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We have studied neutrinoless double beta decay and charged lepton flavour violation in broken $mu-tau$ symmetric neutrino masses in a generic left-right symmetric model (LRSM). The leading order $mu-tau$ symmetric mass matrix originates from the type I (II) seesaw mechanism, whereas the perturbations to $mu-tau$ symmetry in order for generation of non-zero reactor mixing angle $theta_{13}$, as required by latest neutrino oscillation data, originates from the type II (I) seesaw mechanism. In our work, we considered four different realizations of $mu-tau$ symmetry, viz. Tribimaximal Mixing (TBM), Bimaximal Mixing (BM), Hexagonal Mixing (HM) and Golden Ratio Mixing (GRM). We then studied the new physics contributions to neutrinoless double beta decay (NDBD) ignoring the left-right gauge boson mixing and the heavy-light neutrino mixing within the framework of LRSM. We have considered the mass of the gauge bosons and scalars to be around TeV and studied the effects of the new physics contributions on the effective mass and the NDBD half life and compared with the current experimental limit imposed by KamLAND-Zen. We further extended our analysis by correlating the lepton flavour violation of the decay processes, $left(murightarrow 3eright)$ and $left(murightarrow egammaright)$ with the lightest neutrino mass and atmospheric mixing angle $theta_{23}$ respectively.
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We analyse in detail the scalar triplet contribution to the low-energy lepton flavour violating (LFV) and lepton number violating (LNV) processes within a TeV-scale left-right symmetric framework. We show that in both type-I and type-II seesaw dominance for the light neutrino masses, the triplet of mass comparable to or smaller than the largest right-handed neutrino mass scale can give sizeable contribution to the LFV processes, except in the quasi-degenerate limit of light neutrino masses, where a suppression can occur due to cancellations. In particular, a moderate value of the heaviest neutrino to scalar triplet mass ratio $rlesssim {cal O}(1)$ is still experimentally allowed and can be explored in the future LFV experiments. Similarly, the contribution of a relatively light triplet to the LNV process of neutrinoless double beta decay could be significant, disfavouring a part of the model parameter space otherwise allowed by LFV constraints. Nevertheless, we find regions of parameter space consistent with both LFV and LNV searches, for which the values of the total effective neutrino mass can be accessible to the next generation ton-scale experiments. Such light triplets can also be directly searched for at the LHC, thus providing a complementary probe of this scenario. Finally, we also study the implications of the triplet contribution for the left-right symmetric model interpretation of the recent diboson anomaly at the LHC.
The observation of neutrinoless double beta decay will have important consequences. First it will signal that lepton number is not conserved and the neutrinos are Majorana particles. Second, it represents our best hope for determining the absolute neutrino mass scale at the level of a few tens of meV. To achieve the last goal, however, certain hurdles have to be overcome involving particle, nuclear and experimental physics. Particle physics is important since it provides the mechanisms for neutrinoless double beta decay. In this review we emphasize the light neutrino mass mechanism. Nuclear physics is important for extracting the useful information from the data. One must accurately evaluate the relevant nuclear matrix elements, a formidable task. To this end, we review the recently developed sophisticated nuclear structure approaches, employing different methods and techniques of calculation. We also examine the question of quenching of the axial vector coupling constant, which may have important consequences on the size of the nuclear matrix elements. From an experimental point of view it is challenging, since the life times are extremely long and one has to fight against formidable backgrounds. One needs large isotopically enriched sources and detectors with good energy resolution and very low background.
Leptonic CP Violating Phase $ delta_{CP} $ in the light neutrino sector and leptogenesis via present matter antimatter asymmetry of the Universe entails each other. Probing CP violation in light neutrino oscillation is one of the challenging tasks today. The reactor mixing angle $ theta_{13} $ measured in reactor experiments, LBL, DUNE with high precision in neutrino experiments indicates towards the vast dimension of scope to detect $ delta_{CP} $. The correlation between leptonic Dirac CPV phase $ delta_{CP} $, reactor mixing angle $ theta_{13} $, lightest neutrino mass $ m_{1} $ and matter antimatter asymmetry of the Universe within the framework of $ mu-tau $ symmetry breaking assuming the type I seesaw dominance is extensively studied here. Small tiny breaking of the $ mu-tau $ symmetry allows a large Dirac CP violating phase in neutrino oscillation which in turn is characterised by awareness of measured value of $ theta_{13} $ and to provide a hint towards a better understanding of the experimentally observed near maximal value of $ u_{mu} - u_{tau} $ mixing angle $ theta_{23}simeq frac{pi}{4}$. Precise breaking of the $ mu-tau $ symmetry is achieved by adding a 120 plet Higgs to the 10 $+$ $bar{126}$ dimensional representation of Higgs. The estimated three dimensional density parameter space of lightest neutrino mass $ m_{1} $, $ delta_{CP} $, reactor mixing angle $ theta_{13} $, is constrained here for the requirement of producing the observed value of baryon asymmetry of the Universe through the mechanism of leptogenesis. Carrying out numerical analysis the allowed parameter space of $ m_{1} $, $ delta_{CP} $, $ theta_{13} $, is found out which can produce the observed baryon to photon density ratio of the Universe.
Taking account of possible CP violation, we discuss about the constraints on the lepton mixing angles from the neutrinoless double beta decay and from the neutrino oscillation for the three flavour Majorana neutrinos. From the CHORUS oscillation experiment, combined with the data of neutrinoless double beta decay, we show that the large angle solution of (theta_{23}) is improbable if the neutrino mass (m_3) of the third generation is a candidate of hot dark matters.
Study of the neutrinoless double beta decay and searches for the manifestation of the neutrino mass in ordinary beta decay are the main sources of information about the absolute neutrino mass scale, and the only practical source of information about the charge conjugation properties of the neutrinos. Thus, these studies have a unique role in the plans for better understanding of the whole fast expanding field of neutrino physics.
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