high-scale parity restoration, these results coexist without any contravention with neutrino oscillation data and the relevant formula for light neutrino masses is obtained via gauged inverse seesaw mechanism. The most dominant contribution to the double beta decay is shown to be via W − L −W − R mediation involving both light and heavy neutrino exchanges, and the model predictions are found to discriminate whether the Dirac neutrino mass is of quark-lepton symmetric origin or without it. We also discuss associated lepton flavor violating decays.

I. INTRODUCTION:
Evidences of tiny neutrino masses uncovered by the solar, atmospheric, and reactor neutrino oscillation experiments while calling for physics beyond the Standard Model (SM) might be strongly hinting at the fundamental nature of the particle i.e. whether Dirac [1] or Majorana [2]. In fact popular theories based upon seesaw mechanisms like type-I seesaw [3], type-II [4,5], type-III [6,7], inverse seesaw [8][9][10][11], and others [14][15][16]18] come out with natural predictions of light Majorana neutrino masses. With lepton number violating mass insertion term by two units, confirmation of any events at the experimental search programmes for the neutrinoless double beta decay (0ν2β) would not only indicate the Majorana nature of the particles, but also it would strongly support the underlying seesaw mechanism for their mass generation. There have been attempts [19][20][21][22][23] on the experimental side to observe such a rare process, even with a present claim [24] while others are trying to improve the life time for this 0ν2β process [25][26][27]. So far, the Heidelberg-Moscow experiment using 76 Ge [24] has given the best limit on the half life, T 1/2 < 3 × 10 25 Yrs. which gives an upper bound on effective neutrino mass, m eff ≤ 0.21 − 0.53 eV. There are several interesting discussions and models using different seesaw mechanisms [28][29][30][31][33][34][35][36][37][38] exploring possible non-standard contributions to 0ν2β transition.
Another important mysterious phenomenon of SM, namely, the origin of parity violation as monopoly of weak interactions, has been suggested to be having its underlying origin in the left-right (LR) symmetric interactions [39] which could be through the existence of mirror particles [40] of the SM or via left-right symmetric gauge theories [41,42]. A very attractive aspect of LR gauge theory is its potential to explain the origin of parity (P ) and CP violations in weak interactions and small neutrino masses. If left-right gauge theory has to make any significant impact on weak interactions phenomenology, the associated W ± R and Z R boson masses have to be low. While current searches at the Large Hadron Collider restricts the lower bound on the scale of the RH gauge boson masses (M R ) to be O(1) TeV, K L − K S mass difference gives M R > 2.5 TeV [43]. Such a low scale W R boson associated with right-handed charged currents can give additional contributions to 0ν2β and can be also accessible to LHC and future accelerator searches. As a result of this, there can be various non-standard contributions to 0ν2β in LR gauge theories mediated by: (1.) two W L gauge bosons (associated with left-handed currents), (2.) two W R gauge bosons (associated with right-handed currents), (3.) one W L and one W R gauge boson at each vertex (mixed diagram) accompanied by both light and heavy neutrinos [33,34]. In addition, there could be other contributions to 0ν2β in LR model due to doubly charged Higgs scalar exchanges where Majorana neutrino mass insertion has no role to play [32]. It is important to note here that the contributions to 0ν2β from the mixed diagram has been either ignored or considered to be sub-dominant [44], although this has been taken into account in the inverse process e − e − → W − L W − R in Ref. [45] for linear collider searches.
The natural TeV mass scale for RH Majorana neutrinos in conventional low scale LR gauge models emphasizing upon light neutrino mass generation mechanisms however predicts very large contribution to the light neutrino masses through canonical or type-II seesaw mechanisms [4,41,42]. Thus, it turns out that new dominant contributions to observable neutrinoless double beta decay (0ν2β) can not coexist with the experimentally determined tiny neutrino masses [46]. Alternatively, interesting proposals have been advanced where type-II seesaw dominance [33,34] has been invoked by suppressing Dirac neutrino mass matrix in which case LR gauge theories may have only sub-dominant roles to play in representing charged fermion masses. The purpose of this letter is two fold: while showing that a crossed diagram with simultaneous W − L and W − R exchanges predicts the most dominant contribution to the (0ν2β), we provide a class of TeV scale left-right gauge theories where this is implemented without any suppression of naturally permitted Dirac neutrino masses and without any contravention with the neutrino oscillation data. The neutrino mass generation mechanism in these models turns out to be through gauged inverse seesaw. II. THE MODEL: In conventional LR gauge theories, the type-I [3] and type-II seesaw [4] contributions to light neutrino masses are where the Dirac neutrino mass matrix M D is similar to the charge lepton mass matrix, or the up-quark mass matrix if the model has its origin from Pati-Salam symmetry. The induced triplet vacuum expectation value is v L = λ eff v 2 wk /M ∆L . Then the natural seesaw scales consistent with neutrino oscillation data are M N ≥ (10 11 − 10 14 ) GeV and the TeV scale LR gauge models relevant for 0ν2β are ruled out. We now construct a class of LR gauge models where W ± R and M N are allowed near the TeV scale which contribute predominantly to 0ν2β, yet the model does not upset small neutrino mass predictions consistent with the neutrino oscillation data. In our model although the parity restoration scale is large, yet the asymmetric left-right (LR) gauge theory survives down to the TeV scale subsequent to the D-parity breaking [47]. To implement the idea we use the set of Higgs scalars with their gauge quantum numbers under G 2213 σ(1, It is well known that by assigning large parity breaking vacuum expectation value (vev); σ ∼ M P , the model gives all the left-handed (LH) Higgs scalars to have heavy masses i.e. O(M P ) while those of the right-handed (RH) scalars can have much lighter masses near the TeV scale with In fact M ∆R and M χR can have any value below M P depending upon the degree of fine tuning in λ and λ ′ . The asymmetry in the Higgs sector at the energy scales below µ ∼ M P causes asymmetry in the gauge couplings, g 2L = g 2R for the surviving left-right gauge group. Alternatively, the asymmetric LR model may emerge from high scale Pati-Salam symmetry SU (2) L × SU (2) R × SU (4) C × D (g 2L = g 2R ) with similar choice on the Higgs scalars. In particular, we examine the TeV scale phenomenology for neutrino masses and 0ν2β with the following two possible cases of symmetry breaking: A: One important difference between the two scenarios is that in model-A, the Dirac neutrino mass matrix is similar to the charged lepton mass matrix while in model-B, it is similar to up-quark mass matrix. In addition to the standard 16-fermions of each generation, we require one additional fermion singlet for each generation (S i , i=1, 2, 3) which is essential for the implementation of inverse seesaw mechanism [9] or, the so called extended seesaw mechanism [16][17][18]. The renormalizable Yukawa Lagrangian near the TeV scale with asymmetric LR gauge theory then turns out to be where µ S is the singlet fermion mass matrix. We break the LR gauge theory spontaneously to SM by the vev ∆ 0 The SM breaks to the low energy symmetry by the VEV of the SM Higgs doublet in Φ. With this structure of the Yukawa Lagrangian, the full (9 × 9) neutrino mass matrix in the (ν L , N R , S L ) basis is given by For implementation of the light neutrino mass generation mechanism the desired hierarchy M N ≫ M ≫ M D ≫ µ S with a fine tuned small lepton number violating parameter µ S can be easily satisfied in the model after spontaneous symmetry breaking. Since the right-handed neutrinos are assumed to be larger than other mass scales, they eventually decouple at low scales [16][17][18]. It is important to note that this extended seesaw scenario is very different from the inverse seesaw scenario [8,9,11] due to the simultaneous presence of both the heavy and small lepton number violating scales M N and µ S . Complete block diagonalization of eq. (4) gives the usual inverse seesaw formula for light neutrino masses The relevant charged current interactions of leptons for this TeV scale LR gauge theory in the flavor basis is given by where, in terms of mass eigenstates (ν mi , S mj , N m k ) [35], The non-unitarity matrices in our model are X In particular, we show that a dominant contribution to 0νββ arises due to mixed diagrams with simultaneous mediation of W − L and W − R bosons accompanied by light left-handed neutrinos and heavy right-handed Majorana neutrinos [34,45] as shown in Fig. 1. We present analytic expressions for two most dominant contributions to the effective mass term and compare them with the standard contribution, • m ee ν : which is analogous to the standard contributions, in this model, • m ee N : which originates from the mediation of two W R 's with the exchange of heavy RH Majorana neutrinos, • m ee νN : which originates from simultaneous mediation of W − L and W − R and involves the Dirac mass matrix M D m ee where, in our model, ζ LR = LR mixing parameter ≤ 10 −4 . where we have used the hierarchical neutrino massesm diag ν = diag(0.00127 eV, 0.00885 eV, 0.0495 eV) and global fit to the neutrino oscillation data including recent values of θ 13 = 9.0 • and δ = 0.8π [46].
Thus, in the inverse seesaw approach, the light neutrino masses and large neutrino mixings including non-zero values of θ 13 can be easily fitted through the elements of the µ S matrix which may have interesting consequences on leptogenesis [13]. Although we have explicitly fitted the hierarchical light neutrino masses, similar fits can be obtained in the inverted hierarchical as well as the quasi-degenerate cases with corresponding elements of µ S . In the case of M D being similar to charged lepton mass matrix which holds true in conventional LR gauge theories [4,42] neutrino oscillation data are similarly fitted with the corresponding µ S matrix. b. Neutrinoless double beta decay predictions: As explained in equations (7) With |p| = 100 MeV, M WR = 5 TeV and using equations (7) -( 10), we predict the effective mass for 0νββ transition rate for hierarchical light neutrino masses, Our numerical predictions are shown in Fig.2 as a function of W R mass. With Dirac neutrino mass matrix having quarklepton symmetric origin, the most dominant contribution due to W − L -W − R mediation is found to be m ee νN ≃ 1 eV and 0.04 eV for M WR = 5 TeV, and 10 TeV, respectively. These predictions are reduced to m ee νN ≃ 0.07 eV and 0.03 eV for the corresponding values of the M WR when the Dirac neutrino mass matrix is similar to the charged lepton mass matrix. In other words, we predict that the 0νββ process would be able to discriminate LR gauge models having their roots in quarklepton symmetry. We note that the sub-dominant contribution due to W − R -W − R mediation given in eqn. (15) is suppressed as compared to the standard contribution due to W − L -W − L mediation given in eqn. (14) for the same M WR masses shown in  For the sake of comparison with the prediction for the inverse 0νββ processes in the golden channel e − e − → W − L W − R [45] which might be phenomenologically important for Linear Collider searches we used M WR ≥ 2.5 TeV [43] to determine η λ = which enters in cross-section for this process. Our model predicts this parameter to be 8.6 × 10 −8 whereas the limit on this parameter is η λ ≤ 9 × 10 −7 derived from the current experimental limit on 0νββ transition rate.

c. Lepton flavor violation:
Besides the neutrinoless double beta decay process, the light and heavy neutrinos in this model can actively mediate different lepton flavor violating processes, µ → e + γ, τ → e + γ, and τ → µ + γ which are currently under active experimental investigation. The dominant contributions are mainly through the exchange of the six heavy neutrinos [15] with branching ratio Within the allowed range of model parameters M N ≫ M ≫ M D , it is clear that the first term in eq. (17) is negligible. The second term involving the the heavy sterile neutrinos gives dominant contributions which is proportional to j U ν S α j U ν S * β j ≃ 2η αβ and our model predictions are Noting that the present experimental limit at 90% C.L, Br (µ → e + γ) ≤ 1.2 × 10 −11 [50] is almost three orders of magnitude stronger than the limits Br (τ → e + γ) ≤ 3.3 × 10 −8 or Br (τ → µ + γ) ≤ 4.4 × 10 −8 [51], appears to justify why the limit on |η eµ | is at least one orders of magnitude better than the ones on |η eτ | and |η µτ |. The projected reach of future sensitivities of ongoing searches are Br (τ → e + γ) ≤ 10 −9 , Br (τ → µ + γ) ≤ 10 −9 , and Br (µ → e + γ) ≤ 10 −18 [52,53] throughout which the model predictions can be easily verified or falsified. V. CONCLUSION: We have shown that in a class of leftright gauge theories, the light neutrino masses naturally arise though gauged inverse seesaw mechanism consistent with the current neutrino oscillation data. The associated TeV scale masses of W ± R and M N can give dominant non-standard contributions to neutrinoless double beta decay which might be important for experimental searches. Specifically, we have demonstrated that the mixed diagram, via simultaneous mediation of W − L and W − R accompanied by the naturally predicted Dirac neutrino mass terms, gives the dominant contribution to 0νββ rate. Also this mixed diagram has rich phenomenological implication at ILC for the detection of the inverse process like e − e − → W − L W − R . We have explicitly shown that this Dirac neutrino mass matrix could be similar to the up quark mass matrix which may have its high scale quark-lepton symmetric origin, or it may be similar to the charged lepton mass matrix expected from left-right gauge theory. The effective mass prediction in the former case being nearly 10 times larger than the latter case, we suggest that 0νββ signatures may probe high scale quark-lepton symmetry. As in our approach it is not necessary to fine tune the Dirac mass matrices, the left-right models could serve as promising theories for charged fermion masses. The TeV scale masses of W ± R and Z R bosons are accessible to ongoing searches at LHC [54].
The predicted branching ratios for lepton flavor violating decays, being closer to the current experimental search limits, could be used to verify or falsify the left-right model framework considered in this letter.