We suggest a hybrid seesaw model where relatively ``light''right-handed neutrinos give no contribution to the neutrino mass matrix due to a special symmetry. This allows their Yukawa couplings to the standard model particles to be relatively strong, so that the standard model Higgs boson can decay dominantly to a left and a right-handed neutrino, leaving another stable right-handed neutrino as cold dark matter. In our model neutrino masses arise via the type-II seesaw mechanism, the Higgs triplet scalars being also responsible for the generation of the matter-antimatter asymmetry via the leptogenesis mechanism.
A brief overview of the phenomenology related to the seesaw mechanism and the baryogenesis via leptogenesis is presented. In particular, it is explained how large but not maximal lepton mixing can be achieved within the type II seesaw mechanism. Moreover, the consequences for leptogenesis are explored, including flavor effects.
It is shown that the type III seesaw mechanism proposed recently can have certain advantages over the conventional (or type I) seesaw mechanism for leptogenesis. In particular a resonant enhancement of leptogenesis via heavy quasi-Dirac right-handed neutrino pairs can occur without a special flavor form or "texture" of the mass matrices being assumed. Some of the requirements for neutrino mixing and leptogenesis are effectively decoupled.
In left-right symmetric seesaw models an eight-fold degeneracy among the right-handed neutrino mass matrices is known to exist. We use stability and viability of leptogenesis as criteria in order to discriminate among the degenerate solutions and to partially lift the eight-fold degeneracy.
We review the motivations and some results on leptogenesis in seesaw models with an almost conserved lepton number. The paper is based on a talk given at the 5th International Symposium on Symmetries in Subatomic Physics, SSP2012.
In the presence of large extra dimensions, the fundamental scale could be as low as a few TeV. This yields leptogenesis and seesaw at a TeV scale. Phenomenologically two TeV-scale Majorana fermions with a small mass split can realize a resonant leptogenesis whereas a TeV-scale Higgs triplet with a small trilinear coupling to the standard model Higgs doublet can give a verifiable seesaw. We propose an interesting scenario where the small parameters for the resonant leptogenesis and the type-II seesaw can be simultaneously generated by the propagation of lepton number violation from distant bran…
A triangular ansatz for the seesaw mechanism and baryogenesis via leptogenesis is explored. In a basis where both the charged lepton and the Majorana mass matrix are diagonal, the Dirac mass matrix can generally be written as the product of a unitary times a triangular matrix. We assume the unitary matrix to be the identity and then an upper triangular Dirac matrix. Constraints from bilarge lepton mixing and leptogenesis are studied.
We reveal the origin of the CP violation required by the leptogenesis in variously popular seesaw models. Especially we clarify that in a pure type-I/III seesaw with two fermion singlets/triplets, a combined type-I+III seesaw with one fermion singlet and one fermion triplet, or a combined type-I/III+II seesaw with one fermion singlet/triplet and one Higgs triplet, the CP violation for the leptogenesis can exactly come from the imaginary part of the neutrino mass matrix in a special basis where the Yukawa couplings involving one fermion singlet/triplet are allowed to get rid of any CP phases. W…
We study constraints on the fundamental parameters of supersymmetric type I seesaw models imposed by neutrino data, charged lepton flavor violation, thermal leptogenesis and perturbativity of the neutrino Yukawa couplings.
We construct a model realizing the inverse seesaw mechanism. The model has two types of gauge singlet fermions in addition to right-handed neutrinos. A required Majorana mass scale (keV scale) for generating the light active neutrino mass in the conventional inverse seesaw can be naturally explained by a "seesaw" mechanism between the two singlet fermions in our model. We find that our model can decrease the magnitude of hierarchy among the mass parameters by $\mathcal{O}(10^4)$ from that in the conventional inverse seesaw model. We also show that a successful resonant leptogenesis occurs for …
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.
In the framework of seesaw models with only two heavy Majorana neutrinos, nonzero leptonic asymmetries can be radiatively generated when exact heavy neutrino mass degeneracy ($M_1=M_2=M$) is imposed at a scale $Λ_D > M$. For a specific case, we show that an acceptable value for the baryon asymmetry of the Universe can be obtained considering thermal leptogenesis.
We study leptogenesis in three different realisations of the type Ib seesaw mechanism, where the effective masses of the neutrinos are obtained by the spontaneous symmetry breaking of two different Higgs doublets. In the minimal type Ib seesaw model, where two right-handed neutrinos form a Dirac mass, we show that it is impossible to produce the correct baryon asymmetry, even including a pseudo-Dirac mass splitting. In an extended type Ib seesaw model, with a third very heavy Majorana right-handed neutrino, together with the low scale Dirac pair of right-handed (RH) neutrinos and an extra sing…
In the framework of type II seesaw mechanism we propose two simple but instructive ansatze for neutrino mixing and leptogenesis. In each ansatz, the effective Majorana neutrino mass matrix is composed of two parts -- the part with Z_2 symmetry arises from the ordinary type I seesaw mechanism and the part with S_3 symmetry arises from an additional Higgs triplet vacuum expectation value. The two ansatze can simultaneously account for the current neutrino oscillation data and the cosmological baryon number asymmetry via leptogenesis.
We study a seesaw-type extension of the Standard Model in which the symmetry group is enlarged by a global U(1). We introduce adequate scalar and fermion representations which naturally explain the smallness of neutrino masses. With the addition of a viable scalar Dark Matter candidate, an original and successful scenario of leptogenesis emerges.
We discuss leptogenesis within a TeV-scale inverse seesaw model for neutrino masses where the seesaw structure is guaranteed by an SO(10) symmetry. Contrary to the TeV-scale type-I gauged seesaw, the constraints imposed by successful leptogenesis in these models are rather weak and allow for the extra gauge bosons W_R and Z' to be in the LHC accessible range. The key differences in the inverse seesaw compared to the type I case are: (i) decay and inverse decay rates larger than the scatterings involving extra gauge bosons due to the large Yukawa couplings and (ii) the suppression of the washou…
We consider an extended supersymmetric SO(10) seesaw model with only doublet Higgs scalars, in which neutrino masses are suppressed by the scale of D-parity violation. Leptogenesis can occur at the TeV scale through the decay of a singlet Sigma, thereby avoiding the gravitino crisis. Washout of the asymmetry can be effectively suppressed by the absence of direct couplings of Sigma to leptons.
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.
The left-right symmetric model with doublet and bi-doublet Higgs scalars can accommodate linear, inverse or double seesaw for generating small neutrino masses in the presence of three singlet fermions. If the singlet fermions have small Majorana masses, they can form three pairs of quasi-degenerate Majorana fermions with three right-handed neutrinos. The decays of the quasi-degenerate Majorana fermions can realize the resonant leptogenesis. Alternatively, the right-handed neutrinos can obtain seesaw suppressed Majorana masses if the singlet fermions are very heavy. In this case leptogenesis, w…
We study leptogenesis in supersymmetric SO(10) models with a left-right symmetric seesaw mechanism, including flavour effects and the contribution of the next-to-lightest right-handed neutrino. Assuming M_D = M_u and hierarchical light neutrino masses, we find that successful leptogenesis is possible for 4 out of the 8 right-handed neutrino mass spectra that are compatible with the observed neutrino data. An accurate description of charged fermion masses appears to be an important ingredient in the analysis.
We discuss scalar triplet leptogenesis in a specific left-right symmetric seesaw model. We show that the Majorana phases that are present in the model can be effectively used to saturate the existing upper limit on the CP-asymmetry of the triplets. We solve the relevant Boltzmann equations and analyze the viability of triplet leptogenesis. It is known for this kind of scenario that the efficiency of leptogenesis is maximal if there exists a hierarchy between the branching ratios of the triplet decays into leptons and Higgs particles. We show that triplet leptogenesis typically favors branching…
The seesaw theory, the leading theory for particle interactions, provides a viable mechanism for generating the matter-antimatter asymmetry of the universe. Testing the leptogenesis mechanism directly requires measurement of the d=6 operator of the low-energy effective Lagrangian, in addition to the more familiar d=5 operator which generates Majorana masses for the light neutrinos when the electroweak symmetry is spontaneously broken. This important experimental challenge awaits the next generation of particle physicists.
In type I seesaw models with flavor symmetries accounting for the lepton mixing angles the CP asymmetry in right-handed neutrino decays vanishes in the limit in which the mixing pattern is exact. We study the implications that additional degrees of freedom from type II seesaw may have for leptogenesis in such a limit. We classify in a model independent way the possible realizations of type I and II seesaw schemes, differentiating between classes in which leptogenesis is viable or not. We point out that even with the interplay of type I and II seesaws there are generic classes of minimal models…
Given its briefness and predictability, the minimal seesaw -- a simplified version of the canonical seesaw mechanism with only two right-handed neutrino fields -- has been studied in depth and from many perspectives, and now it is being pushed close to a position of directly facing experimental tests. This article is intended to provide an up-to-date review of various phenomenological aspects of the minimal seesaw and its associated leptogenesis mechanism in neutrino physics and cosmology. Our focus is on possible flavor structures of such benchmark seesaw and leptogenesis scenarios and confro…
A novel contribution to the leptonic CP asymmetries in type II seesaw leptogenesis scenarios is obtained for the cases in which flavor effects are relevant for the dynamics of leptogenesis. In the so-called flavoured leptogenesis regime, the interference between the tree-level amplitude of the scalar triplet decaying into two leptons and the one-loop wave-function correction with leptons in the loop, leads to a new nonvanishing CP asymmetry contribution. The latter conserves total lepton number but violates lepton flavour. Cases in which this novel contribution may be dominant in the generatio…
We have studied a leptogenesis scenario in the framework of the minimal seesaw model with tri/bi-maximal mixing. Usually, at least one of the elements in the Dirac mass matrix is fixed to be zero, for example, we denote it by $b_2=0$. We have pointed out that the absolute value of the CP asymmetry has several minimums and maximums with non-zero $b_2$. Thus one can expect that more rich phenomena, such as an enhanced leptogenesis, are hidden in the $b_2 \neq 0$ space.
In this thesis, we study the role of flavours in leptogenesis. In a first time, we review the so-called one flavour picture, where only the lightest right-handed neutrino is taken into account, and where lepton flavours are neglected. After having showed why and how lepton flavours should be included in the computation of the lepton asymmetry, we study their effect in the type I seesaw model, as well as in the type I+II seesaw model, in a specific SO(10) unification realisation. In this model, besides flavours effects, we show that the inclusion of the second lightest right-handed neutrino, to…
We reanalyse leptogenesis via the out-of-equilibrium decay of the lightest right-handed neutrino in type II seesaw scenarios, taking into account flavour-dependent effects. In the type II seesaw mechanism, in addition to the type I seesaw contribution, an additional direct mass term for the light neutrinos is present. We consider type II seesaw scenarios where this additional contribution arises from the vacuum expectation value of a Higgs triplet, and furthermore an effective model-independent approach. We investigate bounds on the flavour-specific decay asymmetries, on the mass of the lighte…
The seesaw mechanism to derive the light masses of left-handed neutrinos using heavy masses of right-handed neutrinos gives rise to a connection between low-energy measurables and GUT-scale mechanism. We expresses the neutrino mixing angles in terms of a single variable $\sinθ_{13}$, whose size was measured recently. The lepton asymmetry from heavy neutrinos via Yukawa coupling is described by CP phases in both Dirac and Majorana type. It is shown that the seesaw scale relevant to the lepton asymmetry can be constrained by CP phase in this minimal model.
The effective Lagrangian for the seesaw model is derived including effects due to CP violation. Besides the usual dimension-5 operator responsible for light neutrino masses, a dimension-6 operator is obtained. For three or less heavy neutrino generations, the inclusion of both operators is necessary and sufficient for all independent physical parameters of the high-energy seesaw Lagrangian to appear in the low-energy effective theory, including the CP-odd phases relevant for leptogenesis. The dimension-6 operator implies exotic low-energy couplings for light neutrinos, providing a link between…
We calculate the lepton electric dipole moments in a class of supersymmetric seesaw models and explore the possibility that they may provide a way to probe some of the CP violating phases responsible for the origin of matter via leptogenesis. We show that in models where the right handed neutrino masses, $M_R$ arise from the breaking of local B-L symmetry by a Higgs field with B-L=2, some of the leptogenesis phases can lead to enhancement of the lepton dipole moments compared to the prediction of models where $M_R$ is either directly put in by hand or is a consequence of a higher dimensional o…
Upcoming Lepton Flavour Violation experiments searching for $μ\rightarrow 3e$ and $μ$ to $ e $ conversion in nuclei processes will provide new opportunities to test the fundamental properties of the neutrino sector, and possibly the origin of matter. In recent work, it was shown that the Type II Seesaw mechanism alone can simultaneously explain the neutrino masses, Leptogenesis, and inflation. A key prediction of this model was the possibility of signals being produced in Lepton Flavour Violation decays. Searches at future experiments such as Mu3e and COMET will be integral to determining the …
We study leptogenesis in two seesaw models where maximal atmospheric neutrino mixing and $U_{e3} = 0$ result from symmetries. Salient features of those models are the existence of three Higgs doublets and a twofold degeneracy of the neutrino Dirac mass matrix. We find that in those models both leptogenesis and neutrinoless double beta decay depend on the same unique Majorana phase. Leptogenesis can produce a baryon asymmetry of the universe of the right size provided the mass of the heavy neutrino whose decays generate the lepton asymmetry is in the range $10^{11}$--$10^{12} \mathrm{GeV}$. Mor…
We study the possibility that the baryon asymmetry of the universe is generated in a minimal seesaw scenario where two right-handed Majorana neutrinos with degenerate masses are added to the standard model particle content. In the usual framework of thermal leptogenesis, a nonzero $CP$ asymmetry can be obtained through the mass splitting induced by the running of the heavy Majorana neutrino masses from their degeneracy scale down to the seesaw scale. Although, in the light of the present neutrino oscillation data, the produced baryon asymmetry turns out to be smaller than the experimental valu…
We suppose that the baryon asymmetry is produced by thermal leptogenesis (with flavour effects), at temperatures $\sim 10^{9} - 10^{10}$ GeV, in the supersymmetric seesaw with universal and real soft terms. The parameter space is restricted by assuming that $l_α\to l_βγ$ processes will be seen in upcoming experiments. We study the sensitivity of the baryon asymmetry to the phases of the lepton mixing matrix, and find that leptogenesis can work for any value of the phases. We also estimate the contribution to the electric dipole moment of the electron, arising from the seesaw, and find that it …
In this paper, we perform a detail analysis on leptogenesis and dark matter form low scale seesaw. In the framework of $ν$2HDM, we further introduce one scalar singlet $ϕ$ and one Dirac fermion singlet $χ$, which are charged under a $Z_2$ symmetry. Assuming the coupling of $χ$ is extremely small, it serves as a FIMP dark matter. The heavy right hand neutrinos $N$ provide a common origin for tiny neutrino mass (via seesaw mechanism), leptogenesis (via $N\to \ell_L Φ_ν^*,\bar{\ell}_L Φ_ν$) and dark matter (via $N\to χϕ$). With hierarchical right hand neutrino masses, the explicit calculation sho…
The scotogenic type I and type III seesaw models are good candidates to explain the existence of neutrino masses and dark matter simultaneously. However, since triplet fermions have SU(2) gauge interaction, they cannot be out of equilibrium before the electroweak symmetry breaking. Thus, leptogenesis seems to be difficult within a framework of the pure type III seesaw model. Some extension seems to be required to solve this fault. A model extended by introducing a singlet fermion could be such a simple example. If the singlet fermion is in the thermal equilibrium even for its extremely small n…
We develop an extension of the basic inverse seesaw model which addresses simultaneously two of its drawbacks, namely, the lack of explanation of the tiny Majorana mass term $μ$ for the TeV-scale singlet fermions and the difficulty in achieving successful leptogenesis. Firstly, we investigate systematically leptogenesis within the inverse (and the related linear) seesaw models and show that a successful scenario requires either small Yukawa couplings, implying loss of experimental signals, and/or quasi-degeneracy among singlets mass of different generations, suggesting extra structure must be …
We propose two Type-II seesaw scenarios for the neutrino mass matrix in the left-right symmetric model, in which the Higgs triplet Yukawa coupling matrix takes the appealing Friedberg-Lee texture. We show that the nearly tri-bimaximal neutrino mixing pattern, which is especially favored by current neutrino oscillation data, can be obtained from both scenarios. We also show that the cosmological baryon number asymmetry can naturally be interpreted in these two scenarios via the flavor-independent leptogenesis mechanism.
We present a study of resonant leptogenesis in a radiative seesaw model. We consider the case where two quasi-degenerate right-handed neutrinos realize resonant leptogenesis, and the CP violation necessary to achieve leptogenesis occurs through the CP phases present in the neutrino mixing matrix. A numerical analysis is performed by taking the best-fit values from the current global data for three neutrino mixing angles and two mass-squared differences. We have shown how the predicted value of baryon asymmetry depends on the Dirac and Majorana CP phases. With the particular choice for the mass…
In the type I + II seesaw formula the mass matrix of light neutrinos m_nu receives contributions from the exchanges of both heavy Majorana neutrinos and SU(2)_L-triplet Higgs bosons. We propose a new parameterization for the Dirac-type Yukawa coupling matrix of neutrinos in this case, which generalizes the well known Casas-Ibarra parameterization to type I + II seesaw and is useful when the triplet term in m_nu is known. Neutrino masses and mixing, lepton flavor violation in decays like mu -> e γwithin mSUGRA models and leptogenesis can then be studied within this framework. We illustrate the …
We propose a simple ansatz for neutrino phenomenology, in which the relevant lepton mass matrices take the universal Fritzsch-like form and the seesaw relation holds under a particular condition. There exist six textures of this nature, but their consequences on neutrino oscillations are exactly the same. We show that our scenario is viable to account for the cosmological baryon number asymmetry via thermal leptogenesis. Its predictions for the lepton-flavor-violating decays μ-> eγ, tau -> μγand τ-> eγare also presented. We find that the branching ratios of these rare processes depend strongly…
We investigate how the baryon asymmetry of our universe via leptogenesis can be achieved within the framework of the seesaw model with Fritzsch type lepton mass matrices proposed by Fukugita $et. al$. We study the cases with CP-violating phases in charged lepton Yukawa matrix, however, with and without Dirac neutrino Yukawa phases. We consider both flavor independent and flavor dependent leptogenesis, and demonstrate how they lead to different amounts of lepton asymmetries in detail. In particular, it is shown that flavor dependent leptogenesis in this model can be worked out only when the CP …
Motivated by the fact that the Dirac phase in the PMNS matrix is the only CP-violating parameter in the leptonic sector that can be measured in neutrino oscillation experiments, we examine the possibility that it is the dominant source of CP violation for leptogenesis caused by the out-of-equilibrium decays of heavy singlet fermions. We do so within a low-scale extended type-I seesaw model, featuring two Standard Model singlet fermions per family, in which lepton number is approximately conserved such that the heavy singlet neutrinos are pseudo-Dirac. We find that this produces a predictive mo…
We consider a variant of seesaw mechanism by introducing extra singlet neutrinos and singlet scalar boson, and show how low scale leptogenesis is successfully realized in this scenario. We examine if the newly introduced neutral particles, either singlet Majorana neutrino or singlet scalar boson, can be a candidate for dark matter. We also discuss the implications of the dark matter detection through the scattering off the nucleus of the detecting material on our scenarios for dark matter. In addition, we study the implications for the search of invisible Higgs decay at LHC, which may serve as…
We show that the four high-energy Littlest Seesaw parameters in the flavour basis,namely two real Yukawa couplings plus the two right-handed neutrino masses, can be determined by an excellent fit to the seven currently constrained observables of low-energy neutrino data and leptogenesis. Taking into account renormalisation group corrections, we estimate $χ^2 \simeq 1.5-2.6$ for the three d.o.f., depending on the high-energy scale and the type of non supersymmetric Littlest Seesaw model. We extract allowed ranges of neutrino parameters from our fit data, including the approximate mu-tau symmetr…
Strong correlations between leptogenesis and low energy CP violating leptonic processes have been shown by us to exist in the minimal left-right symmetric model with spontaneous CP violation. In this note, we investigate the implications of this model for the electric dipole moment of the electron. With an additional broken U(1)_H symmetry, the seesaw scale can be lowered to close to the electroweak scale. This additional symmetry also makes the connection between CP violation in quark sector to that in the lepton sector possible.
Discrete symmetries being preferred to explain the neutrino phenomenology, we chose the simplest $S_3$ group and explore the implication of its modular form on neutrino masses and mixing. Non-trivial transformations of Yukawa couplings under this symmetry, make the model phenomenologically interesting by reducing the requirement of multiple scalar fields. This symmetry imposes a specific flavor structure to the neutrino mass matrix within the framework of less frequented type III seesaw mechanism and helps to explore the neutrino mixing consistent with the current observation. Apart, we also e…
In this talk, we first give a brief review of the so-called minimal seesaw models and then concentrate on the minimal type-I seesaw model with two almost degenerate right-handed Majorana neutrinos of ${\cal O}(1 {\rm TeV})$. A specific texture of the neutrino Yukawa coupling matrix is proposed to achieve the nearly tri-bimaximal neutrino mixing pattern. This ansatz predicts (1) $θ^{}_{23} = π/4$, $|δ| = π/2$ and $\sin^2 θ^{}_{12} = (1 - 2 \tan^2 θ^{}_{13})/3$ in the $m^{}_1 = 0$ case; and (2) $θ^{}_{23} =π/4$ and $θ^{}_{13} = δ= 0$ in the $m^{}_3 = 0$ case. In both cases, the cosmological bary…
We present the various leptogenesis scenarios which may occur if, in addition to the ordinary heavy right-handed neutrinos, there exists a heavy scalar SU(2)_L triplet coupled to leptons. We show that the contributions of the right-handed neutrinos and the triplet to the lepton asymmetry are proportional to their respective contributions to the neutrino mass matrix. A consequence of the triplet contribution to the lepton asymmetry is that there is no more upper bound on the neutrino masses from leptogenesis due to the fact that the neutrino mass constraints do not necessarily induce asymmetry …
We consider a variant of seesaw mechanism by introducing extra singlet neutrinos, with which we show how the low scale leptogenesis is realized without imposing the tiny mass splitting between two heavy Majorana neutrinos required in the resonant leptogenesis. Thus, we can avoid the so-called gravitino problem when our scenario is supersymmetrized. We show that an introduction of the new singlet fermion leads to a new contribution which can enhance the lepton asymmetry for certain range of parameter space. We also examine how both the light neutrino mass spectrum and relatively light sterile n…
This work addresses the viability of \textit {Dirac phase leptogenesis}, in a scenario where the light Majorana neutrinos acquire masses by the inverse seesaw (ISS) mechanism. We show that, a successful leptogenesis in the ISS, driven (only) by the Dirac CP phase can be achieved with the involvement of an unorthodox form of the rotational matrix $R = e^{i{\bf A}} \,\,\,(e^{\bf A})$ in the Casas-Ibarra parametrisation. This particular structure of $R$ turns out to be an artefact in explaining the observed baryon asymmetry of the Universe in a pure ISS scenario. We detail here the confined regio…
The right-handed neutrinos within the type-I seesaw mechanism can induce large radiative corrections to the Higgs mass, and naturalness arguments can then be used to set limits on their mass scale and Yukawa couplings. Driven by minimality, we consider the presence of two degenerate right-handed neutrinos. We compare the limits from naturalness with the ones from the stability of the electroweak vacuum and from lepton flavor violation. Implications from neutrinoless double beta decay are also discussed and renormalization effects for the light neutrino parameters are presented. Adding small pe…
It is pointed out that if a neutrino mass matrix for right-handed neutrinos in seesaw mechanism has mu -tau symmetry and total lepton number L_{e}+L_{μ}+L_τ remains constant (not zero), exact tribimaximal neutrino mixing in this sector is produced. The same follows for the effective Majorana light neutrino mass matrix provided that Yukawa couplings (multiplied by the corresponding Higgs vacuum expectation values) in Dirac mass matrix satisfy some constraints which in general implies zero leptongenesis asymmetry. However this can be avoided when two of the heavy right-hand neutrinos [the third …
A leptogenesis scenario in a supersymmetric standard model extended with introducing right-handed neutrinos is reconsidered. Lepton asymmetry is produced in the condensate of a right-handed sneutrino via the Affleck-Dine mechanism. The LH_u direction develops large value due to a negative effective mass induced by the right-handed sneutrino condensate through the Yukawa coupling of the right-handed neutrino, even if the minimum during the inflation is fixed at the origin. The lepton asymmetry is nonperturbatively transfered to the LH_u direction by this Yukawa coupling.
