A number of recent resonance searches with the √s=8 TeV LHC data have observed excess events around an invariant mass of 2 TeV... Of course, these excesses should be thoroughly scrutinized in light of possible subtleties in the analysis  and must be confirmed with more statistics at the LHC run II before a firm conclusion on their origin could be deduced. Nevertheless, given the lucrative possibility that it could easily be the first glimpse of new physics at the LHC, it seems worthwhile to speculate on some well-motivated beyond SM interpretations.
One class of models that could simultaneously explain all these anomalies is the Left-Right Symmetric Model (LRSM) of weak interactions based on the gauge group SU(2)L×SU(2)R×U(1)B-L , with the right-handed (RH) charged gauge boson mass MWR≈2 TeV and the SU(2)R gauge coupling strength gR≈0.5 at the TeVscale [8, 9a,9b,9c]. The main objective of this paper is to study the implications of this scenario for various low-energy experiments searching for lepton number violation (LNV) and lepton flavor violation (LFV), which are complementary to the direct searches at the LHC.
For concreteness, we work in the Type-II seesaw ... dominance, where the hitherto unknown RH neutrino mixing matrix and mass hierarchy can be directly related to the light neutrino sector. This scenario is known to give potentially sizable contributions to the low-energy LNV and LFV observables [11, 12], apart from its novel LNV signatures at the LHC [13, 14]. We show that for the RH gauge boson mass and coupling values required to explain the LHC anomalies as indicated above, the LRSM parameter space for the RH neutrinos is already constrained by neutrinoless double beta decay (0νββ) experiments for relatively low (MeV-GeV) RH-neutrino masses, whereas the heavier (TeV) RH-neutrino masses are constrained by the searches for LFV processes, such as µ→eγ. Most of the remaining parameter space could be accessible in the next-generation 0νββ and LFV experiments at the intensity frontier. We derive a novel correlation between the 0νββ and µ→eγ rates, which clearly illustrates the testability of this scenario. We further show that future information on the absolute light neutrino mass scale from precision cosmology [with the future Euclid project] could make it even more predictive, irrespective of the neutrino mass hierarchy and uncertainties in the neutrino oscillation parameters or nuclear matrix elements ...
Our predictions for Br(µ → eγ) ... are shown in Fig. 3 [below] for both normal hierarchy [NH] and inverted hierarchy [IH] three benchmark values of M> [the third and heaviest right handed neutrino] where the band in each case is due to the 3σ uncertainties in the neutrino oscillation parameters. The horizontal shaded region is ruled out at 90% CL by the MEG experiment , while the horizontal dashed and dotted lines show the MEG-II  and PRISM/PRIME ... sensitivities, respectively. It is evident that the µ→eγ searches could be more effective in probing the relatively heavier M> values, as compared to the 0νββ searches. Also note that the Planck upper limit on the lightest neutrino mass effectively puts a lower limit on the µ→eγ branching ratio in the quasi-degenerate (QD) region; for instance, for M>=1 TeV, this lower limit is (0.5 − 1.9) [(0.5 − 1.7)]×10−14 for NH [IH], as shown in Fig. 3 [below]. However, for NH with M>/MWR ≥1, there is a destructive interference between the two heaviest neutrino contributions for certain values of the Dirac CP phase, which leads to a cancellation region, unless the third RH neutrino contribution is sizable, as demonstrated in Fig. 3 for M>=9 TeV. On the other hand, smaller M> values lead to a suppression in the µ→eγ rate, pushing it well below the future sensitivity even for M>=100 GeV, which is however accessible to 0νββ experiments. Thus, a combination of the low-energy probes of LNV and LFV is crucial to probe effectively the entire LRSM parameter space in our case. This is complementary to the direct searches at the LHC [5, 39], which can probe RH neutrino masses from about 100 GeV up to MWR  using the same-sign dilepton plus dijet channel... Similarly, the GeV-scale RH neutrinos can also be searched for in the proposed SHiP experiment [41a, 41b].