Sommerfeld corrections to type-II and III leptogenesis
Alessandro Strumia
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12 pages, 4 figures, final version. The group theory of the non-abelian Sommerfeld effect presented in this paper can be relevant for scenarios of Dark Matter charged under new dark gauge groups, as suggested by recent data
We study thermal leptogenesis from decays of the electroweak triplets that mediate neutrino masses in type-II and type-III see-saw. We find that Sommerfeld corrections reduce the baryon asymmetry by ~30%, and that successful leptogenesis needs triplets heavier than 1.6 TeV, beyond the discovery reach of LHC.
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.
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…
The See-Saw mechanism provides a nice way to explain why neutrino masses are so much lighter than their charged lepton partners. It also provides a nice way to explain baryon asymmetry in our universe via the leptogenesis mechanism. In this talk we review leptogenesis and LHC physics in a See-Saw model proposed in 1989, now termed the Type III See-Saw model. In this model, $SU(2)_L$ triplet leptons are introduced with the neutral particles of the triplets playing the role of See-Saw. The triplet leptons have charged partners with standard model gauge interactions resulting in many new features…
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…
We make an attempt to study neutrino phenomenology in the framework of type-III seesaw by considering $A_4$ modular symmetry in the super-symmetric context. In addition, we have included a local $U(1)_{B-L}$ symmetry which eventually helps us to avoid certain unwanted terms in the superpotential. Hitherto, the seesaw being type-III, it involves three fermion triplet superfields $Σ_R$, along with which, we have included a singlet weighton field $(ρ)$. In here, modular symmetry plays a crucial role by avoiding the usage of excess flavon (weighton) fields. Also, the Yukawa couplings acquire modul…
Towards Testable Type-III Leptogenesis in Non-Standard Early Universe Scenarios
Department of Physics and Astronomical Science, Central University of Himachal Pradesh(喜马偕尔邦中央大学物理与天文科学系);Department of Physics, Pragjyotish College(普拉吉约提什学院物理系)
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…
A seesaw mechanism is presented in the neutrino sector and a new phase of CP violation ($α$) emerges in the interplay between the type-I and type-III seesaw schemes. This phase is inside the mixing term, and thus it cannot be rotated away in the Yukawa Lagrangian and, therefore, the heavy symmetry states cannot be in a diagonal weak basis in the broken phase. Some particular descriptions are analyzed suggesting that if the usual Yukawa couplings are suppressed, leptogenesis still occurs due to a new interacting vertex with fermion triplet $T$, fermion singlets $N$, and an ad-hoc scalar triplet…
The link between low-energy CP violation and leptogenesis became more accessible with the understanding of flavor effects. However, a definite well-motivated model where such a link occurs was still lacking. Adjoint SU(5) is a simple grand unified theory where neutrino masses are generated through the Type I and Type III seesaw mechanisms, and the lepton asymmetry is generated by the fermionic triplet responsible for the Type III seesaw. We focus exclusively on the case of inverted hierarchy for neutrinos, and we show that successful flavored leptogenesis in this theory strongly points towards…
This paper concludes the presentation of the non-relativistic effective field theory formalism designed to calculate the radiative corrections that enhance the pair-annihilation cross sections of slowly moving neutralinos and charginos within the general minimal supersymmetric standard model (MSSM). While papers I and II focused on the computation of the tree-level annihilation rates that feed into the short-distance part, here we describe in detail the method to obtain the Sommerfeld factors that contain the enhanced long-distance corrections. This includes the computation of the potential in…
We show that by adding to the standard model plus the type I seesaw different types of scalars, it is possible to construct models that satisfy the three requirements of (i) generating neutrino masses at the TeV scale, (ii) being testable at the LHC via direct production of new states, and (iii) allowing for leptogenesis at temperatures $T\sim O$(TeV).
The possibility to explain the baryon asymmetry in the Universe through the leptogenesis mechanism in the context of Adjoint SU(5) is investigated. In this model the neutrino masses are generated through the Type I and Type III seesaw mechanisms, and the field responsible for the Type III seesaw, called rho_3, generates the B-L asymmetry needed to satisfy the observed value of the baryon asymmetry in the Universe. We find that the CP asymmetry originates only from the vertex correction, since the self-energy contribution is not present. When neutrino masses have a normal hierarchy, successful …
We explain the electron-positron excess reported by the DAMPE collaboration recently in a radiative Dirac seesaw model where a dark $U(1)_X$ gauge symmetry can (i) forbid the tree-level Yukawa couplings of three right-handed neutrinos to the standard model lepton and Higgs doublets, (ii) predict the existence of three dark fermions for the gauge anomaly cancellation, (iii) mediate a testable scattering of the lightest dark fermion off the nucleons. Our model can also accommodate a successful leptogenesis to generate the cosmic baryon asymmetry.
We investigate baryogenesis via leptogenesis and generation of neutrino masses and mixings through the Type I plus Type III seesaw plus an one-loop mechanism in the context of Renormalizable Adjoint SU(5) theory. One light neutrino remains massless, because the contributions of three heavy Majorana fermions ρ_0, ρ_3 and ρ_8 to the neutrino mass matrix are not linearly independent. However none of these heavy fermions is decoupled from the generation of neutrino masses. This opens a new range in parameter space for successful leptogenesis, in particular, allows for inverted hierarchy of the neu…
An SO(10) grand unified model considered previously by the authors featuring lopsided down quark and charged lepton mass matrices is successfully predictive and requires that the lightest two right-handed Majorana neutrinons be nearly degenerate in order to obtain the LMA solar neutrino solution. Here we use this model to test its predictions for baryogenesis through resonant-enhanced leptogenesis. With the conventional type I seesaw mechanism, the best predictions for baryogenesis appear to fall a factor of three short of the observed value. However, with a proposed type III seesaw mechanism …
The presence of flavor symmetries in the lepton sector may have several consequences for the generation of the baryon asymmetry of the Universe via leptogenesis. We review the mechanism in general type-I, type-II and type-III seesaw models. We then turn to the discussion of the cases when the asymmetry is generated in the context of seesaw models extended with flavor symmetries, before or after flavor symmetry breaking. Finally we explain how the interplay between type-I and type-II seesaws can (or not) lead to viable models for leptogenesis even when there is an exact mixing pattern enforced …
In this paper, we consider the possibility of generating the observed baryon asymmetry of the Universe via leptogenesis in the context of triplet fermion mediated type-III seesaw model of neutrino mass. With a hierarchical spectrum of the additional fermions, the lower bound on the lightest triplet mass is $\sim 10^{10} {\rm~GeV}$ for successful leptogenesis, a couple of orders higher than that of the type-I case. We investigate the possibility of lowering this bound in the framework of two-Higgs-doublet models. We find that the bounds can be lowered down to $10^7$ GeV for a hierarchical spect…
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 sc…
Using the density matrix equations (DME) for high scale leptogenesis based on the type I seesaw mechanism, in which the CP violation (CPV) is provided by the low-energy Dirac or/and Majorana phases of the neutrino mixing (PMNS) matrix, we investigate the 1-to-2 and the 2-to-3 flavour regime transitions, where the 1, 2 and 3 leptogenesis flavour regimes in the generation of the baryon asymmetry of the Universe $η_B$ are described by the Boltzmann equations. Concentrating on the 1-to-2 flavour transition we determine the general conditions under which $η_B$ goes through zero and changes sign in …
We demonstrate a unified scenario for neutrino mass, baryon asymmetry, dark matter and inflation. In addition to a fermion triplet for the so-called minimal dark matter, we extend the standard model by three heavy fields including a scalar singlet, a fermion triplet and a fermion singlet/Higgs triplet. The heavy scalar singlet, which is expected to drive an inflation, and the dark matter fermion triplet are odd under an unbroken $Z_2^{}$ discrete symmetry, while the other fields are all even. The heavy fermion triplet offers a tree-level type-III seesaw and then mediates a three-body decay of …
We have investigated the constrained minimal supersymmetric standard model with three right-handed Majorana neutrinos whether there still is a parameter region which is consistent with all existing experimental data/limits such as Leptogenesis and the dark matter abundance and we also can solve the Lithium problem. Using Casas-Ibarra parameterization, we have found that a very narrow parameter space of the complex orthogonal matrix elements where the lightest slepton can have a long lifetime, that is necessary for solving the Lithium problem. Further, under this condition, there is a parameter…
Numerous recent evidences for neutrino masses have established the leptogenesis mechanism as a very natural possible explanation for the baryon asymmetry of the Universe. The explicit realization of this mechanism depends on the neutrino mass model considered. If the right-handed type-I seesaw model of neutrino masses is certainly the most straightforward, it is not the only natural one, especially in the framework of explicit GUT realizations of the seesaw. In this review we discuss in detail the various seesaw scenarios that can implement the leptogenesis mechanism successfully, beyond the p…
We show that, within SO(10)-inspired leptogenesis, there exists a solution, with definite constraints on low energy neutrino parameters, able simultaneously to reproduce the observed baryon asymmetry and to satisfy the conditions for the independence of the final asymmetry of the initial conditions (strong thermal leptogenesis). We find that the wash-out of a pre-existing asymmetry as large as O(0.1) requires: i) reactor mixing angle in the range θ_13 = (2 - 20) degrees, in agreement with the experimental result θ_13 = (8 - 10) degrees; ii) atmospheric mixing angle in the range θ_23 = (16 - 41…
Predictions of Modular Symmetry Fixed Points on Neutrino Masses, Mixing, and Leptogenesis
Central University of Himachal Pradesh(喜马偕尔邦中央大学);Indian Institute of Science Education and Research Berhampur(印度科学教育研究所布兰普分校);Sichuan University(四川大学)
The neutral component of an inert scalar multiplet with hypercharge can provide a stable dark matter particle when its real and imaginary parts have a splitting mass spectrum. Otherwise, a tree-level dark matter-nucleon scattering mediated by the $Z$ boson will be much above the experimental limit. In this paper we focus on a mixed inert scalar triplet dark matter scenario where a complex scalar triplet with hypercharge can mix with another real scalar triplet without hypercharge through their renormalizable coupling to the standard model Higgs doublet. We consider three specified cases that c…
The seesaw and leptogenesis commonly depend on the masses of same particles, and thus are both realized at the same scale. In this work, we demonstrate a new possibility to realize a TeV-scale neutrino seesaw and a natural high-scale leptogenesis. We extend the standard model by two gauge-singlet scalars, a vector-like iso-doublet fermion and one iso-triplet Higgs scalar. Our model respects a softly broken lepton number and an exactly conserved $Z_2$ discrete symmetry. It can achieve three things altogether: (i) realizing a testable type-II seesaw at TeV scale with two nonzero neutrino mass-ei…
We study the renormalization group equations (RGEs) of the neutrino parameters in models of Minimal Lepton Flavor Violation. In such models, the RGEs can be described in terms of flavor spurions, such that only the coefficients depend on the specific model. We explicitly demonstrate this method for the SM and MSSM for both Type-I and Type-III seesaw models. For that purpose, the RGEs of neutrino parameters in the MSSM Type-III seesaw have been computed. We have extended this method to get the evolution equations at second order. The implications for leptogenesis are also discussed.
The implementation of the Type III seesaw mechanism for neutrino masses in the context of left-right theories where parity is broken spontaneously is investigated. We propose a simple left-right symmetric theory where the neutrinos masses are generated through a double seesaw mechanism which is a combination of Type I and Type III seesaw. In this context we find a possible candidate for the cold dark matter in the Universe and discuss the Baryogenesis via Leptogenesis mechanisms. The spectrum of the theory, the phenomenological constraints and the possibility to test the theory at the Large Ha…
Taking into account the recent progress in the understanding of the lepton flavour effects in leptogenesis, we investigate in detail the possibility that the CP-violation necessary for the generation of the baryon asymmetry of the Universe is due exclusively to the Dirac and/or Majorana CP-violating phases in the PMNS neutrino mixing matrix U, and thus is directly related to the low energy CP-violation in the lepton sector (e.g., in neutrino oscillations, etc.). We first derive the conditions of CP-invariance of the neutrino Yukawa couplings lambda in the see-saw Lagrangian, and of the complex…
Near a critical value of the wino mass where there is a zero-energy S-wave resonance at the neutral-wino-pair threshold, low-energy winos can be described by a zero-range effective field theory (ZREFT) in which the winos interact nonperturbatively through a contact interaction and through Coulomb interactions. The effects of wino-pair annihilation into electroweak gauge bosons are taken into account through the analytic continuation of the real parameters for the contact interaction to complex values. The parameters of ZREFT can be determined by matching wino-wino scattering amplitudes calcula…
We extend the Type I and Type III seesaw mechanisms to generate neutrino masses within the left-right symmetric theories where parity is spontaneously broken. We construct a next to minimal left-right symmetric model where neutrino masses are generated through a variant $double$ seesaw mechanism. In our model at least one of the triplet fermions and the right handed neutrinos are at TeV scale and others are heavy. The phenomenological aspects and testability of the TeV scale particles at collider experiments are discussed. The decays of heavy fermions leading to leptogenesis are pointed out.
We study a real scalar septuplet model which has a neutral component regarded as a dark matter particle candidate. The calculation of its thermal relic abundance without (with) the Sommerfeld effect suggests that the observed value corresponds to the mass of the dark matter particle $m_0 \gtrsim 8.8~(25)~\mathrm{TeV}$. Two extra quartic couplings $λ_2$ and $λ_3$ introduced in this model affect the running of other couplings, and hence the vacuum stability and the perturbativity up to the Planck scale. Therefore, the vacuum stability and the perturbativity conditions can constrain these couplin…
We present a fully flavour-covariant formalism for transport phenomena, by deriving Markovian master equations that describe the time-evolution of particle number densities in a statistical ensemble with arbitrary flavour content. As an application of this general formalism, we study flavour effects in a scenario of resonant leptogenesis (RL) and obtain the flavour-covariant evolution equations for heavy-neutrino and lepton number densities. This provides a complete and unified description of RL, capturing three distinct physical phenomena: (i) the resonant mixing between the heavy-neutrino st…
Gravitational Wave Spectral Shapes as a probe of Long Lived Right-handed Neutrinos, Leptogenesis and Dark Matter: Global versus Local B-L Cosmic Strings
Nanjing Normal University(南京师范大学);University of Warsaw(华沙大学);University of Southampton(南安普顿大学)
We hunt for and discuss manifestly CP-violating effects which are mediated by Majorana phases. These phases are present if the Standard Model neutrinos are Majorana particles. We argue that while Majorana phases do affect the strength of neutrinoless double beta decay (a well known fact), they do so in a way that involves no manifest violation of CP. The conditions for manifestly CP-violating phenomena -- differences between the rates for CP-mirror-image processes -- are presented, and three examples are discussed: (i) neutrino-antineutrino oscillation; (ii) rare decays of K and B mesons and t…
Recently we have proposed a renormalizable grand unified theory, based on the SU(5) gauge symmetry, where the neutrino masses are generated through the type I and type III seesaw mechanisms. In this letter we study the supersymmetric version of this theory. As in the non-susy version it is possible to generate all fermion masses with the minimal number of Higgses, the theory predicts one massless neutrino and the leptogenesis mechanism can be realized. All contributions to the decay of the proton and the properties of neutralinos are discussed. This theory can be considered as the simplest ren…
It is noted that one is now in possession of a set of facts, which may be viewed as the matching pieces of a puzzle ; in that all of them can be resolved by just one idea - that is grand unification. These include : (i) the observed family-structure, (ii) quantization of electric charge, (iii) meeting of the three gauge couplings, (iv) neutrino oscillations; in particular the mass of $ν_τ$ suggested by SuperK), (v) the intricate pattern of the masses and mixings of the fermions, including the smallness of $V_{cb}$ and the largeness of $θ^{osc}_{ν_μν_τ}$, and (vi) the need for $B$-$L$ to implem…
Lepton flavour violation and neutrino masses are a signal for new Physics beyond the Standard Model and are deeply related. The minimal extension of the Standard Model to make it include neutrino masses is not satisfactory from a conceptual point of view, since it requires a severe fine-tuning of Yukawa couplings. See-saw models provide a consistent and natural mechanism to generate neutrino masses and require Physics beyond the Standard Model. In this thesis, the connections between models for neutrino masses and processes that violate lepton flavour are explored. The reconstruction of high e…
As a tribute to Abdus Salam, I recall the initiation in 1972-73 of the idea of grand unification based on the view that lepton number is the fourth color. Motivated by aesthetic demands, these attempts led to the suggestion that the existing $SU(2)\times U(1)$ symmetry be extended minimally to the quark-lepton and left-right symmetric non-Abelian gauge structure $G(2,2,4) = SU(2)_L\times SU(2)_R\times SU(4)$-color. This unified members of a family within a single L-R self-conjugate multiplet. It also explained: the quantization of electric charge, the co-existence of quarks and leptons, and th…