Search

We examine the prospect of observing genuine lepton number violating (LNV) signals at hadron colliders in the context of the Type II seesaw mechanism. The model features smoking gun signals involving same-sign di-leptons and jets that may be the primary observable channel in certain regions of the parameter space. The flavour composition of final-state charged leptons in the minimal model is related to the origin of neutrino masses and is correlated with other rare processes, such as neutrinoless double beta decay. We review existing collider limits and provide sensitivity estimates from LNV signals at upcoming runs of the LHC, for zero and non-zero mass splittings between the scalar triplet components., Comment: 7 pages, 7 figures

We revisit the decay rate of the electroweak vacuum in the Standard Model with the full one-loop prefactor. We focus on the gauge degrees of freedom and derive the degeneracy factors appearing in the functional determinant using group theoretical arguments. Our treatment shows that the transverse modes were previously overcounted, so we revise the calculation of that part of the prefactor. The new result modifies the gauge fields' contribution by $7\%$ and slightly decreases the previously predicted lifetime of the electroweak vacuum, which remains much longer than the age of the universe. Our discussion of the transverse mode degeneracy applies to any calculation of functional determinants involving gauge fields in four dimensions., Comment: 5 pages + Supplemental, 2 figures

We consider a single real scalar field in flat spacetime with a polynomial potential up to $\phi^4$, that has a local minimum, the false vacuum, and a deeper global minimum, the true vacuum. When the vacua are almost degenerate we are in the thin wall regime, while as their difference in potential energy increases, we approach the thick wall regime. We give explicit simple formulae for the decay rate of the false vacuum in 3 and 4 spacetime dimensions. Our results include a careful treatment both of the bounce action, which enters at the exponent of the decay rate, and of the functional determinant at one loop, which determines the prefactor. The bounce action is computed analytically as an expansion in the thin wall parameter in generic $D$ dimensions. We find that truncating such an expansion at second order we obtain a remarkably accurate bounce action also deep into thick wall regimes. We calculate the functional determinant numerically in 3 and 4 dimensions and fit the results with simple polynomials of the same thin wall parameter. This allows us to write the complete one-loop decay rate as a compact expression, which works accurately from thin to thick wall regimes.

We develop a comprehensive implementation of the minimal Left-Right symmetric model within a FeynRules model file. We derive the complete set of mass spectra and mixings for the charged and neutral gauge bosons, would-be-Goldstones and gauge fixing, together with the ghost Lagrangian. In the scalar sector, we analytically re-derive all the massive states with mixings and devise a physical input scheme, which expresses the model couplings in terms of masses and mixing angles of all states. Fermion couplings are determined in closed form, including the Dirac mixing in the neutrino sector, evaluated explicitly with the Cayley-Hamilton method. We calculate the one loop next-to-leading QCD corrections and provide a complete UFO file for NLO studies, demonstrated on relevant benchmarks. We provide various restricted variants of the model file with different gauges, massless states, neutrino hierarchies and parity violating $g_L \neq g_R$ gauge couplings., Comment: 23 pages, 4 figures. For associated material, see http://sites.google.com/site/leftrighthep/ or http://feynrules.irmp.ucl.ac.be/wiki/LRSM_NLO

Temporary matter domination and late entropy dilution, injected by a "long-lived" particle in the early universe, serves as a standard mechanism for yielding the correct dark matter relic density. We recently pointed out the cosmological significance of diluting particle's partial decay into dark matter. When repopulated in such a way, dark matter carries higher momentum than its thermal counterpart, resulting in a suppression of the linear matter power spectrum that is constrained by the large scale structure observations. In this work, we study the impact of such constraints on the minimal left-right symmetric model that accounts for the origin of neutrino mass. We map out a systematic anatomy of possible dilution scenarios with viable parameter spaces, allowed by cosmology and various astrophysical and terrestrial constraints. We show that to accommodate the observed dark matter relic abundance the spontaneous left-right symmetry breaking scale must be above PeV and cosmology will continue to provide the most sensitive probes of it. In case the dilutor is one of the heavier right-handed neutrinos, it can be much lighter and lie near the electroweak scale., Comment: 48 pages, 11 figures

We study the production of right-handed $W_R$ bosons and heavy neutrinos $N$ at a future 100 TeV high energy hadron collider in the context of Left-Right symmetry, including the effects of $W_L-W_R$ gauge-boson mixing. We estimate the collider reach for up to 3/ab integrated luminosity using a multi-binned sensitivity measure. In the Keung-Senjanovi\'c and missing energy channels, the 3$\sigma$ sensitivity extends up to $M_{W_R}=35$ and 37 TeV, respectively. We further clarify the interplay between the missing energy channel and the (expected) limits from neutrinoless double beta decay searches, Big Bang nucleosynthesis and dark matter., Comment: 19 pages, version to appear in PRD

We present a fully analytical calculation of the false vacuum decay rate for a self-interacting scalar field in the thin-wall approximation. We obtain the bounce solution, together with the Euclidean action, counter-terms and renormalization group running, and we extract the functional determinant via the Gel'fand-Yaglom theorem. Our procedure is valid for a generic spacetime dimension $D$, and we provide an explicit finite renormalized decay rate in $D=3,4$., Comment: Conference proceedings for Corfu Summer Institute 2022 "School and Workshops on Elementary Particle Physics and Gravity", August 28 - October 1, 2022, Corfu, Greece. Based on arXiv:2202.04498

Entropy production is a necessary ingredient for addressing the over-population of thermal relics. It is widely employed in particle physics models for explaining the origin of dark matter. A long-lived particle that decays to the known particles, while dominating the universe, plays the role of the dilutor. We point out the impact of its partial decay to dark matter on the primordial matter power spectrum. For the first time, we derive a stringent limit on the branching ratio of the dilutor to dark matter from large scale structure observation using the SDSS data. This offers a novel tool for testing models with a dark matter dilution mechanism. We apply it to the left-right symmetric model and show that it firmly excludes a large portion of parameter space for right-handed neutrino warm dark matter., Comment: 6 pages, 4 figures. v2: added supplement material. Accepted for publication in Physical Review Letters

The existence of non-zero neutrino masses points to the likely existence of multiple SM neutral fermions. When such states are heavy enough that they cannot be produced in oscillations, they are referred to as Heavy Neutral Leptons (HNLs). In this white paper we discuss the present experimental status of HNLs including colliders, beta decay, accelerators, as well as astrophysical and cosmological impacts. We discuss the importance of continuing to search for HNLs, and its potential impact on our understanding on key fundamental questions, and additionally we outline the future prospects for next-generation future experiments or upcoming accelerator run scenarios., Comment: 82 pages, 34 figures. Contribution to Snowmass 2021

We derive a closed-form false vacuum decay rate at one loop in the thin wall limit, where the true and false vacua are nearly degenerate. We obtain the bounce configuration in $D$ dimensions, together with the Euclidean action with a higher order correction, counter-terms and renormalization group running. We extract the functional determinant via the Gel'fand-Yaglom theorem for low and generic orbital multipoles. The negative and zero eigenvalues appear for low multipoles and the translational zeroes are removed. We compute the fluctuations for generic multipoles, multiply and regulate the orbital modes. We find an explicit finite renormalized decay rate in $D = 3, 4$ and give a closed-form expression for the finite functional determinant in any dimension., Comment: 22 pages plus 5 appendices, published in JHEP. In v4 we updated the final result in D=4, after the addition of a term missed in the previous versions. The result in D=3 is unchanged

We discuss an exact false vacuum decay rate at one loop for a real and complex scalar field in a quartic-quartic potential with two tree-level minima. The bounce solution is used to compute the functional determinant from both fluctuations. We obtain the finite product of eigenvalues and remove translational zero modes. The orbital modes are regularized with the zeta function and we end up with a complete renormalized decay rate. We derive simple expansions in the thin and thick wall limits and determine their validity., Comment: 34 pages, 2 figures, ancillary Mathematica notebook, v2: title change, added figure, references and explanations, accepted for publication in Phys. Rev. D

We are launching FindBounce, a Mathematica package for the evaluation of the Euclidean bounce action that enters the decay rate of metastable states in quantum and thermal field theories. It is based on the idea of polygonal bounces, which is a semi-analytical approach to solving the bounce equation by discretizing the potential into piecewise linear segments. This allows for a fast and robust evaluation of arbitrary potentials with specified precision and any number of scalar fields. Time cost grows linearly with the number of fields and/or the number of segments. Computation with 20 fields takes $\sim 2$ seconds with $0.5\%$ accuracy of the action. The FindBounce function is simple to use with the native Mathematica look and feel, it is easy to install, and comes with detailed documentation and physical examples, such as the calculation of the nucleation temperature. We also provide timing benchmarks with comparisons to existing tools, where applicable., Comment: 30 pages, 8 figures. Package homepage is available at https://github.com/vguada/FindBounce

We present a systematic comparison of doubly charged Higgs boson production mechanisms at hadron colliders in the context of the Type II Seesaw model, emphasizing the importance of higher-order corrections and subdominant channels. We consider the Drell-Yan channel at next-to-leading order in QCD, photon fusion at leading order, gluon fusion with resummation of threshold logarithms up to next-to-next-to-next-to-leading logarithmic accuracy, and same-sign weak boson fusion at next-to-leading order in QCD. For Drell-Yan processes, we study the impact of a static jet veto at next-to-leading order matched to the resummation of jet veto scale logarithms at next-to-next-to-leading logarithmic accuracy. For the photon fusion channel, the dependence on modeling photon parton distribution functions is definitively assessed. To model vector boson fusion at next-to-leading order, we include all interfering topologies at $\mathcal{O}(\alpha^4)$ and propose a method for introducing generator-level cuts within the MC@NLO formalism. Our results are obtained using a Monte Carlo tool chain linking the \textsc{FeynRules}, \textsc{NloCT} and \textsc{MadGraph5\_aMC@NLO} programs and have necessitated the development of new, publicly available, Universal FeynRules Output libraries that encode the interactions between the Type II Seesaw scalars and Standard Model particles. Libraries are compatible with both the normal and inverted ordering of Majorana neutrino masses., Comment: Journal version (27 pages, seven figures). Extended discussions on uncertainties and discovery potential. Type II Seesaw NLO FeynRules UFO available from https://feynrules.irmp.ucl.ac.be/wiki/TypeIISeesaw

Particles beyond the Standard Model (SM) can generically have lifetimes that are long compared to SM particles at the weak scale. When produced at experiments such as the Large Hadron Collider (LHC) at CERN, these long-lived particles (LLPs) can decay far from the interaction vertex of the primary proton-proton collision. Such LLP signatures are distinct from those of promptly decaying particles that are targeted by the majority of searches for new physics at the LHC, often requiring customized techniques to identify, for example, significantly displaced decay vertices, tracks with atypical properties, and short track segments. Given their non-standard nature, a comprehensive overview of LLP signatures at the LHC is beneficial to ensure that possible avenues of the discovery of new physics are not overlooked. Here we report on the joint work of a community of theorists and experimentalists with the ATLAS, CMS, and LHCb experiments --- as well as those working on dedicated experiments such as MoEDAL, milliQan, MATHUSLA, CODEX-b, and FASER --- to survey the current state of LLP searches at the LHC, and to chart a path for the development of LLP searches into the future, both in the upcoming Run 3 and at the High-Luminosity LHC. The work is organized around the current and future potential capabilities of LHC experiments to generally discover new LLPs, and takes a signature-based approach to surveying classes of models that give rise to LLPs rather than emphasizing any particular theory motivation. We develop a set of simplified models; assess the coverage of current searches; document known, often unexpected backgrounds; explore the capabilities of proposed detector upgrades; provide recommendations for the presentation of search results; and look towards the newest frontiers, namely high-multiplicity "dark showers", highlighting opportunities for expanding the LHC reach for these signals.

We propose a new approach for computing tunneling rates in quantum or thermal field theory with multiple scalar fields. It is based on exact analytical solutions of piecewise linear potentials with many segments that describes any given potential to arbitrary precision. The method is first developed for the single field case in 3 and 4 space-time dimensions and demonstrated on examples of classical potentials as well as the calculation of quantum fluctuations. A systematic expansion of the potential beyond the linear order is considered, taking into account higher order corrections, which paves the way for multiple scalar fields. We thereby provide a fast semi-analytical tool for evaluating the bounce action for theories with an extended scalar sector., Comment: 15 pages, 12 figures, polygonal bounces extended to multi-fields, computation of the prefactor, added references

In the context of Left-Right symmetry, we revisit the Keung-Senjanovi\'{c} production of right-handed $W_R$ bosons and heavy neutrinos $N$ at high energy colliders. We develop a multi-binned sensitivity measure and use it to estimate the sensitivity for the entire range of $N$ masses, spanning the standard and merged prompt signals, displaced vertices and the invisible $N$ region. The estimated sensitivity of the LHC with 300/fb integrated luminosity ranges from 5 to beyond 7 TeV, while the future 33(100) TeV collider's reach with 3/ab extends to 12(26) TeV., Comment: Added references, minor polishing

Collider signals of heavy Majorana neutrino mass origin are studied in the minimal Left-Right symmetric model, where their mass is generated spontaneously together with the breaking of lepton number. The right-handed triplet Higgs boson $\Delta$, responsible for such breaking, can be copiously produced at the LHC through the Higgs portal in the gluon fusion and less so in gauge mediated channels. At $\Delta$ masses below the opening of the $VV$ decay channel, the two observable modes are pair-production of heavy neutrinos via the triplet gluon fusion $gg \to \Delta \to NN$ and pair production of triplets from the Higgs $h \to \Delta \Delta \to 4N$ decay. The latter features tri- and quad same-sign lepton final states that break lepton number by four units and have no significant background. In both cases up to four displaced vertices may be present and their displacement may serve as a discriminating variable. The backgrounds at the LHC, including the jet fake rate, are estimated and the resulting sensitivity to the Left-Right breaking scale extends well beyond 10 TeV. In addition, sub-dominant radiative modes are surveyed: the $\gamma \gamma$, $Z \gamma$ and lepton flavour violating ones. Finally, prospects for $\Delta$ signals at future $e^+ e^-$ colliders are presented., Comment: 30 pages, 12 figures. v2: added clarifications and discussion on event selection, displacement, backgrounds; updated figures and added references, version as accepted in JHEP

The scalar sector of the minimal Left-Right model at TeV scale is revisited in light of the large quartic coupling needed for a heavy flavor-changing scalar. The stability and perturbativity of the effective potential is discussed and merged with constraints from low-energy processes. Thus the perturbative level of the Left-Right scale is sharpened. Lower limits on the triplet scalars are also derived: the left-handed triplet is bounded by oblique parameters, while the doubly-charged right-handed component is limited by the $h \to \gamma \gamma, Z \gamma$ decays. Current constraints disfavor their detection as long as $W_R$ is within the reach of the LHC., Comment: Added references, clarifications and acknowledgments

We show that within the Left-Right symmetric model, lepton number violating decays of the Higgs boson can be discovered at the LHC. The process is due to the mixing of the Higgs with the triplet that breaks parity. As a result, the Higgs can act as a gateway to the origin of heavy Majorana neutrino mass. To assess the LHC reach, a detailed collider study of the same-sign di-leptons plus jets channel is provided. This process is complementary to the existing nuclear and collider searches for lepton number violation and can probe the scale of parity restoration even beyond other direct searches., Comment: 6 pages. Version matching PRL one. Updated references, minor clarifications, conclusions unchanged. Enjoy

In the minimal Left-Right model the choice of left-right symmetry is twofold: either generalized parity $\mathcal P$ or charge conjugation $\mathcal C$. In the minimal model with spontaneously broken strict $\mathcal P$, a large tree-level contribution to strong CP violation can be computed in terms of the spontaneous phase $\alpha$. Searches for the neutron electric dipole moments then constrain the size of $\alpha$. Following the latest update on indirect CP violation in the kaon sector, a bound on $W_R$ mass at $20 \text{TeV}$ is set. Possible ways out of this bound, either by an additional relaxation mechanism or explicit breaking of $\mathcal P$ are considered. To this end, the chiral loop of the neutron electric dipole moment at next-to-leading order is re-computed and provides an estimate of the weak contribution. Combining this constraint with other CP violating observables in the kaon sector allows for $M_{W_R} \gtrsim 3 \text{TeV}$. On the other hand, $\mathcal C$-symmetry is free from such constraints, leaving the right-handed scale within the experimental reach., Comment: 9 pages, 3 figures, two-columns. Added references and an additional discussion on UV counter-terms, matches the version accepted by PRD

We study the scenario of dark matter in the minimal left-right symmetric theory at the TeV scale. The only viable candidate is found to be the lightest right-handed neutrino with a mass of keV. To satisfy the dark matter relic abundance, the relic yield is diluted by late decays of the two heavier neutrinos. We point out that the QCD phase transition temperature coincidences with the typical freeze-out temperature governed by right-handed interactions, which helps to alleviate the problem of overproduction. A careful numerical study reveals a narrow window for the mass of the right-handed gauge boson, within the reach of the LHC., Comment: Article in proceedings of the CETUP* 2012 workshop in Lead, South Dakota; 10 pages, 5 figures, v2: references added

Probing the origin of neutrino mass by disentangling the seesaw mechanism is one of the central issues of particle physics. We address it in the minimal left-right symmetric model and show how the knowledge of light and heavy neutrino masses and mixings suffices to determine their Dirac Yukawa couplings. This in turn allows one to make predictions for a number of high and low energy phenomena, such as decays of heavy neutrinos, neutrinoless double beta decay, electric dipole moments of charged leptons and neutrino transition moments. We also discuss a way of reconstructing the neutrino Dirac Yukawa couplings at colliders such as the LHC., Comment: 6 pages, 5 figures. Clarification, discussion and references added, together with a new subsection on probing neutrino Dirac Yukawa couplings at the LHC

We investigate the viability of having dark matter in the minimal left-right symmetric theory. We find the lightest right-handed neutrino with a mass around keV as the only viable candidate consistent with a TeV scale of left-right symmetry. In order to account for the correct relic density with such low scales, the thermal overproduction of the dark matter in the early universe is compensated by a sufficient late entropy production due to late decay of heavier right-handed neutrinos. We point out that the presence of the right-handed charge-current interactions, operative around the QCD phase transition, has a crucial impact on the amount of dilution, as does the nature of the phase transition itself. A careful numerical study, employing the Boltzmann equations, reveals the existence of a narrow window for the right-handed gauge boson mass, possibly within the reach of LHC (in disagreement with a previous study). We also elaborate on a variety of astrophysical, cosmological and low energy constraints on this scenario., Comment: 32 pages, 7 figures; reference added, further discussion on the flavor structure added, final version accepted by JCAP

Experiments in progress may confirm a nonzero neutrinoless double beta decay rate in conflict with the cosmological upper limit on neutrino masses and thus require new physics beyond the Standard Model. A natural candidate is the Left-Right symmetric theory, which led originally to neutrino mass and the seesaw mechanism. In the absence of cancelations of large Dirac Yukawa couplings, we show how such a scenario would require a low scale of Left-Right symmetry breaking roughly below 10 TeV, tantalizingly close to the LHC reach., Comment: 5 pages, 4 figures, clarification and references added

In this Letter, we propose a new possible connection between dark matter relic density and baryon asymmetry of the universe. The portal between standard model sector and dark matter not only controls the relic density and detections of dark matter, but also allows the dark matter to trigger the first order electroweak phase transition. We discuss systematically possible scalar dark matter candidates, starting from a real singlet to arbitrary high representations. We show that the simplest realization is provided by a doublet, and that strong first-order electroweak phase transition implies a lower bound on the dark matter direct detection rate. The mass of dark matter lies between 45 and 80 GeV, allowing for an appreciable invisible decay width of the Standard Model Higgs boson, which is constrained to be lighter than 130 GeV for the sake of the strong phase transition., Comment: 6 pages, 3 figures, discussions and references added

In this Letter we revisit the type-II seesaw mechanism based on the addition of a weak triplet scalar to the standard model. We perform a comprehensive study of its phenomenology at the LHC energies, complete with the electroweak precision constraints. We pay special attention to the doubly-charged component, object of collider searches for a long time, and show how the experimental bound on its mass depends crucially on the particle spectrum of the theory. Our study can be used as a roadmap for future complete LHC studies., Comment: 5 pages, 4 figures; added discussion on collider signatures including the impact on SM Higgs searches and accommodating Higgs to two photon rate, and references; latest version agrees with the published one

It was shown recently that mirror fermions, naturally present in a number of directions for new physics, seem to require an inert scalar doublet in order to pass the electroweak precision tests. This provides a further motivation for considering the inert doublet as a dark matter candidate. Moreover, the presence of extra families enhances the Standard Model Higgs-nucleon coupling, which has crucial impact on the Higgs and dark matter searches. We study the limits on the inert dark matter mass in view of recent Xenon100 data. We find that the mass of the inert dark matter must lie in a very narrow window 74-76 GeV while the Higgs must weigh more than 400 GeV. For the sake of completeness we discuss the cases with fewer extra families, where the possibility of a light Higgs boson opens up, enlarging the dark matter mass window to m_h/2-76 GeV. We find that Xenon100 constrains the DM-Higgs interaction, which in turn implies a lower bound on the monochromatic gamma-ray flux from DM annihilation in the galactic halo. For the mirror case, the predicted annihilation cross section lies a factor of 4-5 below the current limit set by Fermi LAT, thus providing a promising indirect detection signal., Comment: 10 pages, 7 figures; reference added

We use the early Large Hadron Collider data to set the lower limit on the scale of Left-Right symmetry, by searching for the right-handed charged gauge boson $W_R$ via the final state with two leptons and two jets, for 33/pb integrated luminosity and 7 TeV center-of-mass energy. In the absence of a signal beyond the Standard Model background, we set the bound M_WR > 1.4 TeV at 95% C.L.. This result is obtained for a range of right-handed neutrino masses of the order of few 100 GeV, assuming no accidental cancelation in right-handed lepton mixings., Comment: 4 pages, added references

The Large Hadron Collider has a potential to probe the scale of left-right symmetry restoration and the associated lepton number violation. Moreover, it offers hope of measuring the right-handed leptonic mixing matrix. We show how this, together with constraints from lepton flavor violating processes, can be used to make predictions for neutrinoless double beta decay. We illustrate this deep connection in the case of the type-II seesaw., Comment: 4 pages, 5 figures, PRL version

We analyze the importance of flavor effects in models in which leptogenesis proceeds via the decay of Majorana electroweak triplets. We find that depending on the relative strengths of gauge and Yukawa reactions the $B-L$ asymmetry can be sizably enhanced, exceeding in some cases an order of magnitude level. We also discuss the impact that such effects can have for TeV-scale triplets showing that as long as the $B-L$ asymmetry is produced by the dynamics of the lightest such triplet they are negligible, but open the possibility for scenarios in which the asymmetry is generated above the TeV scale by heavier states, possibly surviving the TeV triplet related washouts. We investigate these cases and show how they can be disentangled at the LHC by using Majorana triplet collider observables and, in the case of minimal type III see-saw models even through lepton flavor violation observables., Comment: 22 pages, 9 figures, extended discussion on collider phenomenology, references added. Version matches publication in JHEP

We revisit the issue of the limit on the scale of Left-Right symmetry breaking. We focus on the minimal SU(2)_L x SU(2)_R x U(1)_B-L gauge theory with the seesaw mechanism and discuss the two possibilities of defining Left-Right symmetry as parity or charge conjugation. In the commonly adopted case of parity, we perform a complete numerical study of the quark mass matrices and the associated left and right mixing matrices without any assumptions usually made in the literature about the ratio of vacuum expectation values. We find that the usual lower limit on the mass of the right-handed gauge boson from the K mass difference, M_WR>2.5TeV, is subject to a possible small reduction due to the difference between right and left Cabibbo angles. In the case of charge conjugation the limit on M_WR is somewhat more robust. However, the more severe bounds from CP-violating observables are absent in this case. In fact, the free phases can also resolve the present mild discrepancy between the Standard Model and CP-violation in the $B$-sector. Thus, even in the minimal case, both charged and neutral gauge bosons may be accessible at the Large Hadron Collider with spectacular signatures of lepton number violation., Comment: 32 pages

We study a CP and T violating triple (spin) correlation in the muon to electron conversion in nuclei in the context of the seesaw mechanism. After concluding that the results are negative for all three seesaw types, we turn to the left-right symmetric theories as the original source of seesaw. We find that in general this correlation is of order one which offers a hope of observing CP violation in lepton flavor violating processes for a L-R scale below around 10-30 TeV. We discuss the conditions that could render to (unlikely) conspiracies as to suppress the CP violating effects., Comment: 15 pages, 2 figures

In the presence of a low scale seesaw of type I + III, flavor violating effects in the leptonic sector are expected. Their presence in the charged sector is due to the mixing of the fermionic vector-like weak triplets with the chiral doublets, which cause non-universality of the tree-level Z coupling. We investigate the bounds on the Yukawa couplings which are responsible for the mixing and present the results for two minimal cases, a fermionic triplet with a singlet or two fermionic triplets. Different channels for these processes are considered and their current and future potential to probe these couplings is discussed., Comment: 20 pages, 2 figures; corrected misprints, conclusions unchanged

A good fit of the fermion masses and mixings has been found in the minimal renormalizable supersymmetric SO(10). This solution needs a strongly split supersymmetry breaking scenario with gauginos and higgsinos around 100 TeV, sfermions close to 10^14 GeV and a low GUT scale of around 6 10^15 GeV. We predict fast proton decays through SO(10) type of d=6 operators and the leptonic mixing angle theta_13 approximately 0.1., Comment: 26 pages, 3 figures

We have recently proposed a simple SU(5) theory with an adjoint fermionic multiplet on top of the usual minimal spectrum. This leads to the hybrid scenario of both type I and type III seesaw and it predicts the existence of the fermionic SU(2) triplet between 100 GeV and 1 TeV for a conventional GUT scale of about 10^{16} GeV, with main decays into W (Z) and leptons, correlated through Dirac Yukawa couplings, and lifetimes shorter than about 10^{-12} sec. These decays are lepton number violating and they offer an exciting signature of Delta L=2 dilepton events together with 4 jets at future pp (p\bar p) colliders. Increasing the triplet mass endangers the proton stability and so the seesaw mechanism could be directly testable at LHC., Comment: 19 pages, discussion on leptogenesis added, new references, main conclusions unchanged