Advances in High Energy Physics

Volume 2018 (2018), Article ID 9785318, 16 pages

https://doi.org/10.1155/2018/9785318

## Searching for the Minimal Seesaw Models at the LHC and Beyond

School of Physics, KIAS, Seoul 130-722, Republic of Korea

Correspondence should be addressed to Arindam Das; moc.liamg@scisyhpmadnirasad

Received 28 July 2017; Accepted 21 February 2018; Published 19 April 2018

Academic Editor: Ning Chen

Copyright © 2018 Arindam Das. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

The existence of the tiny neutrino mass and the flavor mixing can be naturally explained by type I Seesaw model which is probably the simplest extension of the Standard Model (SM) using Majorana type SM gauge singlet heavy Right Handed Neutrinos (RHNs). If the RHNs are around the Electroweak- (EW-) scale having sizable mixings with the SM light neutrinos, they can be produced at the high energy colliders such as Large Hadron Collider (LHC) and future 100 TeV proton-proton (pp) collider through the characteristic signatures with the same-sign dilepton introducing lepton number violations (LNV). On the other hand Seesaw models, namely, inverse Seesaw, with small LNV parameter can accommodate EW-scale pseudo-Dirac neutrinos with sizable mixings with SM light neutrinos while satisfying the neutrino oscillation data. Due to the smallness of the LNV parameter of such models, the “smoking-gun” signature of same-sign dilepton is suppressed where the RHNs in the model will be manifested at the LHC and future 100 TeV pp collider dominantly through the Lepton number conserving (LNC) trilepton final state with Missing Transverse Energy (MET). Studying various production channels of such RHNs, we give an updated upper bound on the mixing parameters of the light-heavy neutrinos at the 13 TeV LHC and future 100 TeV pp collider.

#### 1. Introduction

The experimental evidence of the neutrino oscillation and flavor mixings from neutrino oscillation experiments [1–6] indicates that the SM is not enough to explain the existence of the tiny neutrino mass and flavor mixing. After the pioneering discovery of the operator [7] within the SM using the SM leptons, SM Higgs doublets, and unit of LNV, it turned out that the Seesaw mechanism [8–14] could be the simplest idea to explain the small neutrino mass and flavor mixing where the SM can be extended by the SM-gauge singlet Majorana type RHNs. After the Electroweak (EW) symmetry breaking, the light Majorana neutrino masses are generated after the so-called type I Seesaw mechanism.

In type I Seesaw, we introduce SM gauge-singlet Majorana RHNs where is the flavor index. couples with the SM lepton doublets and the SM Higgs doublet . The relevant part of the Lagrangian iswhere is the Yukawa coupling, is the SM lepton doublet, and is the Majorana mass term. After the spontaneous EW symmetry breaking by the vacuum expectation value (VEV), , we obtain the Dirac mass matrix as suppressing the indices. Using the Dirac and Majorana mass matrices we can write the neutrino mass matrix as where is the Dirac mass matrix and is the Majorana mass term. Diagonalizing we obtain the Seesaw formula for the light Majorana neutrinos as For GeV, we may find with eV. However, in the general parameterization for the Seesaw formula [15], can be large and sizable , and this is the case we consider in this paper.

The searches of the Majorana RHNs can be performed by the “smoking-gun” of the same-sign dilepton plus di-jet signal which is suppressed by the square of the light-heavy neutrino mixing parameter . A comprehensive general study on the parameters of has been given in [16] using the data from the neutrino oscillation experiments [1–6], bounds from the Lepton Flavor Violation (LFV) experiments [17–19], Large Electron-Positron (LEP), and Electroweak Precision test [20–27] experiments using the nonunitarity effects [28, 29] applying the Casas-Ibarra conjecture [15, 30–33]. At this point we mention that [16] has a good agreement with a previous analysis [34] on the sterile neutrinos. The bounds in [16] have been compared with the existing results in [23, 26, 27, 35–37] considering the degenerate Majorana RHNs. In case of Seesaw mechanism the Dirac Yukawa matrix can carry the flavors where the RHN mass matrix is considered to be diagonal. This case is favored by the neutrino oscillation data as studied in [16, 30, 38–42]. Such a scenario for the Seesaw scenario is called the Flavor Nondiagonal (FND). The other possibility of considering both of the diagonal and is not supported by the neutrino oscillation data.

Since any number of singlets can be added in a gauge theory without contributing to anomalies, one can utilize such freedom to find a natural alternative of the low-scale realization of the Seesaw mechanism. Simplest among such scenarios is commonly known as the inverse Seesaw mechanism [43, 44] where a small Majorana neutrino mass originates from tiny LNV parameters rather than being suppressed by the RHN mass as done in the case of conventional Seesaw mechanism. In the inverse Seesaw model two sets of SM-singlet RHNs are introduced which are pseudo-Dirac by nature and their Dirac Yukawa couplings can be even order one, while reproducing the neutrino oscillation data. Therefore, at the high energy colliders such pseudo-Dirac neutrinos can be produced through a sizable mixing with the SM light neutrinos [45–52].

In the inverse Seesaw mechanism the relevant part of the Lagrangian is given by where and are two SM-singlet heavy neutrinos with the same lepton numbers, is the Dirac mass matrix, and is a small Majorana mass matrix violating the lepton numbers. After the EW symmetry breaking we obtain the neutrino mass matrix as Diagonalizing this mass matrix we obtain the light neutrino mass matrix Note that the smallness of the light neutrino mass originates from the small LNV term . The smallness of allows the parameter to be on the order one even for an EW scale RHNs. In the inverse Seesaw case we can consider as nondiagonal when and are diagonal which is called the Flavor Nondiagonal (FND) case. On the other hand we can also consider the diagonal , when will be nondiagonal. This situation is called the Flavor Democratic scenario. For the inverse Seesaw both of the FND and FD cases are supported by the neutrino oscillation data. In this article we will consider the FND case from the Seesaw and the FD case from the inverse Seesaw mechanisms.

Through the Seesaw mechanism, a flavor eigenstate () of the SM neutrino is expressed in terms of the mass eigenstates of the light and heavy () Majorana neutrinos such as

Using the mass eigenstates, the charged current (CC) interaction for the heavy neutrino is given by where denotes the three generations of the charged leptons in the vector form, and is the projection operator. Similarly, the neutral current (NC) interaction is given by where with being the weak mixing angle and , are the SM gauge bosons.

The main decay modes of the heavy neutrino are . The corresponding partial decay widths [47] are, respectively, given by The decay width of heavy neutrino into charged gauge bosons is twice as large as neutral one owing to the two degrees of freedom . We plot the branching ratios of the respective decay modes with respect to the total decay width of the heavy neutrino into , and Higgs bosons in Figure 1 as a function of the heavy neutrino mass . Note that for larger values of such as GeV, the branching ratios can be obtained as