content_image/418308.jpg content_image/418309.jpg content_image/418310.jpg content_image/418311.jpg
# Resonant Leptogenesis and Verifiable Seesaw from Large Extra Dimensions 

Max-Plank-Institut f¨ ur Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany 

Pei-Hong Gu ∗ 

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 branes to our world. 

In the theory of large extra dimensions [1], the Planck scale of the 4-dimensional theory is related to that of the (4 + n )-dimensional theory by 

where M$_{Pl}$ ≃ 2 . 4 × 10 $^{18}$GeV is the reduced Planck mass and R is the size of the extra dimensions. Therefore the fundamental scale M$_{∗}$ of quantum gravity could be as low as a few TeV for solving the hierarchy problem be- tween the electroweak and Planck scales. Clearly, all of other scales in this theory couldn’t be larger than a few TeV. This can give interesting implications on neutrino physics. In this direction, there have been many works [2–6]. For example, ones [6] find the lepton number vio- lation in a distant brane can induce a very small trilinear coupling of the Higgs triplet to the standard model (SM) Higgs doublet in our world. This naturally makes the type-II [7] seesaw [8] model accessible at colliders. 

The low fundamental scale also constrains leptogen- esis [9–16] for baryon asymmetry. In the leptogenesis scenario, the decaying particles should be very heavy for generating a sizable CP asymmetry unless their masses are quasi-degenerate, which is simply input by hand or is induced by radiative correction in some special mod- els [17], so that the CP asymmetry can be resonantly enhanced [11, 12]. Remarkably the resonant leptogenesis allows us to produce the baryon asymmetry below the low fundamental scale. The author of [14] have studied the resonant leptogenesis with bulk right-handed neutrinos. In the present work, we shall introduce two right-handed neutrinos with equal but opposite lepton numbers and lo- calize them in our brane. In our model, the lepton num- ber is maximally broken in the distant branes and then is shined to our brane by a bulk scalar. Therefore the lep- ton number violation is highly suppressed in our world, where the right-handed neutrinos mix together through a lepton number conserving mass term and both have Yukawa couplings to the bulk scalar so that they can naturally have a quasi-degenerate mass spectrum. The 

PACS numbers: 98.80.Cq, 14.60.Pq, 11.10.Kk, 12.60.Fr 

<img src='content_image/418308.jpg'>

induced Majorana fermions can accommodate a resonant leptogenesis by their decays into the SM lepton and Higgs doublets. Within this context, the small trilinear cou- pling of the Higgs triplet to the SM Higgs doublet is also ready for the verifiable type-II seesaw. 

In our model, besides two right-handed neutrinos N$_{R}$$_{1}$$_{,}$$_{2}$ and the SM fields, there are three scalars: triplet ξ , dou- blet η and singlet χ . We assign L = 1 for N$_{R}$$_{1}$ and N c R$_{2}$ while L = 2 for ξ $^{∗}$, η and χ . The lepton number conserv- ing interactions would be 

<img src='content_image/418309.jpg'>

where ψ$_{L}$ and φ denote the SM lepton and Higgs dou- blets, respectively. The right-handed neutrinos N$_{R}$$_{1}$$_{,}$$_{2}$ , the triplet ξ , the doublet η and the SM fields are local- ized in our brane ( x, y a = 0) while the singlet χ propa- gates in the bulk. Here a = 1 , ..., n runs over the extra dimensions. We further introduce a singlet scalar σ with a lepton number L = 2. This singlet is localized in a dis- tant brane ( x $^{′}$, y a = y a $_{∗}$). The transverse distance from the distant brane to our brane is r = | y$_{∗}$ | . 

The singlet χ can interact with our brane through its couplings to the right-handed neutrinos and the triplet and doublet scalars as shown in Eq. (2). In the distant brane, it can also have lepton number conserving inter- action with the singlet σ [2], 

So, the singlet χ can mediate the communication from the distant brane to ours. In particular, it can carry the lepton number violation to our world through its shined value 〈 χ 〉 , 

Here the vacuum expectation value (VEV) 〈 σ 〉 acts as a point source whereas Δ$_{n}$( r ) is the Yukawa potential in 

<img src='content_image/418310.jpg'>

<img src='content_image/418311.jpg'>

