Analytical Soft SUSY Spectrum in Supersymmetric Models in Light of $ S_{4} \times Z_{n} $ flavor symmetric SUSY SO(10) theory
Gayatri Ghosh
备注：
23 pages,8 figures, 3 Tables
发表信息：
International Journal of Innovative Research in Science, Engineering and Technology, Vol. 9, Issue 3, March 2020,ISSN(Online): 2319-8753 ISSN (Print): 2347-6710
The heavy right-handed neutrinos in supersymmetric models can act as the source of lepton flavor violation (LFV). LFV processes like $ μ\rightarrow e γ$, $ τ\rightarrow μγ$, $ τ\rightarrow e γ$ is an effective way to explore new physics beyond the SM. Among the possible processes, $ μ$ decays have the greatest discovery potential in most of the supersymmetric models. Experimental inference of lepton flavor-violating processes within a supersymmetric type-II seesaw framework in the non-universal Higgs model (NUHM) and non-universal Scalar Mass model for Yukawa mixing scenarios in the $ S_{4} $ theory with an additional discrete symmetry is presented. The numerical analysis includes full 2 loop renormalization group running effects for the the above mentioned Yukawa coupling matrices. The projected discovery reach of LFV experiments (MEG-II) is mentioned and those regions in mSUGRA, NUHM, NUSM models that have already been excluded by the LHC searches or that which is probed by MEG experiments is specified here. The results presented in this work can influence experimental challenges and physics motivations to construct various BSM theories and sensitivity to test these theories at next run of HE/HL LHC is also considered.
We systematically analyze the correlations between the various leptonic and hadronic flavor violating processes arising in SUSY Grand Unified Theories. Using the GUT-symmetric relations between the soft SUSY breaking parameters, we assess the impact of hadronic and leptonic flavor observables on the SUSY sources of flavor violation.
I present SUSY_FLAVOR - a Fortran 77 program able to calculate simultaneously 29 low-energy flavor and CP-violating observables in the general R-parity conserving MSSM, including the case of large flavor violation in the sfermion sector. SUSY_FLAVOR v2 performs also the resummation of chirally enhanced corrections, arising in large $\tanβ$ regime and/or large trilinear soft mixing terms, to all orders of perturbation theory. I discuss an example of application of SUSY_FLAVOR to analysis of the $B_s \to μ^+ μ^-$ decay rate in the MSSM.
We propose a SUSY scenario to explain the current electron and muon $g-2$ discrepancies without introducing lepton flavor mixings. Threshold corrections to the Yukawa couplings can enhance the electron $g-2$ and flip the sign of the SUSY contributions. The mechanism predicts a flavor-dependent slepton mass spectrum. We show that it is compatible with the Higgs mediation scenario.
The neutrino flavor mixing may induce rich flavor and CP violating phenomena in the SUSY GUTs. In this paper we discuss the hadronic EDMs and the correlation among low-energy processes induced by the mixings between second and third generations in the SUSY SU(5) GUT with the right-handed neutrinos.
SUSY_FLAVOUR 2.0 is a FORTRAN code calculating over 30 low-energy flavour- and CP-related observables in the R-parity conserving MSSM. The code admits for the most general flavour structure of the SUSY breaking terms and complex flavour-diagonal couplings. It includes the numerically important resummation of chirally enhanced effects and it is fast enough for scanning over a large SUSY-parameter space. The program can be obtained from http://www.fuw.edu.pl/susy_flavor.
In 5D SUSY GUTs, wave-function localization permits to reproduce flavour hierarchy. As this mechanism also acts on SUSY breaking parameters, it can potentially solve the SUSY flavour problem. We carry out an analysis of the Holographic Grand Unification framework, where we take properly into account effects of matrix anarchy. In this contribution, we focus on brane-localized SUSY breaking and its consequences.
We discuss the decoupling solution to SUSY flavor problem in the fat brane scenario. We present a simple model to yield the decoupling sfermion spectrum in a five dimensional theory. Sfermion masses are generated by the overlap between the wave functions of the matter fields and the chiral superfields on the SUSY breaking brane. Two explicit examples of the spectrum are given.
Lepton flavor and CP violation in supersymmetric models are briefly reviewed. After a short motivation and an introduction to the phenomenology, model independent constraints on mass insertions, predictions of SUSY GUT models and rates for several LFV and CPV processes are presented.
We study effects of SUSY particles in the unitarity triangle analysis and the CP asymmetries in b -> s decays. We consider three different SUSY models, the minimal supergravity, SU(5) SUSY GUT with right-handed neutrinos, and MSSM with U(2) flavor symmetry, and show that the patterns and correlations of deviations from the standard model will be useful to discriminate the different SUSY models in future B experiments.
We study hadronic and leptonic flavor physics in a SUSY SO(10) model proposed by Chang, Masiero, and Murayama, which links b -> s transitions to the observed large atmospheric neutrino mixing angle. We find large effects in B_s-B_s-bar mixing and BR(tau -> mu gamma) and comment on B_d -> phi K_S.
We propose an $SO(10)$ supersymmetric grand unified theory (SUSY GUT), where the $SO(10)$ gauge symmetry breaks down to $SU(3)_c \times SU(2)_L \times U(1)_Y\times U(1)_{X}$ at the GUT scale and $U(1)_X$ is radiatively broken at the SUSY-braking scale. In order to achieve the observed Higgs mass around $126$ GeV and also to satisfy constraints on flavor- and/or CP-violating processes, we assume that the SUSY-breaking scale is $O(100)$ TeV, so that the $U(1)_X$ breaking scale is also $O(100)$ TeV. One big issue in the SO(10) GUTs is how to realize realistic Yukawa couplings. In our model, not o…
We study a finite SU(5) grand unified model based on the non-Abelian discrete symmetry A_4. This model leads to the democratic structure of the mass matrices for the quarks and leptons. In the soft supersymmetry breaking sector, the scalar trilinear couplings are aligned and the soft scalar masses are degenerate, thus solving the SUSY flavor problem.
This study indicates that in E6 grand unified theories (GUTs), once a hierarchical structure of up-quark-type Yukawa couplings is given as a basic structure of flavor, larger lepton mixings than the quark mixings and milder down-quark-type (and charged-lepton-type) mass hierarchies than up-quark-type mass hierarchy can generically be obtained under a few natural assumptions. The basic flavor structure is compatible with non-Abelian horizontal symmetry, which can solve the SUSY flavor problem. It is shown that in solving the SUSY flavor problem, the E6 structure, which realizes bi-large neutrin…
We address the problem of rationalizing the pattern of fermion masses and mixings by adding a nonabelian flavor symmetry in a grand unified framework. With this purpose, we include an A4 flavor symmetry into a unified renormalizable SUSY GUT SU(5) model. With the help of the "Type II Seesaw" mechanism we are able to obtain the pattern of observed neutrino mixings in a natural way, through the so called tribimaximal matrix.
We present SUSY_FLAVOR version 2.5 - program that calculates over 30 low-energy flavor observables in the general $R$-parity conserving MSSM. Comparing to previous versions, in SUSY_FLAVOR v2.5 parameter initialization in SLHA2 formats has been significantly generalized, so that the program accepts most of the output files produced by other libraries analyzing the MSSM phenomenology. Number of bugs and inconsistencies have been fixed, based on users feedback. Calculations of several processes implemented in earlier versions have been corrected. New processes of rare decays of the top quark to …
If supersymmetry (SUSY) solves the hierarchy problem, then naturalness considerations coupled with recent LHC bounds require non-trivial superpartner flavor structures. Such "Natural SUSY" models exhibit a large mass hierarchy between scalars of the third and first two generations as well as degeneracy (or alignment) among the first two generations. In this work, we show how this specific beyond the standard model (SM) flavor structure can be tied directly to SM flavor via "Flavor Mediation". The SM contains an anomaly-free SU(3) flavor symmetry, broken only by Yukawa couplings. By gauging thi…
Although the sneutrino is a viable NLSP candidate with gravitino LSP, spectra of this type occupy a part of SUSY parameter space in which collider signatures are poorly studied. In this paper we will extend previous work on this topic to include sneutrino NLSP spectra with non-minimal phenomenology. Generally, these spectra exhibit very leptophilic behavior, which can be easily observed at the LHC. We show that a variety of such spectra can be analysed with similar techniques, leading in each case to very suggestive evidence for complicated decay chains that end in sneutrinos. Amongst the vari…
We present the program package SUSY-HIT for the computation of supersymmetric particle decays within the framework of the Minimal Supersymmetric extension of the Standard Model. The code is based on two existing programs HDECAY and SDECAY for the calculation of the decay widths and branching ratios of, respectively, the MSSM Higgs bosons and the SUSY particles, and calls a program for the calculation of the SUSY particle spectrum such as SuSpect. Including all important higher order effects, the package allows the consistent calculation of the MSSM particle spectrum and decays with the present…
Radiative flavor models where the hierarchies of Standard Model (SM) fermion masses and mixings are explained via loop corrections are elegant ways to solve the SM flavor puzzle. Here we build such a model in the context of Mini-Split Supersymmetry (SUSY) where both flavor and SUSY breaking occur at a scale of 1000 TeV. This model is consistent with the observed Higgs mass, unification, and WIMP dark matter. The high scale allows large flavor mixing among the sfermions, which provides part of the mechanism for radiative flavor generation. In the deep UV, all flavors are treated democratically,…
Modular flavor symmetry can be used to explain the quark and lepton flavor structures. The SUSY partners of quarks and leptons, which share the same superpotential with the quarks and leptons, will also be constrained by the modular flavor structure and show a different flavor(mixing) pattern at the GUT scale. So, in realistic modular flavor models with SUSY completion, constraints from the collider and DM constraints can also be used to constrain the possible values of the modulus parameter. In the first part of this work, we discuss the possibility that the $S_3$ modular symmetry can be pres…
In supersymmetric (SUSY) models the misalignment between fermion and sfermion families introduces unsuppressed flavor-changing processes. Even if the mass parameters are chosen to give no flavor violation, family dependent radiative corrections make this adjustment not stable. In particular, due to the observed large neutrino mixings and potentially large neutrino Yukawa couplings, sizable lepton flavor violation (LFV) is expected. After introducing the basic concepts, the framework and the main assumptions, we report on a recent study of rare leptonic decays in a class of SUSY-GUT models with…
We show how an intermediate gauge symmetry breaking scale can be a source of lepton flavor violation and EDM of electron and neutron in SUSY GUTs. The Universal soft supersymmetry breaking operators can be introduced at the GUT scale or above.
We consider the renormalization group approach to the SUSY flavor problem in the supersymmetric SU(5) model with one extra dimension. In higher dimensional SUSY gauge theories, it has been recently shown that power corrections due to the Kaluza-Klein states of gauge fields run the soft masses generated at the orbifold fixed point to flavor conserving values in the infra-red limit. In models with GUT breaking at the brane where the GUT scale can be larger than the compactification scale, we show that the addition of a bulk Higgs multiplet, which is necessary for the successful unification, is c…
Within supersymmetric SU(5) Grand Unified Theory, we present several new scenarios with anomaly free flavor symmetry U(1)_F. Within each scenario, a variety of cases offer many possibilities for phenomenologically interesting model building. We present three concrete and economical models with anomaly free U(1)_F leading to natural understanding of observed hierarchies between charged fermion masses and CKM mixing angles.
We analyze the flavor structure of the trilinear couplings in the different theoretical models of SUSY breaking. We generically obtain A_{ij}= A^L_i + A^R_j in all the models examined. In fact, this is the rigorous form when SUSY breaking effects appear through the Kahler metric of chiral fields or through wave-function renormalization. Indeed, the low-energy phenomenological requirements from the absence of charge and color breaking minima and the measurements in flavor changing neutral current (FCNC) observables strongly favor this restricted form of the trilinear matrices. As a straightforw…
In this talk, I will present the general structure of RPV couplings when a Froggatt-Nielsen horizontal symmetry is responsible for the flavor structure of both the SM and the MSSM. For sub-TeV ({\it natural}) SUSY, lepton number must be an accidental symmetry, while low-energy SUSY is still allowed by baryonic RPV, which lowers the MET signature of superparticles decays. The largest RPV coupling involves the stop, and it is constrained between $10^{-3}$ (from FCNCs) and $10^{-9}$ (from LHC searches).
We obtain predictions for the neutrino masses, the effective Majorana mass in neutrinoless double beta decay and for the rates of the lepton flavor violating processes $μ\rightarrow e + γ$, $τ\rightarrow e + γ$ and $ τ\rightarrow μ+ γ$ in a SUSY $SU(5) \times T^{\prime}$ Model of flavour, which gives rise to realistic masses and mixing patterns for quarks and leptons.
Flavor structure of soft supersymmetry breaking parameters is studied in a certain type of effective supergravity theory derived from moduli/dilaton dominated supersymmetry breaking. Some interesting sum rules for soft scalar masses are presented. They constrain their flavor structure and predict some interesting patterns appeared in soft scalar masses in the non-universal case. We also study the alignment phenomena in the flavor space of soft breaking parameters due to Yukawa couplings and discuss their phenomenological consequences.
We discuss slepton mass matrices in the $S_4$ flavor model with SUSY SU(5) GUT. By considering the gravity mediation within the framework of supergravity theory, we estimate the SUSY breaking terms in the slepton mass matrices, which contribute to the $μ\rightarrow e + γ$ decay. We obtain a lower bound for the ratio of $μ\rightarrow eγ$ as $10^{-13}$ if $m_{\text{SUSY}}$ and $m_{1/2}$ are below 500GeV. The off diagonal terms of slepton mass matrices also contribute to EDM of leptons. The predicted electron EDM is around $10^{-29}-10^{-28}$cm. Our predictions are expected to be tested in the ne…
Realizing that couplings related by supersymmetry (SUSY) can be disentangled when SUSY is broken, it is suggested that unwanted flavor and CP violating SUSY couplings may be suppressed via quenched gaugino-flavor interactions, which may be accomplished by power-law running of sfermion anomalous dimensions. A simple theoretical framework to accomplish this is exemplified and the defeated constraints are tallied. One key implication of the scenario is the expectation of enhanced top, bottom and tau production at the LHC, accompanied by large missing energy. Also, direct detection signals of dark…
High precision electroweak tests, such as deviations from the Standard Model expectations of the Lepton Flavor Universality breaking in K->lnu (with l= e or mu), represent a powerful tool to test the Standard Model and, hence, to constrain or obtain indirect hints of New Physics beyond it. We explore such a possibility within Supersymmetric theories. Interestingly enough, a process that in itself does not need lepton flavor violation to occur, i.e. the violation of mu-e non-universality in K_l2, proves to be quite effective in constraining not only relevant regions of SUSY models where lepton …
The (B_{d}\longrightarrow ΦK_{s}) process is without tree level decay amplitude . Then the SUSY contributions may be significant . We calculate the neutralino and gluino penguin contributions to the CP violating phase in (SU(5) ) grand unified theory with right-handed neutrino (SU(5)_{RN}) . We find that the SUSY contribution may change the phase in (B_{d}\longrightarrow ΦK_{s} ).
We discuss the phenomenological impact of a particularly interesting corner of the MSSM: the large tan(beta) regime. The capabilities of leptonic and hadronic Flavor Violating processes in shedding light on physics beyond the Standard Model are reviewed. Moreover, we show that tests of Lepton Universality in charged current processes can represent an interesting handle to obtain relevant information on New Physics scenarios.
Patterns of flavor violation induced by neutrino Yukawa couplings are discussed in realistic ``minimal'' SUSY SU(5) models, obtained by adding nonrenormalizable operators to the minimal one, in order to fix the fermion spectrum and suppress proton decay. Results are presented for the three possible implementations of the seesaw mechanisms, i.e. of Type I, II and III.
We discuss a GUT realization of the supersymmetric triplet seesaw mechanism(recently proposed by us in hep-ph/0604083 and further analyzed in hep-ph/0607298) where the exchange of the heavy triplet states generates both neutrino masses and soft SUSY breaking terms.
Rare decays of B and K mesons and CP violations thereof are considered in SUSY models with S_3^3 flavor symmetry. SUSY contributions to epsilon_K and epsilon'/epsilon_K can be large, but not to B0 - B0 bar mixing because of strong constraint from B -> X_d gamma for (delta^d_{13})_{LR}. Still large deviations from the SM predictions are possible in the branching ratio for B -> X_d gamma and direct CP violations therein, even if the KM angle gamma is in the range preferred by the SM CKM fit. Experimental study of B -> X_d gamma is strongly recommended as a probe for new physics with nontrivial f…
The flavor changing top quark decays t -> cV (V=Z,photon,gluon) induced by R-parity-violating couplings in the minimal supersymmetric standard model (MSSM) are evaluated. We find that the decays t -> cV can be significantly enhanced relative to those in the R-parity conserving SUSY model. Our results show that the top quark FCNC decay can be as large as Br(t->cg)=10^-3, Br(t->cZ)=10^-4 and Br(t-> cγ)= 10^-5, which may be observable at the upgraded Tevatron and/or the LHC.
We analyze the scalar lepton mass matrices in a supersymmetric SO(10) grand unified model with soft SUSY breaking terms generated at Planck scale and a Georgi-Jarslkog Yukawa texture at GUT scale induced by higher dimensional operators. This model predicts lepton flavor violation. The predictive features of the Georgi-Jarlskog texture are used to estimate branching ratios for the radiative decays $e_{a} \rightarrow e_{b}+γ,$ and we find rates that could provide an experimental test for this kind of model.
Neutrino oscillations give clear evidence for non-vanishing neutrino masses and lepton-flavor violation (LFV) in the neutrino sector. This provides strong motivation to search for signals of LFV also in the charged lepton sector, and to probe the SUSY see-saw mechanism. We compare the sensitivity of rare radiative decays on the right-handed Majorana mass scale M_R with the reach in slepton-pair production at a future linear collider.
Supersymmetric flavor models for the radiative generation of fermion masses offer an alternative way to solve the SUSY-CP problem. We assume that the supersymmetric theory is flavor and CP conserving. CP violating phases are associated to the vacuum expectation values of flavor violating susy-breaking fields. As a consequence, phases appear at tree level only in the soft supersymmetry breaking matrices. Using a U(2) flavor model as an example we show that it is possible to generate radiatively the first and second generation of quark masses and mixings as well as the CKM CP phase. The one-loop…
An SO(10) SUSY GUT model which leads to maximal atmospheric neutrino mixing and the LMA solar neutrino solution, developed in collaboration with S.M. Barr, is briefly described. Since the model is quantitatively predictive, it can be used to assess the need for a neutrino factory, as shown in collaboration with S. Geer.
We study the constraints on a minimal supersymmetric seesaw model imposed by neutrino data, charged lepton flavor violation, thermal leptogenesis and perturbativity. We show that it is possible to constrain the three heavy Majorana neutrino masses as well as the complex Yukawa coupling matrix. Our results provide a first step towards a seesaw benchmark model for further phenomenological studies and model building.
It is sometimes argued that a virtue of pushing the supersymmetry breaking scale above 1 PeV is that no particular flavor structure is required in the soft sector in order to evade bounds on flavor-changing neutral currents. However, without flavor structure, suppressing generic Planck-suppressed contributions to proton decay requires even higher SUSY scales, of order $10^{11}$ ($10^9$) GeV for degenerate (mini-split) gauginos and scalars. With flavor structure, the question of whether proton decay or flavor symmetries are more constraining is model-dependent, but it straightforward to find si…
A Supersymmetric Grand unified model is constructed based on SO(10)xSO(10) symmetry in which new types of Yukawa matrices couple standard and exotic fermions. Evolution of these couplings from the Grand Unified scale to the electroweak scale causes some of them to be driven to their fixed points. This solves the supersymmetric alignment problem and ensures that there are no observable flavor changing neutral currents mediated by supersymmetric particles. Fermion hierarchy and neutrino mixing constraints are automatically satisfied in this formalism.
I discuss the effects of QCD radiative corrections in Supersymmetric theories. After summarizing the SUSY--QCD lagrangian in the Minimal Supersymmetric extension of the Standard Model, I will discuss the new features introduced by SUSY, and the main complications compared to standard QCD corrections. I will then discuss a few examples of QCD calculations in SUSY theories, for standard processes and for processes involving SUSY particles including the extended Higgs sector. [Talk given at "QCD 97", Montpellier 3-9 July 1997.]
I review some of the latest directions in supersymmetric model building, focusing on SUSY breaking mechanisms in the minimal supersymmetric standard model [MSSM], the "little" hierarchy and $μ$ problems, etc. I then discuss SUSY GUTs and UV completions in string theory.
Constraints from flavour changing neutral currents are discussed in the context of predictive Grand Unified Supersymmetric Theories. Uncertainties in the estimation of their amplitudes are minimized by using a successful mass matrix ansatz which predicts the arbitrary parameters of the Standard Model. Furthermore, Renormalization Group Equations are used in order to express the sparticle masses involved, in terms of the gaugino mass $m_{1/2}$, the universal scalar mass $m_0$ and the trilinear coupling $A$ at the GUT scale. Modifications in the low energy expressions for the squark masses due t…
Motivated by the recent measurements of the B_s-\bar{B}_s mass difference from the D0 and CDF collaborations, we probe new physics effects in the B_q-\bar{B}_q mixing within the context of the supersymmetric grand unified model (SUSY GUT). We find that new physics effects in B_{s(d)}-\bar{B}_{s(d)} mixing lead to the correlated information in the branching fractions of the lepton flavor violating decays, which may serve as a test of the SUSY GUT. We also discuss the implication of such new physics effects on the quark-lepton complementarity in the neutrino mixings.
Three topics on phenomenology in supersymmetric models are reviewed, namely, the Higgs sector in the supersymmetric model, B and K meson decay in the supergravity model and lepton flavor violation processes in supersymmetric grand unified theory.
Neutrino oscillation experiments suggest existence of new flavor-violating interactions in high energy scale. It may be possible to probe them by the flavor- and CP-violating processes in leptons and hadrons in the supersymmetric (SUSY) models. In this article the third-generation flavor violation is reviewed in the SUSY seesaw model and SUSY SU(5) GUT with the right-handed neutrinos.
We consider a supersymmetric extension of the standard model, which possess a family symmetry based on a binary dihedral group Q6, and investigate the consequences of the family symmetry on the mixing of fermions, FCNCs and the stability of proton.
We demonstrate that supersymmetric decay modes of the neutral Higgs bosons of the MSSM could well make their detection extremely difficult when produced singly in $\gam\gam$ collisions at a back-scattered laser beam facility.
We present a quantitative analysis of the flavor physics of a SUSY SO(10) model proposed by Chang, Masiero, and Murayama, linking b -> s transitions to the large observed atmospheric neutrino mixing. We consider B_s-B_s-bar mixing and tau -> mu gamma and discuss their correlation paying careful attention to their different dependences on model parameters. Our analysis shows that an order-of-magnitude enhancement of the mass difference with respect to the Standard Model is possible and can be reconciled with the most stringent bounds on lepton flavor violation. The situation for various Delta B…
We study leptonic CP and flavor violations in supersymmetric (SUSY) grand unified theory (GUT) with right handed neutrinos, paying attention to the renormalization group effects on the slepton mass matrices due to the neutrino and GUT Yukawa interactions. In particular, we study in detail the impacts of the so-called Casas- Ibarra parameters on CP and flavor violating observables. The renormalization group effects induce CP and flavor violating elements of the SUSY breaking scalar mass squared matrices, which may result in sizable leptonic CP and flavor violating signals. Assuming seesaw formu…
We review the theoretical and experimental status of minimal grand unified theories (GUTS), contrasting the failure of minimal non-supersymmetric $SU(5)$ with the success of the minimal supersymmetric $SU(5)$ and minimal supersymmetric Flipped $SU(5)\times U(1)$ models. We show that a reasonable value for the universal soft supersymmetry-breaking gaugino mass, $45\GeV<m_{1/2}<1\TeV$, and a $1-σ$ range of the other inputs constrains the strong coupling, $\as>.114$. We define the supersymmetric standard model (SSM), the minimal supersymmetric extension of the standard model with gauge coupling u…
Taking the supersymmetric inverse seesaw mechanism as the explanation for neutrino oscillation data, we investigate charged lepton flavor violation in radiative and 3-body lepton decays as well as in neutrinoless $μ-e$ conversion in muonic atoms. In contrast to former studies, we take into account all possible contributions: supersymmetric as well as non-supersymmetric. We take CMSSM-like boundary conditions for the soft supersymmetry breaking parameters. We find several regions where cancellations between various contributions exist, reducing the lepton flavor violating rates by an order of m…
We address the SUSY CP problem in the framework of Minimal Flavor Violation (MFV), where the SUSY flavor problem finds a natural solution. By contrast, the MFV principle does not solve the SUSY CP problem as it allows for the presence of new {\it flavor blind} CP-violating phases. Then, we generalize the MFV ansatz accounting for a natural solution of it. The phenomenological implications of the generalized MFV ansatz are explored for MFV scenarios defined both at the electroweak (EW) and at the GUT scales.
