Advances in High Energy Physics

Volume 2018, Article ID 9314613, 6 pages

https://doi.org/10.1155/2018/9314613

## A Heavy Scalar at the LHC from Vector-Boson Fusion

Department of Physics, Chongqing University, Chongqing 401331, China

Correspondence should be addressed to Sibo Zheng; moc.liamg@ujz.gnehzobis

Received 11 May 2018; Revised 3 July 2018; Accepted 26 July 2018; Published 2 August 2018

Academic Editor: Enrico Lunghi

Copyright © 2018 Qiurong Mou and Sibo Zheng. 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

A hypothetical scalar mixed with the standard model Higgs appears in few contexts of new physics. This study addresses the question what mass range is in the reach of TeV LHC given different magnitudes of mixing angle , where event simulations are based on production from vector-boson fusion channel and decays into SM leptons through or . It indicates that heavy scalar mass up to GeV and GeV can be excluded by integrated luminosity of 300 and 3000 , respectively, for larger than .

#### 1. Introduction

After the discovery of Higgs scalar at the LHC [1, 2], Standard Model (SM) as the effective field theory (EFT) of weak scale is established. While this EFT has not been violated at nowadays astrophysical and collider experiments, it must be incomplete in the light of a few indirectly experimental as well as theoretic hints. One of most robustly experimental hints arises from Plank and WIMP data [3], which suggests that there should be a new particle beyond SM serving as the thermal dark matter. On the other hand, one of theoretic challenges is the need of some novel mechanism to stabilize the divergence involving Higgs mass.

In a few new physics models attempted to complete the EFT of SM such as SM with doublets and supersymmetry, there usually exists a new scalar of the same spin, parity, and quantum numbers with SM Higgs but with heavier mass. Unless forbidden by some hidden symmetry, it generally mixes with the SM Higgs. If so, such scalar may leave signatures at dark matter facilities which are in the reach of TeV mass scale. See, e.g., [4–6] for very recent studies on this subject.

Alternatively, can mix with the SM Higgs and be examined at the LHC. Due to mixing effect couplings to SM particles are similar to those of SM Higgs but with an universal scaling factor related to mixing angle smaller than unity. As a result, the diboson decay channels with referring to or boson dominate others for mass above GeV. In this case, is mainly generated at the LHC through gluon-gluon fusion (GGF) and vector-boson fusion (VBF) channels similar to the SM Higgs [7]. Early constraints [8–10] on the model parameters were obtained according to measurements on SM Higgs couplings, decay width, and direct detection at the LHC. Updated analyses based on the TeV LHC data [11–17] can be found in [18–23].

In this paper, we will employ the techniques reported in [15] and study the prospect for the discovery of at the TeV LHC through processes of VBF production and subsequent diboson decays to SM leptons final states (The analysis here is more general than in the earlier version, which focused on the model interpretations of diboson excess reported in [24].). One reason is that although the GGF channel yields larger contribution to the production cross section than the VBF channel, the contribution to SM background cross section arising from GGF process is also larger than VBF process. Moreover, the ratio between GGF and VBF contribution to the production cross section declines from about ~10 to ~2.5 when increases from GeV to TeV.

The paper is organized as follows. In Section 2, we briefly discuss general parameterization of mixing effect in a model-independent way. The key point is that only two model parameters appear in the following study of direct detection. In Section 3, we address the production cross sections from VBF channel at the LHC for mass above GeV. Our main results are presented in Section 4, where we show the luminosities required for the exclusion and discovery. Finally we conclude in Section 5.

#### 2. Model

Without mixing effect such as in the case of scalar dark matter model, the mass squared matrix for state vector reads as where and denote the mass of and , respectively. There is little chance for direct detection on this kind of scalar at the LHC [25]. In contrast, in the case of mixing effect mass squared matrix in (1) should be replaced with where characterizes the mixing effect.

At present status only small mixing effect is allowed based on the LHC searches such as dijet, diphoton, and four-lepton signals. The mass eigenvalues can be approximated to be (Note that the analytic rather than approximations here will be utilized for the numerical calculation in the next section.) together with their couplings to SM particles relative to SM Higgs Here, refers to the SM vector bosons and fermions, and the mixing angle is given by From (3) to (5) one finds that the productions and decays of these two scalars are totally determined by heavier mass and mixing angle after identifying as the SM-like Higgs. The magnitude of has been up bounded to be less than ~0.2 at CL in the light of precise measurement [9, 10] on the SM Higgs couplings at the TeV LHC, and it will be improved to be of order ~0.04 at the future TeV LHC with designed integrated luminosity [26].

#### 3. Vector-Boson Fusion

In this section, we address event simulation for the production cross section from VBF channel and branching ratios at the TeV LHC. In particular, we use package FeynRules [27] to generate model files prepared for MadGraph5 [28], which includes Pythia 6 [29] for parton showering and hadronization and the package Delphes 3 [30] for fast detector simulation.

##### 3.1. Production Cross Section

We show in Figure 1 the strengths of cross sections for two different four-lepton final states, where the dependence on the mixing angle can be understood as follows. Firstly, according to (4), the VBF induced cross section is proportional to . Secondly, with the definition on branching ratios , where ( is a SM fermion or vector boson), depends on the magnitude of relative to . Unlike which is determined by the mixing effects in quadratic term of scalar potential, is directly related to the cubic term in the scalar potential, which is model-dependent. For example, in the minimal supersymmetric standard model, the ratio is small for above GeV [31], which implies that mildly depends on the mixing angle. In contrast, can be important in models such as extended Higgs doublet models, where will be related to parameters such as mixing angle and quadratic and cubic terms in the scalar potential. For simplicity, we consider the case in which can be ignored.