Flavor violating processes have been, are and will be crucial for the construction and development of Particle Physics theory. In the last years, the observation of lepton flavor violation in the neutral sector via neutrino oscillations has established that neutrinos do have masses, which is at present the most clear experimental evidence telling us that the SM must be extended. In the same manner, any evidence of LFV transitions in the charged sector would automatically imply the presence of new physics, even beyond the SM with neutrino masses minimally added. This fact makes charged LFV processes an optimal place to look for new physics. Unfortunately, no such cLFV processes have been observed yet, although a strong experimental effort is being made in this direction, and future experiments are planning to improve the sensitivities up to really impressive levels.

In general, any modification of the neutral lepton sector in order to account for neutrino masses will affect directly or indirectly, mainly via quantum corrections, to the charged lepton sector, leaving a trail of phenomenological implications that experiments could potentially observe. Among the many different extensions for addressing neutrino mass generation, we have focused on low scale seesaw models, in particular in the ISS and SUSY-ISS models, which share the appealing feature of adding new right-handed neutrinos with masses at the TeV range, i.e., at the energy scale that present colliders as the LHC are exploring. Therefore, in this Thesis we have explored the connection between the presence of right-handed neutrinos at the TeV mass scale and the potential existence of processes with charged LFV.

As we discussed when introducing the inverse seesaw model in Chap. 2, one of its most important features is that it introduces three different mass scales with three different purposes: a small lepton number violating scale, \(\mu _X\), responsible of explaining the smallness of the light neutrino masses; a large \(M_R\) scale that governs the masses of the heavy pseudo-Dirac neutrino pairs; and a Dirac mass at the electroweak scale, \(m_D=vY_\nu \), which controls the interaction between the (mainly left-handed) light and (mainly right-handed) heavy neutrinos with the Higgs boson. Along this Thesis, we have clearly seen that the most relevant parameters for the cLFV processes that we are interested in are \(M_{R}\) and \(Y_\nu \). Consequently, we have introduced a new parametrization for accommodating neutrino oscillation data, the \(\mu _X\) parametrization, alternative to the often used Casas-Ibarra parametrization, that allows to choose precisely \(M_R\) and \(Y_\nu \) as independent input parameters of the model.

In order to gain intuition on the general properties of cLFV processes in the ISS model, we have first revisited in Chap. 3 the LFV lepton decays, meaning the radiative decays \(\ell _m\rightarrow \ell _k\gamma \) and the three body decays \(\ell _m\rightarrow \ell _k\ell _k\ell _k\) with \(k\ne m\). This study has allowed us to establish the basic ideas of our analysis, as well as to understand the main differences of using the Casas-Ibarra parametrization or the \(\mu _X\) parametrization. We have seen that, although physics must not depend on the parametrization one chooses, the efficiency of an analysis in reaching some particular but interesting directions in the parameter space may radically change. As a particular example of this idea, we have studied the LFV radiative decays when using the \(\mu _X\) parametrization, where the Yukawa coupling matrix is one of the independent input parameters. Using this freedom, and the geometrical interpretation of the Yukawa matrix discussed in Sect. 3.21, we were able to define directions in the parameter space where the cLFV transitions are favored between two particular flavors, while keeping \(\mu \)-e transitions always highly suppressed. This is particularly interesting in the light of present experimental constraints on cLFV processes, since there are very strong bounds in the \(\mu \)-e sector, while they are weaker in the \(\tau \)-e and \(\tau \)-\(\mu \) sectors and, therefore, there is more room for larger allowed LFV predictions in these two latter sectors.

In Chap. 4 we have studied in full detail the LFV Higgs decays \(H \rightarrow \ell _k\bar{\ell }_m\) induced at the one-loop level from the ISS right-handed neutrinos. We have presented a full one-loop computation of the BR(\(H \rightarrow \ell _k\bar{\ell }_m\)) rates for the three possible channels, \(\ell _k\bar{\ell }_m=\mu \bar{\tau }, e \bar{\tau }, e \bar{\mu }\), and have also analyzed in full detail the predictions as functions of the various relevant ISS parameters. We found, as in the LFV lepton decays, that the most relevant parameters are \(M_R\) and \(Y_\nu \). Nevertheless, we have seen that, interestingly, the dependence of the LFVHD rates on these parameters is not the same as that of the LFV radiative decays.

In order to better understand these differences, we have performed a new and independent computation using a very different approach which turns out to provide simpler and more useful analytical results. Instead of applying the usual diagrammatic method of the full one-loop computation, we have used the mass insertion approximation, which works with the chiral EW neutrino basis, including the left- and right-handed states \(\nu _L\) and \(\nu _R\) and the extra singlets X of the ISS, instead of dealing with the nine physical neutrino states, \(n_{1\dots 9}\), of the mass basis.

To further simplify this MIA computation, we have first prepared the chiral basis in a convenient way, such that all the effects of the singlet X states are collected into a redefinition of the \(\nu _R\) propagator, which we have called here fat propagator, and then we have derived the set of Feynman rules for these proper chiral states that summarizes the relevant interactions involved in the one-loop computation of the LFVHD rates. The peculiarity of using this particular chiral basis is that it leads to a quite generic set of Feynman rules for the subset of interactions involving the neutrino sector, mainly \(\nu _L\) and \(\nu _R\), which are the relevant ones for the LFV observables of our interest here, and therefore our results could be valid for other low scale seesaw models sharing these same Feynman rules. With the MIA we have then organized the one-loop computation of the LFVHD rates in terms of a perturbative expansion in powers of the neutrino Yukawa coupling matrix \(Y_\nu \). It is worth recalling that in the ISS model, the \(Y_\nu \) matrix is the unique relevant origin of LFV and, thus, it is the proper expansion parameter in the MIA computation.

We have presented the analytical results using the MIA for the form factors that define the one-loop LFVHD amplitude, and we have done this computation first to leading order, \(\mathcal{O}((Y_\nu ^{} Y_\nu ^\dagger )_{km})\), and later to the next to leading order, i.e., including terms up to \(\mathcal{O}((Y_\nu ^{} Y_\nu ^\dagger Y_\nu ^{} Y_\nu ^\dagger )_{km})\). Moreover, we have demonstrated that our analytical results are gauge invariant, obtaining the same result in the Feynman-’t Hooft gauge and in the unitary gauge. This is certainly a good check of our analytical results. Numerically, we have found that in order to get a good numerical convergence of the MIA with the full results, it is absolutely necessary to include both \(\mathcal O(Y_\nu ^2)\) and \(\mathcal O(Y_\nu ^4)\) terms. Indeed, the presence of the \(\mathcal O(Y_\nu ^4)\) terms is what explains the different functional behavior with the parameters that we observed for the LFVHD rates with respect to the radiative decays, which are well described with only the \(\mathcal O(Y_\nu ^2)\) terms. We have then checked numerically that the MIA works pretty well in a big range of the relevant model parameters \(Y_\nu \) and \(M_R\). For a small Yukawa coupling, given in our notation by a small global factor, say \(f<0.5\), we have obtained an extremely good convergence of the MIA and the full results even for moderate \(M_R\) of a few hundred GeV and above. For larger Yukawa couplings, say with \(0.5< f< 2\) we have also found a good convergence, but for heavier \(M_R\) of above \(\mathcal{O}(1 \mathrm{TeV})\).

In addition to the form factors, we have also derived in Sect. 4.3.3 an analytical expression of the LFV effective vertex describing the \(H\ell _k\ell _m\) coupling that is radiatively generated to one-loop from the heavy right-handed neutrinos. For that computation we have presented our systematic expansion of the form factors in inverse powers of \(M_R\), which is valid in the mass range of our interest, \(m_\ell \ll m_D,m_W,m_H\ll M_R\), and we have found the most relevant terms of \(\mathcal{O}(v^2/M_R^2)\) in this series. In doing this expansion, we have taken care of the contributions from the external Higgs boson momentum which are relevant since in this observable the Higgs particle is on-shell, and we have also followed the track of all the EW masses involved, like \(m_W\) and \(m_H\), which are both of order v and therefore contribute to the wanted \(\mathcal{O}(v^2/M_R^2)\) terms. The lepton masses (except for the global factor from the heaviest lepton \(m_{\ell _k}\gg m_{\ell _m}\)) do not provide relevant corrections and have been neglected in this computation of the effective vertex. We have shown with several examples that this simple MIA formula works extremely well for the interesting window in the \((Y_\nu , M_R)\) parameter space which is allowed by the present experimental constraints. Therefore, we believe that our final analytical formula for the LFV effective \(H\ell _k\ell _m\) vertex given in Eq. 4.34 is very simple and can be useful for other authors who wish to perform a fast estimate of the LFVHD rates in terms of their own preferred input parameter values for \(Y_\nu \) and \(M_R\).

For the numerical estimates of the full one-loop results of the LFVHD rates, we have explored the ISS parameter space considering again the two discussed parametrizations for accommodating light neutrino masses and mixings. First, we have considered the Casas-Ibarra parametrization and explored the LFVHD rates from the simplest case of diagonal \(\mu _X\) and \(M_R\) matrices with degenerate entries for \(M_{R_i}\), to a more general case with hierarchical heavy neutrinos. In these cases, we concluded that the largest maximum LFV Higgs decay rates within the ISS that are allowed by the constraints on the LFV radiative decays are for BR(\(H \rightarrow e \bar{\tau }\)) and BR(\(H \rightarrow \mu \bar{\tau }\)) and reach at most \(10^{-10}\) for the degenerate heavy neutrino case and \(10^{-9}\) for the hierarchical case. Second, we have considered the \(\mu _X\) parametrization and explored the phenomenologically well motivated scenarios that are more promising for LFVHD searches in the \(\tau \)-e and \(\tau \)-\(\mu \) sectors. We have demonstrated that in this kind of ISS scenarios there are solutions with much larger allowed LFVHD rates than in the previous cases, leading to maximal rates allowed by the bounds on the radiative decays of around \(10^{-5}\) for either BR(\(H \rightarrow \mu \bar{\tau }\)) or BR(\(H \rightarrow e \bar{\tau }\)).

Finally, we have considered the effects of other kind of constraints to the ISS parameter space by making use of the global fit analysis to present data and the perturbativity requirements on the Yukawa couplings. These constraints result in allowed BR(\(H\rightarrow e \bar{\tau }\)) and BR(\(H\rightarrow \mu \bar{\tau }\)) ratios being at most of about \(10^{-7}\), which are unfortunately far below the present experimental sensitivities and, therefore, future experiments would be needed for testing these predictions.

In Sect. 4.2, we have also addressed the question of whether the SUSY realization of the ISS model can lead to enhanced predictions for the LFV Higgs decay rates. We have considered the MSSM model with the lightest CP-even Higgs boson h identified as the SM-like Higgs boson, and extended with three pairs of ISS neutrinos and their corresponding SUSY partners, the sneutrinos. We have then presented the results of an updated and full one-loop calculation of the SUSY contributions to lepton flavor violating Higgs decays in the SUSY-ISS model. These contributions come from chargino-sneutrino loops with sneutrino couplings off-diagonal in flavor, and from neutralino-slepton loops, due to the misalignment in flavor between the slepton and lepton sectors caused by running effects. We found much larger contributions than in the type-I seesaw model coming from the lower values of \(M_R \sim \mathcal{O}(1\) TeV), an increased RGE-induced slepton mixing, and the presence of new right-handed sneutrinos at the TeV scale. Then, the couplings of both sleptons and sneutrinos can transmit sizable LFV due to the large \(Y_\nu ^2/(4 \pi ) \sim \mathcal{O} (1) \) we considered. We showed that the branching ratio of \(h \rightarrow \tau \bar{\mu }\) exhibits different behaviors as a function of the seesaw and SUSY scale if it is dominated by chargino or neutralino loops. Moreover, a non-zero trilinear coupling \(A_\nu \) leads to increased LFVHD rates. Choosing different benchmark points, we found that BR(\(h \rightarrow \tau \bar{\mu }\)) of the order of \(10^{-2}\) can be reached while agreeing with the experimental limits on radiative decays, which can be tested at the present runs of the LHC. This calls up for a complete study including non-supersymmetric contributions in the SUSY-ISS model, like those from the extended Higgs sector, and a detailed analysis of experimental constraints beyond radiative LFV decays, which will be addressed in a future work.

In Chap. 5 we have revisited the LFV Z decays in presence of right-handed neutrinos with TeV range masses, which are very interesting observables that are currently being searched for at the LHC and will be further explored by the next generation of experiments. A first study of these observables within the ISS context with three pairs of fermionic singlets was done in Ref. [1], finding maximum allowed ratios of about \(10^{-9}\). Here, we have alternatively studied in full detail the LFVZD rates in our selected TM and TE scenarios, which as we said are designed to find large rates for processes including a \(\tau \) lepton, and we have investigated those that are allowed by all the present constraints. In addition to the radiative decays, important constraints come from experimental upper bounds on the LFV three body lepton decays, since they are strongly correlated to the LFVZD in these scenarios. Taking into account all the relevant bounds, we found that heavy ISS neutrinos with masses in the few TeV range can induce maximal rates of BR\((Z\rightarrow \tau \mu )\sim 2 \times 10^{-7}\) and BR\((Z\rightarrow \tau e)\sim 2 \times 10^{-7}\) in the TM and TE scenarios, respectively. These rates are considerably larger than what was found in previous studies and potentially measurable at future linear colliders and FCC-ee. Therefore, we have seen that searches for LFVZD at future colliders may be a powerful tool to probe cLFV in low scale seesaw models, in complementarity with low-energy (high-intensity) facilities searching for cLFV processes.

Another appealing feature of our results is that the predictions for the cLFV processes come together with the possibility that the heavy neutrinos could be directly produced at the LHC. Being the ISS neutrinos pseudo-Dirac fermions, the standard same-sign dilepton searches for heavy Majorana neutrinos are not effective, implying that new search strategies need to be explored. In Chap. 6 we have proposed a new interesting way of studying the production and decay of the heavy neutrinos of the ISS in connection with LFV. We have presented the computation of the predicted number of exotic \(\mu \tau jj\) events, which can be produced in the TM scenarios with large LFV, where the heavy pseudo-Dirac neutrinos are produced together with a lepton of a given flavor, both via Drell-Yan and \(\gamma W\) fusion processes, and then decay into a W and a lepton of different flavor. We have concluded that, for the studied benchmark scenarios, a number of \(\mathcal O(10-100)\) total \(\mu \tau jj\) exotic events without missing energy can be produced at the next run of the LHC when \(300~\mathrm{fb}^{-1}\) of integrated luminosity are reached, and for values of \(M_R\) from 200 GeV to 1 TeV respecting the constraints from LFV violating observables. Similarly, other rare processes like \(\tau e jj\) or \(\mu e jj\) could be produced within other ISS scenarios with large LFV, although for the latter ones the number of events would be strongly limited by the \(\mu \rightarrow e \gamma \) upper bound. These promising results deserve a more realistic study of these exotic events, including detector simulation, together with a full background study, which should be done in order to reach a definitive conclusion and it will be addressed in a future work.

As an overall conclusion of this Thesis, we can state that searching for charged lepton flavor violating processes is a very powerful strategy for testing the presence of low scale seesaw neutrinos with masses of a few TeV or below, which on the other hand are common in many models for explaining the observed neutrino masses. As we have seen along this Thesis, the addition to the SM of these new states, not much heavier that the EW scale and with a potentially complex flavor structure, has an important impact in the phenomenology of the charged leptons, which could be seen at lepton flavor violating processes. Flavor physics has been crucial in the history of the SM and it will play a major role in the discovery of new physics.