We study the $Y=0$ triplet extended supersymmetric model in the light of the recent Higgs boson discovery. We calculate full one loop Higgs mass spectrum in this model where the possible doublet-triplet mixing is considered in the charged Higgs sector. This mixing changes the prediction of $\mathcal{B}r(B_s\to X_s γ)$ in this model, compared to the MSSM. The constraints from the $\sim 125$ GeV Higgs along with $\mathcal{B}r(B_s\to X_s γ)$ are incorporated to find out the allowed parameter space. The lower bounds on the third generation squark masses coming from 125 GeV Higgs are rather week in this scenario compared to most constrained supersymmetric scenarios, e.g. a 200 GeV squark mass is still possible.
We propose a novel supersymmetric unified scenario of the triplet seesaw mechanism where the exchange of the heavy triplets generates both neutrino masses and soft supersymmetry breaking terms. Our framework is very predictive since it relates neutrino mass parameters, lepton flavour violation in the slepton sector, sparticle and Higgs spectra and electroweak symmetry breakdown. The phenomenological viability and experimental signatures in lepton flavor violating processes are discussed.
The experimental determination of the muon magnetic moment and its theoretical prediction within the Standard Model and the MSSM are reviewed. A 3 sigma deviation between experiment and Standard Model prediction has been established, and supersymmetry could provide a natural explation of this deviation. Possible future improvements and the case for a new experiment are discussed.
We review: 1) constraints on low energy supersymmetry from the search for Higgs boson and from precision data, 2) dependence of coupling unification on the superpartner spectrum, 3) naturalness and fine tuning in the minimal and non-minimal scenarios.
A short summary of constraints on the parameter space of supersymmetric models is given. Experimental limits from high energy colliders, electroweak precision data, flavor and Higgs physics, and cosmology are considered. The main focus is on the MSSM with conserved R- and CP-parity and minimal flavor violation, but more general scenarios and extended models will also be discussed briefly.
Supersymmetry remains compelling theory over 30 years in spite of lack of its discovery. It could be already near the corner our days, therefore present and upcoming experiments are crucial for constraining or even discovery of the supersymmetry.
Supersymmetry searches are about to enter an important new era. With LEP 200 and the Main Injector, they will, for the first time, begin to probe significant regions of the supersymmetric parameter space. There is a real chance that supersymmetry might indeed be found before the advent of the LHC.
We present an example of the gauge mediated SUSY breaking flipped SU(5) model. The messengers of the SUSY breaking are either only colour triplets which belong to the minimal content of the scalar supermultiplets or together with triplets as a messengers emerge the ordinary Higgs doublets. In both cases the model predicts light gauginos in respect of the squarks and sleptons, which could be tested in the nearest LEP experiments. In both cases ''all order`` solution of the doublet-triplet splitting problem is obtained, the $μ$-term of the order of 100 GeV is generated and the left handed neutri…
Anomaly mediated supersymmetry breaking (AMSB), when implemented in MSSM is known to suffer from the problem of negative slepton mass squared leading to breakdown of electric charge conservation. We show however that when MSSM is extended to explain small neutrino masses by including a pair of superheavy Higgs triplet superfields (the type II seesaw mechanism), the slepton masses can be deflected from the pure AMSB trajectory and become positive. In a simple model we present in this paper, the seesaw scale is about $10^{13}-10^{14}{\rm GeV}$. Gauge coupling unification can be maintained by emb…
In this talk we discuss the constraints on supersymmetry arising from data from a number of recent experiments. There appears to be good cumulative evidence from experiment in favor of positivity of the sign of the Higgs mixing parameter $μ$. Implications of this result for Yukawa unification are discussed since Yukawa unification is sensitive to the $μ$ sign. An analysis of dark matter under the constraints of Yukawa unification is also given. It is shown that the simultaneous imposition of all existing constraints sharply defines the parameter space of models. Specifically models with nonuni…
In the first lecture we review the current status of local supersymmetry. In the second lecture we focus on D=11 supergravity as the low-energy limit of M-theory and pose the questions: (1) What are the D=11 symmetries? (2) How many supersymmetries can M-theory vacua preserve?
We study soft supersymmetry breaking parameters in a supersymmetric unified model which potentially solves the doublet-triplet splitting problem. In the model the doublet-triplet splitting is solved by the discrete symmetry which is allowed to be introduced due to the direct product structure of the gauge group. The messenger fields for the gauge mediated supersymmetry breaking are naturally embedded in the model. The discrete symmetry required by the doublet-triplet splitting makes the gaugino masses non-universal and also induces a different mass spectrum for the scalar masses from the ordin…
We consider the minimal supersymmetric triplet seesaw model as the origin of neutrino masses and mixing as well as of the baryon asymmetry of the Universe, which is generated through soft leptogenesis employing a CP violating phase and a resonant behavior in the supersymmetry breaking sector. We calculate the full gauge--annihilation cross section for the Higgs triplets, including all relevant supersymmetric intermediate and final states, as well as coannihilations with the fermionic superpartners of the triplets. We find that these gauge annihilation processes strongly suppress the resulting …
The purely leptonic rare decay Bs -> mu+mu- is very sensitive to supersymmetric contributions which are free from the helicity suppression of its Standard Model diagrams. The recent observation of the decay by the LHCb experiment and the first determination of its branching fraction motivate a review of their impact on the viable parameter space of supersymmetry. In this paper we discuss the implications of the present and expected future accuracy on BR(Bs -> mu+mu-) for constrained and unconstrained MSSM scenarios, in relation to the results from direct SUSY searches and the Higgs data at the…
We studied the extension of Standard Model (SM) Higgs sector with $SU(2)$ triplet and SM gauge singlet in the context of supersymmetry. For a $Z_3$ symmetric superpotential where the singlet field generates the bi-linear Higgs mixing term between two Higgs doublets dynamically. Models like this often have a very light pseudoscalar as pseudo-Nambu Goldstone model of an extra $U(1)$ symmetry. We investigate the possibility of such light hidden Higgs boson with the data of the discovered Higgs boson around 125 GeV. Along with the neutral sector, the charged Higgs bosons in the triplet extended ca…
The ATLAS and CMS experiments at the Large Hadron Collider (LHC) at CERN have searched for signals of new physics, in particular for supersymmetry. The data collected until 2012 at center-of-mass energies of 7 and 8 TeV and integrated luminosities of 5 fb^-1 and 20 fb^-1, respectively, agree with the expectation from standard model processes. Constraints on supersymmetry have been calculated and interpreted in different models. Limits on supersymmetry particle masses at the TeV scale have been derived and interpreted generally in the context of simplified model spectra. The constrained minimal…
An overview of supersymmetry searches is presented, covering collider experiments, direct and indirect searches for supersymmetric dark matter. Recent LHC experimental results are reviewed, and the constraints from B-meson decays are reported. Implications for supersymmetry of the latest direct and indirect searches are thoroughly discussed. The focus is on the complementarity of the various probes -- particle and astrophysical -- for constraining Supersymmetry.
Experiments at particle colliders have reached center of mass energies well above 100 GeV, equivalent to temperatures which existed shortly after the big bang. These experiments, testing the initial conditions of the universe have, with great precision, established the Standard Model of Particle Physics. In contrast, the existence of the Higgs boson and perhaps Supersymmetry remain speculative, as todays searches have failed to find signs of their existence. However, the next generation of high energy collider experiments and especially CERN's 14 TeV LHC, expected to start operation in the yea…
I provide a brief summary of the status of supersymmetric models with parameters defined at either the unification or weak scale, based on global fits using the GAMBIT framework.
For decades, the unnaturalness of the weak scale has been the dominant problem motivating new particle physics, and weak-scale supersymmetry has been the dominant proposed solution. This paradigm is now being challenged by a wealth of experimental data. In this review, we begin by recalling the theoretical motivations for weak-scale supersymmetry, including the gauge hierarchy problem, grand unification, and WIMP dark matter, and their implications for superpartner masses. These are set against the leading constraints on supersymmetry from collider searches, the Higgs boson mass, and low-energ…
The fine tuning in models of low energy gauge mediated supersymmetry breaking required to obtain the correct $Z$ mass is quantified. To alleviate the fine tuning problem, a model with split $(5+\bar{5})$ messenger fields is presented. This model has additional triplets in the low energy theory which get a mass of $O(500)$ GeV from a coupling to a singlet. The improvement in fine tuning is quantified and the spectrum in this model is discussed. The same model with the above singlet coupled to the Higgs doublets to generate the $μ$ term is also discussed. A Grand Unified version of the model is …
In the supersymmetric triplet (type-II) seesaw model, in which a single SU(2)_L-triplet couples to leptons, the high-energy neutrino flavour structure can be directly determined from the low-energy neutrino data. We show that even with such a minimal triplet content, leptogenesis can be naturally accommodated thanks to the resonant interference between superpotential and soft supersymmetry breaking terms.
I summarize recent devlopments in supersymmetry scenarios which leave some or all gauginos light. The emphasis is on experimental and phenomenological progress in the past year.
We discuss a supersymmetric SU(6) grand unified theory with the GUT flat direction being lifted by soft supersymmetry breaking, and the doublet-triplet splitting being achieved with Higgs as a pseudo-Goldstone boson. The theory offers a simple solution to the false vacuum and monopole problems.
The second period of datataking at the Large Hadron Collider (LHC) has provided a large dataset of proton-proton collisions that is unprecedented in terms of its centre-of-mass energy of 13 TeV and integrated luminosity of almost 140 fb$^{-1}$. These data constitute a formidable laboratory for the search for new particles predicted by models of supersymmetry. The analysis activity is still ongoing, but a host of results on supersymmetry has already been released by the general purpose LHC experiments ATLAS and CMS. In this paper, we provide a map into this remarkable body of research, which sp…
We thoroughly discuss a new supersymmetric grand unified scenario of the triplet seesaw mechanism where the exchange of heavy SU(2)_W triplet states generates both neutrino masses and soft supersymmetry breaking terms. This framework, recently proposed by us in a previous work, is highly predictive since it contains only three free parameters connecting low-energy neutrino parameters, lepton and quark flavour violation, sparticle and Higgs boson spectra and electroweak symmetry breakdown. These three parameters are the triplet mass M_T, the effective supersymmetry breaking scale B_T and a coup…
Supersymmetry (SUSY) is a complete and renormalisable candidate for an extension of the Standard Model. At an energy scale not too far above the electroweak scale it would solve the hierarchy problem of the SM Higgs boson, dynamically explain electroweak symmetry breaking, and provide a dark-matter candidate. Since it doubles the Standard Model degrees of freedom, SUSY predicts a large number of additional particles, whose properties and effects on precision measurements can be explicitly predicted in a given SUSY model. In this review the motivation for SUSY is outlined, the various searches …
The basics of a supersymmetric left-right model are reviewed. The production and subsequent decays of the doubly charged triplet higgsino $ \tildeΔ^{\pm\pm}$ in the Next Linear Collider are discussed. The slepton pair production in the framework of this model is also analysed.
We briefly review the current status and future prospects for supersymmetry searches at colliders, and discuss strategies by which further information about sparticle properties may be obtained at the LHC.
The lightest neutralino in supersymmetry is the most studied dark matter candidate. This writeup reviews the status of neutralino dark matter in minimal and nonminimal supersymmetric models in light of recent null results at the XENON100 experiment and the observation of a 130 GeV gamma ray signal from the Galactic Center by the Fermi LAT.
Grand Unified Theories based on the group SO(10) generically provide interesting and testable relations between the charged fermions and neutrino sector masses and mixings. In the light of the recent neutrino data, we reexamine these relations both in supersymmetric and non-supersymmetric models, and give a brief review of their present status.
The status of coupling constant unification in standard supersymmetric SU(5) model and its extensions is discussed. Taking into account uncertainties related with the initial coupling constants and threshold corrections at low and high scales we find that in supersymmetric SU(5) model the scale of supersymmetry breaking could be up to $10^8$ Gev. In the extensions of standard SU(5) model it is possible to increase the supersymmetry breaking scale up to $10^{11}$ Gev.
We construct the minimal supersymmetric left-right theory and show that at the renormalizable level it requires the existence of an intermediate $B-L$ breaking scale. The subsequent symmetry breaking down to MSSM automatically preserves R-symmetry. Furthermore, unlike in the nonsupersymmetric version of the theory, the see-saw mechanism takes its canonical form. The theory predicts the existence of a triplet of Higgs scalars much lighter than the $B-L$ breaking scale.
In this paper, we minimize and compare two different fine-tuning measures in four high-scale supersymmetric models that are embedded in the MSSM. In addition, we determine the impact of current and future dark matter direct detection and collider experiments on the fine-tuning. We then compare the low-scale electroweak measure with the high-scale Barbieri-Giudice measure, which generally do not agree. However, we find that they do reduce to the same value when the higgsino parameter drives the degree of fine-tuning. Depending on the high-scale model and fine-tuning definition, we find a minima…
Recent results in study of the Minimal Supersymmetric Standard Model as the effective low energy theory give important hints for experimental search for supersymmetry. Also, in the bottom-up approach to explore weak scale - GUT scale connection, they constrain strongly physics at the GUT scale. Several theoretical ideas about the GUT physics are in stunning agreement with the low energy data.
We study natural supersymmetry in the Generalized Minimal Supergravity (GmSUGRA). For the parameter space with low energy electroweak fine-tuning measures less than 50, we are left with only the $Z$-pole, Higgs-pole and Higgsino LSP scenarios for dark matter (DM). We perform the focused scans for such parameter space and find that it satisfies various phenomenological constraints and is compatible with the current direct detection bound on neutralino DM reported by the LUX experiment. Such parameter space also has solutions with correct DM relic density besides the solutions with DM relic dens…
I review the status of supersymmetry after the 2011 LHC search results. I concentrate in particular on interpretations beyond the conventional CMSSM, including i) natural SUSY with light stops, and ii) the so-called phenomenological MSSM, which is a general parametrization of the MSSM at the weak scale, without boundary conditions imposed by specific SUSY breaking schemes. We will see that the current searches are not yet sensitive to some of the theoretically most interesting scenarios.
Models for dynamical breaking of supersymmetric grand unified theories are presented. The doublet-triplet splitting problem is absent since the Higgs doublet superfields can be identified with the massless mesons of the strong gauge group whereas there are no massless states corresponding to the colored Higgs fields. Various strong gauge groups SU(Nc), Sp(Nc) and SO(Nc) are examined. In a model with SO(9) strong gauge group, adding the mu-term for the Higgs fields triggers to break supersymmetry in a meta-stable vacuum. The pattern of the supersymmetry breaking parameters is predicted to be th…
Higgs triplet models are known to have difficulties obtaining agreement with electroweak precision data and in particular constraints on the $ρ$ parameter. Either a global $SU(2)_L \otimes SU(2)_R$ symmetry has to be imposed on the scalar potential at the electroweak scale, as done in the well-known Georgi-Machacek (GM) model, or the triplet vacuum expectation values must be very small. We construct a supersymmetric model that can satisfy constraints on the $ρ$ parameter, even if these two conditions are not fulfilled. We supersymmetrize the GM model by imposing the $SU(2)_L \otimes SU(2)_R$ s…
A summary of neutrino oscillation results is given along with a discussion of neutrino mass generation mechanisms, including high and low-scale seesaw, with and without supersymmetry, as well as recent attempts to understand flavor. I argue that if the origin of neutrino masses is intrinsically supersymmetric, it may lead to clear tests at the LHC. Finally, I briefly discuss thermal leptogenesis and dark matter.
While LHC has discovered a very Standard Model-like Higgs boson of mass m_h~ 125 GeV, no solid signal for physics beyond the Standard Model has emerged so far at LHC or at WIMP seach experiments. For the case of weak scale supersymmetry (SUSY), LHC has found rather generally that gluinos are beyond about 2.2 TeV whilst top squark must lie beyond 1.1 TeV. These limits contradict older simplistic notions of naturalness that emerged in the 1980s-1990s, leading to the rather pessimistic view that SUSY is now excluded except for perhaps some remaining narrow corners of parameter space. Yet, this pi…
We review the status of heavy neutral gauge bosons, Z', with emphasis on constraints that arise in supersymmetric models, especially those motivated from superstring compactifications. We first summarize the current phenomenological constraints and the prospects for Z' detection and diagnostics at the LHC and NLC. After elaborating on the status and (lack of) predictive power for general models with an additional Z', we concentrate on motivations and successes for Z' physics in supersymmetric theories in general and in a class of superstring models in particular. We review phenomenologically v…
In this paper, we consider a chaotic inflation model where the role of inflaton is played by the Higgs triplet in type II seesaw mechanism for generating the small masses of left-handed neutrinos. Leptogenesis could happen after inflation. This model is constructed without introducing supersymmetry (SUSY).
The established results concerning the BRS cohomology of supersymmetric theories in four space-time dimensions are briefly reviewed. The current status of knowledge concerning supersymmetry anomalies and the possibility that supersymmetry breaks itself through anomalies in local composite operators is then discussed. It turns out that the simplest allowable supersymmetry anomalies occur only in conjunction with the spontaneous breaking of gauge symmetry. A simple example of such a possible supersymmetry anomaly is presented.
This Letter addresses a provocative question: ``Can the standard electroweak Higgs doublets and their color-triplet partners be the messengers of a low energy gauge-mediated SUSY breaking?" Such a possibility does not seem to be immediately ruled out. If so, it can lead to a very economical scheme with clear-cut predictions quite distinct from those of the conventional gauge-mediated scenario. Namely, we get (i) a single light Higgs below the original SUSY- breaking scale; (ii) tan(beta) = 1; (iii) flavor non-universal, but automatically flavor-conserving soft scalar masses; (iv) a light color…
We examine $E_6$ GUT models (both SUSY and non-SUSY) with D-parity violating intermediate trinification symmetry $\left(SU(3)_C\otimes SU(3)_L\otimes SU(3)_R\right)(g_{3L}\neq g_{3R})$ where the D-parity breaking is achieved by quantum gravity effect through dimension-5 operators. Inclusion of the gravitational effect significantly lowers the intermediate scale, being as low as $10$ TeV. However with a given choice of the intermediate mass $M_I$, the gauge unification mass $M_U$ as well as the GUT coupling constant are unaffected by the effects. The predicted value of $M_U$ is shown to be comp…
After briefly reviewing the status of epsilon'/epsilon in the Standard Model, I discuss SUSY contributions to epsilon'/epsilon, K^+ to pi^+ nu bar nu, K_L to pi^0 nu bar nu and K_L to pi^0 e^+ e^-. While in the simplest case of the MSSM with Minimal Flavour Violation the main effect is a suppression of these transitions with respect to the Standard Model, large enhancements are possible in more general SUSY models, with interesting correlations among the different processes.
Using properties of Goldstino, we show that in generic grand unified theories with gravity-mediated supersymmetry breaking the $μ$-problem is non-existent. What happens is that supersymmetry breaking universally induces the shifts of the heavy fields that generate $μ$ and $B_μ$ terms. In the leading order, these are given by the mass of gravitino and are insensitive to the scale of grand unification. The mechanism works regardless whether doublet-triplet splitting is achieved via fine-tuning or not. Moreover, we illustrate this general phenomenon on explicit examples of theories that achieve d…
We propose that a modified version of string-inspired supersymmetry breaking schemes in \cite{wit2} and \cite{ross} may make affine level one SU(5) and SO(10) string models with intermediate gauge symmetry breaking scale $M_{GUT}=10^{16}GeV$ possible; doublet-triplet problem can also be solved. In particular, we propose that some charged gauge background VEVs might be turned on when gaugino condensation happens in the hidden sector and would break gauge symmetry. One can dynamically determine gaugino condensation scale, local supersymmetry breaking scale and intermediate gauge symmetry breakin…
Gauge mediated supersymmetry breaking (GMSB) is an elegant mechanism to transmit supersymmetry breaking from the hidden to the MSSM observable sector, which solves the supersymmetric flavor problem. However the smallness of the generated stop mixing requires superheavy stops to reproduce the experimental value of the Higgs mass. Two possible ways out are: i) To extend GMSB by direct superpotential messenger-MSSM Yukawa couplings to generate sizeable mixing, thus reintroducing the flavor problem; ii) To extend the MSSM Higgs sector with singlets and/or triplets providing extra tree-level correc…
We review the status of searches for Supersymmetry at the Tevatron Collider. After discussing the theoretical aspects relevant to the production and decay of supersymmetric particles at the Tevatron, we present the current results for Runs Ia and Ib as of the summer of 1997. To appear in the book "Perspectives in Supersymmetry", edited by G.L. Kane, World Scientific.
In the framework in which supersymmetry is used for understanding fermion masses rather than stabilizing the electroweak scale, we elaborate the phenomenological analysis for the neutrino physics. A relatively large $\sin{θ_{13}}$ is the natural result. The model further predicts vanishingly small CP violation in neutrino oscillations. And $θ_{23}$ is not necessarily maximal. While the high scale supersymmetry generically results in a Higgs mass of about 141 GeV, our model reduces this mass via introducing SU(2)$_L$ triplet fields which also contribute to neutrino masses.
We analyze the extension of the Minimal Supersymmetric Standard Model which includes extra Y=(0,\pm 1) supersymmetric triplets with a global SU(2)_L \otimes SU(2)_R symmetry spontaneousy broken to the custodial SU(2)_V by the vacuum expectation value of the neutral scalar components of doublets and triplets. The model is the supersymmetrization of the non-supersymmetric model introduced long ago by Georgi and Machacek where the ρ-parameter is kept to unity at the tree-level by the custodial symmetry. Accordingly the scalar sector is classified into degenerate SU(2)_V multiplets: singlets, trip…
The recent discovery of the $\sim 125$ GeV Higgs boson by Atlas and CMS experiments has set strong constraints on parameter space of the minimal supersymmetric model (MSSM). However these constraints can be weakened by enlarging the Higgs sector by adding a triplet chiral superfield. In particular, we focus on the $Y=0$ triplet extension of MSSM, known as TESSM, where the electroweak contributions to the lightest Higgs mass are also important and comparable with the strong contributions. We discuss this in the context of the observed Higgs like particle around 125 GeV and also look into the st…
The minimal supersymmetric extension of the Standard Model (MSSM) is reviewed. In the most general framework with minimal field content and R-parity conservation, the MSSM is a 124-parameter model (henceforth called MSSM-124). An acceptable phenomenology occurs only at exceptional points (and small perturbations around these points) of MSSM-124 parameter space. Among the topics addressed in this review are: gauge coupling unification, precision electroweak data, phenomenology of the MSSM Higgs sector, and supersymmetry searches at present and future colliders. The implications of approaches be…
The status of coupling constant unification -- assuming the validity of the standard model or of its minimal supersymmetric extension at high energies -- and of relations between various Yukawa couplings (assuming the supersymmetri extension) which are implied in certain grand-unified theories, are studied in detail. Theoretical uncertainties in the calculations are emphasized, and low-energy constraints and predictions are derived. In particular, we find that bottom-tau unification favors a Higgs boson lighter than 110 GeV. The structure of the vacuum in the model studied is also discussed. I…
The realization that supersymmetry (SUSY), if softly broken at the weak scale, can stabilize the Higgs sector led many authors to explore the role it may play in particle physics. It was widely anticipated that superpartners would reveal themselves once the TeV scale was probed in high energy collisions. Experiments at the LHC have not yet revealed any sign for direct production of superpartners, or for any other physics beyond the Standard Model. This has led to some authors to question whether weak scale SUSY has a role to play in stabilizing the Higgs sector. We show that SUSY models with j…
Gauge coupling unification and the stability of the Higgs vacuum are among two of the cherished features of low-energy supersymmetric models. Putting aside questions of naturalness, supersymmetry might only be realised in nature at very high energy scales. If this is the case, the preservation of gauge coupling unification and the stability of the Higgs vacuum would certainly require new physics, but it need not necessarily be at weak scale energies. New physics near the unification scale could in principle ensure Grand Unification, while new physics below $μ\sim 10^{10}$ GeV could ensure the …
We investigate the extended Higgs sectors, specially the charged Higgs sector in a supersymmetric $Y=0$ $SU(2)$ triplet and a Standard Model (SM) gauge singlet extension of SM. We show that in this model the allowed data for the Higgs boson interaction eigenstates tend to group into separate blocks for $SU(2)$ triplet, doublet and singlet. The triplet sector has two degenerate paired states, each pair composed of a mostly-triplet charged Higgs and of a mostly-triplet scalar or pseudoscalar state. The mostly-doublet sector involves a Standard Model like Higgs of 125 GeV and extra mass-degenerat…
CP violation in the lepton sector, and other aspects of neutrino physics, are studied within a high scale supersymmetry model. In addition to the sneutrino vacuum expectation values (VEVs), the heavy vector-like triplet also contributes to neutrino masses. Phases of the VEVs of relevant fields, complex couplings and Zino mass are considered. The approximate degeneracy of neutrino masses $m_{ν_1}$ and $m_{ν_2}$ can be naturally understood. The neutrino masses are then normal ordered, $\sim$ 0.020 eV, 0.022 eV, and 0.054 eV. Large CP violation in neutrino oscillations is favored. The effective M…
