Extended double seesaw model for neutrino masses and low scale - PowerPoint PPT Presentation

Extended double seesaw model for neutrino masses and low scale leptogenesis. International workshop on neutrino masses and mixing Decmeber 17-19 2006, Shizuoka, Japan Sin Kyu Kang (Sogang University) in collaboration with C. S. Kim hep-ph/0607072

Outline Introduction Extended Double Seesaw Model Constrains on the active-sterile mixing Low Scale Leptogenesis Numerical Estimation Summary

Introduction: Motivation for postulating the existence of singlet neutrinos: ◮ Smallness of neutrino masses ⇒ introducing heavy singlet neutrinos : seesaw mechanism. ◮ Sterile neutrinos = ⇒ a viable candidate for dark matter ◮ LSND experiment = ⇒ need a sterile neutrino What happen if the sterile neutrinos exist ? ◮ ν s can mix with ν a = ⇒ such admixtures : contribute to various processes forbidden in the SM ◮ They affect the interpretations of cosmological and astrophysical observations.

Virtue and Vice of the Seesaw Mechanism: ◮ ◮ Accomplishment of smallness of neutrino masses ◮ Responsibe for baryon asymmetry of our universe ◮ Seesaw scale 10 10 ∼ 14 GeV : impossible to probe at collider ◮ High scale thermal leptogenesis M > 10 9 GeV = ⇒ encounters gravitino problem in SUSY SM. Low scale seesaw is desirable ! = ⇒ ◮ A successful scenario for a low scale leptogenesis = ⇒ Resonant leptogenesis with very tiny mass splitting of heavy Majorana neutrinos with M 1 ∼ 1 TeV. (Pilaftsis) (( M 2 − M 1 ) / ( M 2 + M 1 ) ∼ 10 − 6 ) ◮ However, such a very tiny mass splitting may appears somewhat unnatural due to the required severe fine-tuning.

Motivation and Aim of this work ◮ In order to remedy above problems, we propose a variant of the seesaw mechanism. ◮ Our model : typical seesaw model + equal # gauge singlet neutrinos = ⇒ a kind of double seesaw model ◮ Unlike to the typical double seesaw model, ◮ Permit both tiny neutrino masses and relatively light sterile neutrinos of order MeV. ◮ Accommodate very tiny mixing between ν a and ν s demanded from the cosmological and astrophysical observations. ◮ We show that a low scale thermal leptogenesis can be naturally achieved.

Extended Double Seesaw Model ◮ The Lagrangian we propose in the charged lepton basis as L = M R i N T ν i φ N j + Y S ij ¯ N i Ψ S j − µ ij S T i N i + Y D ij ¯ i S j + h . c . , ◮ ν i : SU (2) L doublet, N i : RH singlet neutrino ◮ S i : newly introduced singlet neutrinos ◮ φ : SU (2) L doublet Higgs ◮ Ψ : SU (2) L singlet Higgs ◮ The neutrino mass matrix after φ, Ψ get VEVs becomes   0 m D ij 0  , M ν = m D ij M R ii M ij  0 − µ ij M ij where m D ij = Y D ij < φ >, M ij = Y S ij < Ψ > . ◮ Here we assume that M R > M ≫ µ, m D .

◮ After integrating out N R in L , we obtain the following effective lagrangian, ( m 2 D ) ij i ν j + m D ik M kj ν T ν i S j + ¯ −L eff = (¯ S i ν j ) 4 M R 4 M R M 2 ij S T i S j + µ ij S T + i S j . 4 M R ◮ After block diagonalization of the effective mass terms in L eff , 1. The light neutrino mass matrix : m ν ≃ 1 � T m D � m D M µ , 2 M 2. Mixing between the active and sterile neutrinos : 2 m D M tan 2 θ s = . M 2 + 4 µ M R − m 2 D

◮ Note : typical seesaw mass m 2 D / M R = ⇒ cancelled out. ◮ Sterile neutrino mass is approximately given as m s ≃ µ + M 2 . 4 M R ◮ Depending on the relative sizes among M , M R , µ , = ⇒ θ s and m s are approximately given by ( for M 2 > 4 µ M R : 2 m D  Case A ) , M      ( for M 2 ≃ 4 µ M R : m D Case B ) , tan 2 θ s ≃ sin 2 θ s ≃ M    ( for M 2 < 4 µ M R :  m D M  Case C ) , 2 µ M R M 2  ( Case A ) , 4 M R      m s ≃ 2 µ ( Case B ) ,      µ ( Case C ) .

Note on the above formulae : ◮ For M 2 ≤ 4 µ M R , the size of µ is mainly responsible for m s . ◮ The value of θ s is suppressed by the scale of M or M R . ◮ Thus, very small mixing angle θ s can be naturally achieved in our seesaw mechanism. ◮ For Case A and Case B , constraints on θ s leads to constraints on the size of m ν /µ .

Constrains on the active-sterile mixing ◮ Existence of a relatively light sterile neutrino = ⇒ observable consequences for cosmology & astrophyics. ◮ m s and θ s ⇒ subject to the cosmological and astrophysical bounds. ◮ Some laboratory bounds = ⇒ typically much weaker than the astrophysical and cosmological ones. ◮ In the light of laboratory experimental as well as cosmological and astrophysical observations, there exist two interesting ranges of m s , = ⇒ order keV and order MeV.

keV sterile neutrino ◮ A viable “warm” dark matter candidate. ◮ For sin θ s ∼ 10 − 6 − 10 − 4 , sterile neutrinos were never in thermal equilibrium in the early Universe = ⇒ their abundance to be smaller than the predictions in thermal equilibrium. ◮ A few keV sterile neutrino = ⇒ important for the physics of supernova, which can explain the pulsa kick velocities (Kusenko) . ◮ In addition, some bounds on m s from the possibility to observe ν s radiative decays from X-ray observations and Lyman α − forest observations of order of a few keV.

MeV sterile neutrinos ◮ There exists high mass region m s � 100 MeV restricted by the CMB bound, meson decays and SN1987A cooling: sin 2 θ s � 10 − 9 . = ⇒ ◮ Such a high mass region may be very interesting in the sense that induced contributions to the neutrino mass matrix due to the mixing between ν a and ν s can be dominant = ⇒ responsible for peculiar properties of the lepton mixing such as tri-bimaximal mixig (Smirnov, Funchal ’06) . ◮ Sterile neutrinos with mass 1-100 MeV = ⇒ a dark matter candidate for the explanation of the excess flux of 511 keV photons if sin 2 2 θ s � 10 − 17 . ◮ In this work, we will focus on MeV sterile neutrinos. ◮ Similarly, we can realize keV sterile neutrinos (unnatural).

Low Scale Leptogenesis ◮ We propose a scenario that a low scale leptogenesis can be successfully achieved without severe fine-tuning such as very tiny mass splitting between two heavy Majorana neutrinos. ◮ In our scenario, the successful leptogenesis = ⇒ achieved by the decay of the lightest RH Majorana neutrino before the scalar fields get VEVs. ◮ In particular, a new contribution to the lepton asymmetry mediated by the extra singlet neutrinos.

◮ Without loss of generality, taking a basis where the mass matrices M R and µ real and diagonal. ◮ In this basis, the elements of Y D and Y S are in general complex. ◮ The lepton number asymmetry required for baryogenesis : � Γ( N 1 → ¯ l i ¯ � H u ) − Γ( N 1 → l i H u ) � ε 1 = − , Γ tot ( N 1 ) i where N 1 : the lightest RH neutrino Γ tot ( N 1 ) : the total decay rate. ◮ The introduction of S = ⇒ a new contribution which can enhance ε 1 .

◮ As a result of such an enhancement, low scale leptogenesis is successful without severe fine-tuning. ◮ Diagrams contributing to lepton asymmetry : L i L i φ N 1 N 1 N k L j φ φ (a) (b) L i L i φ Ψ N 1 N k N 1 N k L j S j φ φ (c) (d) ◮ In addition to (a-c), there is a new daigram (d) arisen due to the new Yukawa interaction Y S ¯ N Ψ S .

◮ Assuming m φ , m Ψ , m S << m R 1 , to leading order, Γ tot ( N i ) = ( Y ν Y † ν + Y s Y † s ) ii M R i 4 π ◮ The lepton asymmetry : 1 � ε 1 = k � =1 ([ g V ( x k ) + g S ( x k )] T k 1 + g S ( x k ) S k 1 ) , 8 π where ◮ g V ( x ) = √ x { 1 − (1 + x ) ln [(1 + x ) / x ] } , ◮ g S ( x ) = √ x k / (1 − x k ) with x k = M 2 R k / M 2 R 1 for k � = 1, ν ) 2 Im [( Y ν Y † k 1 ] ◮ T k 1 = ( Y ν Y † ν + Y s Y † s ) 11 ◮ S k 1 = Im [( Y ν Y † ν ) k 1 ( Y † s Y s ) 1 k ] : coming from interference of the ( Y ν Y † ν + Y s Y † s ) 11 tree diagram with (d).

◮ For x ≫ 1 , vertex diagram becomes dominant : ν m ν Y † Im [( Y ∗ ε 1 ≃ − 3 M R 1 ν ) 11 ] , 16 π v 2 ( Y ν Y † ν + Y s Y † s ) 11 ◮ it is bounded as ( Davidson, Ibarra ) 3 M R 1 | ε 1 | < v 2 ( m ν 3 − m ν 1 ) , 16 π � ∆ m 2 ◮ For hierarchical m ν , m ν 3 ≃ atm and then it is M R 1 ≥ 2 × 10 9 GeV required : ◮ To see how much the new contribution can be important, let’s consider a case : M R 1 ≃ M R 2 < M R 3 .

◮ In this case, ε 1 : » – k � =1 Im [( Y ν Y † ν ) k 1 ( Y s Y † Im [( Y ∗ ν m ν Y † M R 2 P s ) 1 k ] ν ) 11 ] 1 R , s ) 11 + ε 1 ≃ − 16 π v 2 ( Y ν Y † ν + Y s Y † ( Y ν Y † ν + Y s Y † s ) 11 where R ≡ | M R 1 | / ( | M R 2 | − | M R 1 | ) . ◮ Denominator of ε 1 = ⇒ constrained by Γ N 1 < H | T = M R 1 : = ⇒ the corresponding upper bound on ( Y s ) 1 i : �� | ( Y s ) 1 i | 2 < 3 × 10 − 4 � M R 1 / 10 9 ( GeV ) . i ◮ The first term ( >> 2nd term) : bounded as ( M R 2 / 16 π v 2 ) � ∆ m atm 2 R TeV scale leptogenesis achieved by R ∼ 10 6 − 7 = ⇒ (implying severe fine-tuning).