Advances in High Energy Physics

Volume 2017 (2017), Article ID 7498795, 13 pages

https://doi.org/10.1155/2017/7498795

## LHC Probes of TeV-Scale Scalars in Grand Unification

Department of Physics and Astronomy, Uppsala University, P.O. Box 516, 751 20 Uppsala, Sweden

Correspondence should be addressed to Tanumoy Mandal

Received 14 February 2017; Accepted 24 April 2017; Published 30 May 2017

Academic Editor: Anna Cimmino

Copyright © 2017 Ufuk Aydemir and Tanumoy Mandal. 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

We investigate the possibility of TeV-scale scalars as low energy remnants arising in the nonsupersymmetric grand unification framework where the field content is minimal. We consider a scenario where the gauge symmetry is broken into the gauge symmetry of the Standard Model (SM) through multiple stages of symmetry breaking, and a colored and hypercharged scalar picks a TeV-scale mass in the process. The last stage of the symmetry breaking occurs at the TeV-scale where the left-right symmetry, that is, , is broken into that of the SM by a singlet scalar field of mass TeV, which is a component of an -triplet scalar field, acquiring a TeV-scale vacuum expectation value. For the LHC phenomenology, we consider a scenario where is produced via gluon-gluon fusion through loop interactions with and also decays to a pair of SM gauge bosons through in the loop. We find that the parameter space is heavily constrained from the latest LHC data. We use a multivariate analysis to estimate the LHC discovery reach of into the diphoton channel.

#### 1. Introduction

After the discovery of the Higgs boson at the Large Hadron Collider (LHC) [1, 2], the last piece of the triumphant achievement of the high energy physics community, the Standard Model (SM), the great expectations for the observation of some sort of new physics at the LHC, emanated from the paradigms based on the familiar intuitions, some of which have so far lead the community to success, have turned out to be great disappointments as the LHC searches to date have returned empty-handed. Although there have been a couple of noticeable excesses, such as the diphoton [3, 4] (see [5] for a review and the full list of references) and diboson [6–8] anomalies, which caused excitement among the community, these signals have turned out to be statistical fluctuations as more data accumulates in.

While the LHC is still up and running and looking for any hint of trace pointing to physics beyond the SM (BSM), the community has been in an ambitious effort for projecting out the LHC implications of variety of new physics models for a possible future discovery. Among the various search channels, the diphoton resonance search is one of the most important programs at the LHC since this channel provides a comparatively cleaner background. One of the key predictions of many BSM theories is the existence of diphoton resonances around the TeV-scale arising from the decay of TeV-scale scalars present in those models.

One of the most appealing scenarios for a more fundamental picture is the Grand Unified Theory (GUT) framework, in which the GUT is particularly interesting [9–24] (see [25–31] for analyses of the supersymmetric GUT). Breaking the gauge symmetry into that of the SM can be realized in a single step as well as in multiple steps by various symmetry breaking sequences. The relevant option we consider in this paper is the latter, while one possible intermediate phase, which we assume to be in the TeV-scale, is the left-right model whose gauge symmetry is based on () [32–39], which is different than the left-right symmetric version since in this case and gauge couplings are different, that is, . Adopting the minimalistic approach and, therefore, keeping the initial field content (the multiplets) minimal, and tempted by the least possible fine-tuning intuition, it seems not possible to obtain a plausible scenario where the left-right model lies in the TeV-scale [23]. For instance, if the Higgs content is determined based on the* extended survival hypothesis* (ESH) [40], the model does not allow symmetry breaking scale of the left-right model to be in the TeV-scale. Recall that the ESH states that at every step of a symmetry breaking sequence, the only scalars which survive below the corresponding symmetry breaking scale are the ones which acquire vacuum expectation values (VEVs) at the subsequent levels of the symmetry breaking. However, by slightly relaxing the ESH conjecture by allowing one or more colored scalars to become light (at the TeV-scale), it is possible to have a TeV-scale left-right model in the framework [23].

In this paper, we investigate the phenomenology of TeV-scale scalars as low energy remnants of the nonsupersymmetric GUT. The part of the model that lies in the TeV-scale, as mentioned above, is the left-right model, augmented by a color-triplet scalar , whose one component , we assume for our demonstration, has a mass of ~1 TeV, while its other components are heavier in the TeV range. In particular, we explore the phenomenology of a SM-singlet scalar of mass around 1 TeV which is assumed to be the excitation of the neutral component of an triplet , denoted as . The field breaks the symmetry of the left-right model into that of the SM by acquiring a VEV presumably at the TeV-scale in our set-up. The scalar is responsible for the production and decay of through loop interactions.

In our model, we assume two intermediate energy scales between the electroweak scale and the unification scale . At the scale , the is broken into the Pati-Salam group, (). The Pati-Salam group is broken into the group of the left-right model at the first intermediate energy scale , which is followed by the breaking of the left-right model into the SM at the energy scale . In our scenario, is assumed to be in the TeV-scale, while the values of and come out as predictions of the model. Note that the -parity invariance [10, 11, 41], which is a symmetry that maintains the complete equivalence of the left and the right sectors, is broken together with the in the first stage of the symmetry breaking. Therefore, the gauge couplings associated with the and gauge groups, and , evolve under the influence of different particle contents; hence , below the scale . Remember that the -parity is slightly different from the usual Lorentz parity in that the latter does not transform scalars, while the -parity transforms them nontrivially. Note also that we remain in the minimal picture in terms of the total field content; the model does not have any extra matter field or any scalar multiplet other than the ones required to begin with. Thus, the advantage of having a TeV-scale colored scalar is twofold: it is responsible for the production and decay of and it can successfully be embedded in the minimal nonsupersymmetric GUT scheme while maintaining the field content minimal.

In this paper, we identify the region of parameter space of our model constrained from the latest LHC data. By using a multivariate analysis (MVA), we compute the higher-luminosity LHC discovery reach of into the diphoton channel where, as we will discuss later, the most stringent bounds come from.

The paper is organized as follows. In Section 2, we review the left-right model in the grand unification framework. We discuss how the two scalars, and of our interest, arise in our set-up. In Section 3, we discuss the unification of the couplings, derive the values of the intermediate symmetry breaking scales, and present the resulting predictions of the model. In Section 4, we present the phenomenology of and including the exclusion limits from the LHC data and future discovery prospects. We summarize our conclusions in Section 5.

#### 2. The Model

We consider a left-right model, whose gauge group is , which is assumed to be broken into the SM at the TeV-scale. The breaking is realized by the neutral component ( which we denote as ) of the triplet , which is commonly preferred in the literature. Here, instead of the triplets, the doublet , which originates from the multiplet , can also be used. The advantage of the triplet representation is that it can provide a Majorana mass term for the right-handed neutrino and, hence, the seesaw mechanism [42–46] for small neutrino masses.

In this work, we explore the phenomenology of the SM-singlet which we assume to be produced and decayed through the loop interaction with a color-triplet hypercharged scalar denoted as . originates from the decomposition of component of the multiplet into the SM group as follows:For our purpose, we take the mass of around 1 TeV, while the other components have heavier masses, ~2–5 TeV, and hence their contribution to the production and the decay of are relatively suppressed.

The SM electroweak symmetry breaking (EWSB) in the left-right model, in general, is achieved by the neutral (diagonal) component of the bidoublet field acquiring a VEV. The fermion content of the model is the same as the SM. There are seven gauge bosons in the model, , (with ), and , with the gauge couplings , , and , associated with the , , and gauge symmetries, respectively. Using the notation of [21, 23], the symmetry breaking pattern of our model is given bywhere we assume TeV in our analysis.

In choosing the multiplets for breaking the symmetries (by acquiring appropriate VEVs), we follow the common tradition in the literature as follows. The first stage of the symmetry breaking, where is broken into the Pati-Salam group , is realized by the singlet of . Note that is odd under the -parity [10, 11], and hence it is broken at this stage as well. Therefore, below the scale , we have , since they evolve under the influence of different particle contents below this energy scale according to the ESH and the minimal fine-tuning principle. The second stage, where the Pati-Salam group is broken into the left-right group , can be accomplished by acquiring a VEV. The breaking of down to the SM gauge group is achieved by the multiplet which belongs to the Pati-Salam multiplet which is a member of the multiplet . In our model, acquires a VEV at around TeV which also set the value of the symmetry breaking scale . Note that is the regular triplet usually used in the literature in order to break the symmetry.

#### 3. Unification of the Couplings

In this section, we discuss how the unification of the couplings is achieved and derive the values of the symmetry breaking scales. We have only two intermediate scales in our model in between the unification scale and the EWSB scale , which are and , where the value of is chosen to be 5 TeV.

The TeV-scale left-right model with light colored scalars in the minimal nonsupersymmetric GUT scheme has recently been discussed in [23]. Here, the situation has a slight difference in one of the components in the decomposition of the left-right multiplet (shown in (1)) into the SM gauge group, which is whose mass is ~1 TeV. Therefore, the renormalization group (RG) running of the gauge couplings at this energy scale is slightly different. The other particle which, we assume, has a mass also around ~1 TeV, does naturally not contribute to the running since it is a SM-singlet.

##### 3.1. Basics

We label the energy intervals in between symmetry breaking scales starting from up to with Roman numerals as follows:The boundary/matching conditions we impose on the couplings at the symmetry breaking scales areThe low energy data which we will use as boundary conditions to the RG running are [47, 48]and all are evaluated at GeV, which givesNote that the coupling constants are all required to remain in the perturbative regime during the evolution from down to .

##### 3.2. One-Loop RG Running

For a given particle content; the gauge couplings, in an energy interval , are evolved according to the one-loop RG relationwhere the RG coefficients are given by [49, 50] asHere, the two summations are over irreducible chiral representations of fermions and those of scalars . The coefficient is either 1 or 1/2, depending on whether the representation is complex or real, respectively. The quadratic Casimir for the adjoint representation of the group is and is the Dynkin index of each representation. For group, andwhere is the charge, the factor of coming from the traditional normalizations of the hypercharge and charges. The ’s differ depending on the particle content in each energy interval, which changes every time symmetry breaking occurs. We will distinguish the ’s in different intervals with the corresponding roman numeral superscript, cf. (3).

##### 3.3. Results

The scalar content in the energy intervals are It is common in the literature that another scalar Pati-Salam multiplet, , is included in interval III for a rich Yukawa phenomenology [14, 15]. In terms of the RG evolution, which is our main focus here, this extra multiplet would not alter the results noticeably, because its effect in the RG equations would appear as a contribution in the term (see (14)), which would be very small compared to the rest of the term. Therefore, for the sake of staying minimal, we do not include this multiplet in our set-up.

The values of the RG coefficients for this Higgs content are listed in Table 1. The relations between symmetry breaking scales, which can be derived by using the one-loop running equations and the boundary/matching conditions, can be obtained as (for derivation see [21, 23])where . Using these equations and the experimentally measured quantities in (8) and demanding TeV, we obtain the following values:The value for the scale is sufficiently high to ensure that the effects induced by the presence of scalar and vector-leptoquarks are suppressed adequately enough to remain consistent with the experimental constraints [51]. Besides, the unification scale is high enough to escape the bound on the proton decay induced by gauge boson exchanging operators. We should also note that we have light color-triplets in our model, and as well known they lead to scalar-induced dimension-6 operators that contribute to the proton decay amplitude. Although these contributions are typically suppressed by small Yukawa couplings, the color-triplets being as light as the TeV-scale can cause a potentially dangerous situation [52]. In such a case, a mechanism is required to adequately suppress these interactions, such as the ones proposed in [53, 54].