Parametrized leptogenesis from linear seesaw

We present a purely linear seesaw mechanism in a left-right symmetric framework and then realize a novel leptogenesis scenario for parametrizing the cosmic baryon asymmetty by the charged lepton masses and the light Majorana neutrino mass matrix up to an overall factor. Through the same Yukawa couplings, the lepton-number-conserving decays of the mirror charged leptons can generate three individual lepton asymmetries stored in the ordinary lepton flavors, while the lepton-number-violating processes for the Majorana neutrino mass generation can wash out part of these lepton asymmetries. The remnant lepton asymmetries then can be partially converted to a baryon asymmetry by the sphaleron processes. Our scenario prefers a normal hierarchical neutrino spectrum so that it could be verified by the future data from cosmological observations, neutrino oscillations and neutrinoless double beta decay.


I. INTRODUCTION
The precise measurements on the atmospheric, solar, accelerator and reactor neutrinos have established the phenomenon of neutrino oscillations. This fact implies three flavors of neutrinos should be massive and mixed [1]. Meanwhile, the cosmological observations indicate the neutrinos should be extremely light [1]. The tiny but nonzero neutrino masses call for new physics beyond the SU (3) c ×SU (2) L ×U (1) Y standard model (SM). Furthermore, the SM is challenged by other puzzles such as the cosmic baryon asymmetry [1]. Currently a seesaw [2][3][4][5] extension of the SM has become very attractive since it can simultaneously explain the small neutrino masses and the cosmic baryon asymmetry [6]. In this popular scenario [6][7][8][9][10][11][12][13][14][15], we do not know much about the masses and couplings involving the non-SM fields. Consequently, we cannot get an exact relation between the cosmic baryon asymmetry and the neutrino mass matrix. For example, we can expect a successful leptogenesis in the canonical seesaw model even if the neutrino mass matrix does not contain any CP phases [16].
In this paper we shall develop a novel leptogenesis [6] scenario where the neutrinos can obtain their tiny masses in the so-called linear [17] seesaw way while the cosmic baryon asymmetry can be parameterized by the neutrino and charged lepton mass matrices up to an overall factor [30]. Our scenario is based on an [19][20][21][22]. Some Yukawa interactions can accommodate the lepton-number-conserving decays of the mirror electron-positron pairs to produce three individual lepton asymmetries in the ordinary lepton flavors although the net lepton number is exactly zero. The same Yukawa interactions can participate in the Majorana neutrino mass generation and then can lead to some leptonnumber-violating processes to wash out part of the pro- * Electronic address: peihong.gu@sjtu.edu.cn duced lepton asymmetries. The SU (2) L sphaleron [23] processes then can partially convert the remnant lepton asymmetries to a baryon asymmetry. Our scenario prefers a normal hierarchical neutrino spectrum so that it could be verified by the future data from cosmological observations, neutrino oscillations and neutrinoless double beta decay.
The global U (1) 3B−L symmetry and the discrete leftright symmetry are both conserved exactly. For simplicity we do not write down the full scalar potential. Instead we show the cubic terms and some quartic terms as below, As for the Yukawa interactions, they are given by Note the U (1) 3B−L global symmetry has forbidden the gauge-invariant mass terms of the [SU (2)]-singlet fermions.

III. FERMION MASSES
From the full potential which are not shown for simplicity, we can expect the VEVs to be The Yukawa interactions (6) then can reasonably yield This means we can safely ignore the mixing between the ordinary charged fermions (f = d, u, e) and their mirror partners (F = D, U, E). Thus the mass eigenstates of the charged fermions can come from Meanwhile, we can apply the linear seesaw mechanism to the neutral fermions, i.e.
Note the VEVs φ 0 L , χ 0 L and σ 0 1,2 , should be constrained by which implies In addition, the tiny but nonzero neutrino masses require with m max being the largest eigenvalue of the neutrino mass matrix, Here the PMNS matrix U contains three mixing angles, one Dirac phase and two Majorana phases, i.e.
The linear seesaw can be also understood at the electroweak level. From the Yukawa interactions (6), we can read Here the yukawa couplings y e and the mass matrices M E,N have been chosen to be diagonal and real without loss of generality. As shown in Fig. 1, the left-handed neutrinos ν L can acquire their Majorana masses (10) by integrating out the heavy Dirac pairs N = N L + N R , i.e.

IV. LEPTON AND BARYON ASYMMETRIES
As shown in Fig. 2, the mirror charged leptons E β can decay into the ordinary lepton doublets l Lα and the Higgs doublet σ 2 . These decays can generate three individual lepton asymmetries L e,µ,τ stored in the ordinary lepton flavors l Le,Lµ,Lτ if the CP is not conserved, i.e.
We calculate the decay width at tree level, and then the CP asymmetry at one-loop level, It is easy to check as a result of the lepton number conservation. The decays of the mirror electron-positron pairs should dominate the individual lepton asymmetries L e,µ,τ since the mirror electron is much lighter than the mirror muon and tau. When the mirror electrons and positrons go out of equilibrium at a temperature T D , the individual lepton asymmetries L e,µ,τ can be produced, i.e.
Here n eq Ee is the equilibrium number density and s is the entropy density. For the following demonstration, we specify the decay width, and the CP asymmetries, On the other hand, the model provides the leptonnumber-violating interactions for generating the Majorana neutrino masses, as shown in Fig. 1. The interaction rates of the related lepton-number-violating processes are computed by [37] At the temperature, these lepton-number-violating processes will begin to decouple, i.e.
Γ αβ < H(T ) = 8π 3 g * 90 Here the relativistic degrees of freedom (the SM fields plus one additional Higgs doublet σ 2 ). We thus can expect only the lepton asymmetry stored in certain lepton flavor(s) can survive from the leptonnumber-violating processes, i.e.
The SU (2) L sphaleron processes then can partially transfer the remnant lepton asymmetry L to a baryon asymmetry B. From Eq. (26), the lepton-number-violating processes can go out of equilibrium before the sphalerons become active, i.e.
The final baryon asymmetry B then can be given by [38] B = − 28 79 L .

VI. CONCLUSION
In this paper we have demonstrated a novel linear seesaw scenario for paramerizing the cosmic baryon asymmetty by the charged lepton masses and the light Majorana neutrino mass matrix up to an overall factor. Through the lepton-number-conserving decays of the mirror electron-positron pairs, we can obtain three individual lepton asymmetries stored in the ordinary lepton flavors although the total lepton asymmetrt is exactly zero. The lepton-number-violating processes for the neutrino mass generation can wash out the lepton asymmetry stored in certain ordinary lepton flavor(s). Remarkably, these lepton-number-conserving and leptonnumber-violating interactions originate from the same Yukawa couplings. The remnant lepton asymmetry can be partially converted to a baryon asymmetry by the sphaleron processes. Our scenario seems difficult to work for an inverted hierarchical or a quasi-degenerate neu-trino spectrum. Instead, it prefers to the normal hierarchical neutrinos. This means our scenario can be ruled out if the future cosmological observations, neutrino oscillations and neutrinoless double beta decay confirm the inverted hierarchical or quasi-degenerate neutrino spec-trum.