Probing Heavy Spin-2 Bosons with $\gamma \gamma$ final states from Vector Boson Fusion Processes at the LHC

New massive spin-2 particles are predicted in theoretical extensions to the Standard Model (SM) attempting to solve the hierarchy problem. Such theories postulate that gravity is diluted compared to the other fundamental forces because it can propagate in extra spatial dimensions. While such theoretical models are of high experimental interest because they predict massive spin-2 particles ($Y_{2}$) potentially detectable by collider experiments, searches at the Large Hadron Collider (LHC) have thus far produced no significant evidence for their existence. This work considers a hypothetical physics scenario where low coupling strengths between the $Y_{2}$ and quarks/gluons is the underlying reason behind the null $Y_{2}$ search results at the LHC, which have mainly relied on Drell-Yan and gluon-gluon fusion production mechanisms. The focus of this paper is a feasibility study to search for $Y_{2}$ particles using vector boson fusion (VBF) processes at the LHC. In the context of an effective field theory approach with varying couplings $\kappa_{V}$ between $Y_{2}$ and the weak bosons of the SM, we consider the $Y_{2}\to\gamma\gamma$ decay mode to show that the requirement of a diphoton pair combined with two high $p_{T}$ forward jets with large dijet mass and with large separation in pseudorapidity can significantly reduce the SM backgrounds. Assuming proton-proton collisions at $\sqrt{s} = 13$ TeV, we present the total VBF production cross sections, $Y_{2}$ decay widths, and $Y_{2}\to\gamma\gamma$ branching ratios as a function of $m(Y_{2})$, considering universal and non-universal couplings to the SM particles. The unitarity-violating phase space is described. The proposed VBF $Y_{2}\to\gamma\gamma$ search is expected to achieve a discovery reach with signal significance greater than 5$\sigma$ for $Y_{2}$ masses up to 4.4 TeV and $\kappa_{V}$ couplings down to 0.5.


Introduction
The introduction to this thesis document is structured as follows. In Section 1.1, we outline the Standard Model (SM) by describing the included particles and the fundamental forces by which they can interact. The data from collider experiments offers a powerful tool to study these fundamental particles and their interactions, including the SM and potential new physics beyond our current framework/understanding. Thus, in Section 1.2, we describe the Large Hadron Collider (LHC) and the Compact Muon Solenoid (CMS) experiment, which are the experimental apparatus used to study these fundamental interactions. In particular, the detector parameters and performance of the CMS experiment are ultimately what we will simulate in the phenomenological analysis described in this thesis. In Section 1.3, we will provide further physics motivation behind our analysis.

Introduction to the Standard Model of Particle Physics
Everything in our universe is made from basic building blocks called fundamental particles, which are governed by four fundamental forces: the electromagnetic force, the strong force, the weak force, and gravity. Our best understanding of how particles and three of the forces (excluding gravity) are related to each other is described by a mathematical framework referred to as the Standard Model (SM) of particle physics.
All SM particles are either fermions, which are the building blocks of ordinary matter, or bosons, which are mediators of the fundamental interactions which bind fermions into what we typically refer to as the "ordinary matter" we see in our everyday world. Fermions have half-integer spin. In particular, the fundamental fermions of the SM have spin 1/2.
Bosons have integer spins. The bosons of the SM include the spin-1 vector bosons (photon, gluon, W, and Z), and the spin-0 Higgs boson. As we will later discuss in more detail, the hypothetical particle called the graviton -mediator of gravitational interactions -has spin 2 but is not included in the SM of particle physics. Important properties of these fundamental particles, such as the spin number, charge and mass, are summarized in Table 1.
The SM fermions come in two types: quarks and leptons. As shown in Fig. 3 Similarly, it is easy to check that all mesons have charge ± 1 or 0.
Besides flavor (uniquely determined by its generation and charge), each quark may have any of the following three possible color charges (or simply color): red, green and blue.
However, quarks cannot be isolated (and hence cannot be observed individually), and all composites (baryons and mesons) of quarks and antiquarks existing in nature must be colorless -this phenomena is known as "color confinement." It is worth noting that the "colors" are not real colors but rather a classification scheme used in describing the strong interaction.
The role of a quark's "color" (or "color charge") in strong interaction offers a convenient analogy to that of a particle's electric charge in the electromagnetic interaction. Quarks make up baryonic matter, including all atoms in the universe, accounting for 5% of all the mass of the universe [1].
Leptons are classified by their electron number (L e ), muon number (L µ ) and tau number (L τ ) into three generations (or "weak pairs," as each lepton can be changed to its "paired partner" via charged weak interaction), with the two in each pair further distinguished by the charge: electron, muon and tau have charge −1 while their corresponding neutrinos have zero charge.
In modern particle physics, the fundamental particles interact through four fundamental forces, summarized in Table 2: the strong, electromagnetic, weak, and gravitational forces.
Only the first three are included in the SM. The SM includes four vector bosons: the gluon, photon, W ± boson and Z boson. They are mediators of these three fundamental interactions: for instance, the familiar electromagnetic force between two electrons can be thought of as being "mediated" by exchange of photons between the electrons.
The strong force acts on all the quarks and is mediated by gluons. A gluon has no mass or charge and carries both one "color" and one "anticolor." During the strong interaction, the colors of the participant quarks may change, in which case the color difference is carried away by the mediating gluon. At the scale smaller than a femtometer (fm), the strong force is the strongest of the four fundamental forces, and it holds together the three quarks making up a proton or a neutron. For larger scales of 1-3 fm, the strong force binds protons and neutrons to form nuclei [2]. The strong force shows an interesting characteristic: it becomes vanishingly weak as the quarks are close and grows stronger at large distances. In particular, it takes infinitely high energy to pull apart one quark from a hadron, explaining why we never observe an individual/isolated quark. On the other hand, at very high energies (small distances), the strong force is vanishingly (or asymptotically) weak so that quarks become free particles. This feature of the strong force is known as asymptotic freedom.
The electromagnetic force acts on all the SM fermions with nonzero electric charge (i.e, all SM fermions except for neutrinos), where particles with opposite electric charges attract and those with the same electric charge repel. The electromagnetic force is mediated by photons, which have no mass, charge, or color. Photons make up electromagnetic waves, with frequencies ranging from radio waves to gamma ray. The electromagnetic force has infinite range, and its strength is proportional to the electric charges of the particles and to r −2 , where r is the distance between the particles.
The weak force acts on all quarks and leptons and has two types: (i) neutral, mediated by the Z boson; and (ii) charged, mediated by the W bosons. Note that the W and Z bosons are the only massive vector bosons. In a neutral weak interaction, mediated by the Z boson, two fermions come in, interact with each other, and "annihilate" to produce an intermediate Z boson, which then produces two fermions coming out as final state particles. The charged weak interaction is mediated by the W bosons, which have electric charge +1e (W + ) or -1e (W − ). It changes a lepton into its partner lepton of the same generation (for instance, e to ν e ); for quarks, the charged weak interaction usually acts in the same way, changing a quark to its partner quark of the same generation, but "cross-generational" weak interactions also occur (for instance, changing a strange quark to an up quark). The charge difference between the incoming lepton/quark and the outcoming one is carried away by the W boson. The weak force is weaker than both the electromagnetic and the strong forces, about five orders of magnitude weaker than the strong force at the scale of an atom's nucleus [3]. Yet it is important in processes such as beta decay and in the study of violation of parity (mirror symmetry). Fig. 2 shows the so-called Higgs field, which is a scalar field with a Mexican-hat shape: it has a degenerate ground state and non-zero vacuum expectation value. Though all choices of ground state (related to each other by an SU (2) gauge transformation) give the same physics, any choice of a ground state would result in a "distinguished direction" and simultaneously break the symmetry. This process of spontaneous breaking of the electroweak gauge symmetry is called the Higgs mechanism and explains why photons, mediators of the electromagnetic interaction, are massless, while the W and Z bosons, mediators of the weak interaction, have nonzero mass [7].
The Higgs mechanism predicts the existence of the Higgs boson, a particle with spin zero, no electric charge or color charge. Experimental detection of the Higgs boson can test the Higgs mechanism. In 2012, the ATLAS and CMS experiments at the LHC detected a new particle in the mass region around 125 GeV and confirmed it to be a Higgs particle -the signal observed at the LHC and the experimental measurements (e.g. mass and couplings) agreed well with the theoretical prediction of the Higgs mechanism, and deviated from the background by more than 5 standard deviations. François Englert and Peter Higgs, who proposed the Higgs mechanism, were awarded the 2013 Nobel Prize for the discovery of the Brout-Englert-Higgs mechanism [8].
The SM has been a successful theory, agreeing with decades of experimental observations involving the weak, electromagnetic, and strong forces. However, the SM remains an incomplete theory. As mentioned above, the most familiar force in our everyday lives, gravity, is not included in the Standard Model. In particle physics, the analogy with the other three   [4] .
forces indicates that the gravitational force, too, should have a mediator -known as the "Graviton." (The picture of a Graviton as in Einstein's theory of general relativity is a massless spin-2 particle, which is difficult to detect due to its zero mass.) The reason gravity is not incorporated in the SM is because its strength is diluted compared to the weak force, the weakest of the three interactions in SM, by order of 10 29 [5]. This leads to the so-called hierarchy problem. Models with extra spatial dimensions offer one family of solutions to this problem. As we will see in the next subsection, these types of models, combined with the gravitational interaction, result in the manifestation of several spin-2 gravitons which range in mass from zero to several TeV. Since these massive TeV-scale gravitons do not exist "naturally" in nature, this motivates searching for these hypothetical particles in a very high energy environment such as the LHC. Table 1: Information about the particles of the SM, including their main properties such as electric charge and spin, and the year in which they were predicted/discovered [6] .

Muon Solenoid (CMS)
The LHC is a proton-proton (pp) collider, where two circulating, high-energy beams of protons are accelerated to nearly the speed of light and collide, as shown in Fig. 4. In the remaining of this thesis, we denote as the z-axis the line tangent to the curves of the two incoming beams at the momentum of collision, and we call the transverse plane the xy-plane. for the study of an incredible amount of pp collision data [10].
The CMS detector is cylindrical in shape with dimensions of 21 meter long, 15 meters wide and 15 meters high [10]. Weighing 12,000 tonnes, the solenoid magnet at CMS is the largest superconducting magnet ever built [10]. Thanks to the size of the magnet and the superconducting materials (hence zero resistance!), the CMS magnet creates a 4 Tesla magnetic field, which is 100,000 times stronger than the Earth's magnetic field [10]. This powerful magnetic field can bend the paths of charged particles traveling at relativistic speeds. The strong bending, combined with fine tracker segmentation, allows precise measurements of the particles' momenta [10].
The silicon tracker reconstructs the tracks of the charged particles. A particle passing through the tracker interacts with the silicon via the electromagnetic force and produces an electric signal. The signal is then amplified and detected via internal and external means of readout that communicate. Through this way, the tracker can very accurately measure the particle's position at several key points and thereby reconstruct its path. The tracker is designed to disturb the particle as little as possible [10].
By bending a charged particle and tracing its path, we can measure the charge and momentum of the particle. The sign of the charge determines the bending direction, while the magnitude of charge and the particle's momentum determine how much the particle bends. To see this, let us consider the simple example of a charged point particle moving in arbitrary direction in the xy-plane of the three-dimensional Euclidean space (using Cartesian coordinates), while a constant magnetic field B points in the positive direction along the z-axis (B = Bẑ). Denote absolute value of the charge of the particle as q, its mass as m.
Denote the strength of the magnetic field as B = |B|. With the magnetic force being the only force acting on the particle, the particle takes a circular motion in the xy-plane with constant speed (denoted v). If the charge is positive, the particle moves in a counterclockwise circle.
If the charge is negative, the particle moves in a clockwise circle. The radius of the particle's orbit is given by mv 2 /R = qvB; i.e, R = mv/qB. It is hence clear that the higher momentum p (= mv) the particle has, the larger the radius of its circular orbit, hence the smaller the curvature of the orbit. In addition, the radius R is inversely proportional to absolute value of the charge of the particle. Hence, particles with higher charge and with smaller momentum bend more. Though this example is simple and idealized, the conclusions we get are general.
The charge and momentum of a charged particle, which we can obtain from bending the charged particle and tracing its path, offer crucial information for determining the particle's identity [10].
CMS uses calorimeters to measure the energy of particles produced in the collision. light signals over all the layers gives a measurement of the particle's energy [10].
Detection of muons is difficult since muons can "penetrate several meters of iron without interacting" [10]. Unlike other particles, muons are not stopped by any of the CMS calorimeters. As the name "Compact Muon Solenoid" suggests, muon detection is a main task of the CMS experiment. The CMS has 1,400 muon chambers for detection of muons. These chambers lie at the edge of the detector, where all other particles have been stopped by the calorimeters and are unlikely to penetrate. The path of a muon is traced by measuring its position at four muon stations and fitting a curve to these measurements. Since the CMS magnet is so powerful, it can bend even muons with very high energy, trace their paths, and measure their momenta [10].

Motivation
The most important physics result at the CERN Large Hadron Collider (LHC) to date is undoubtedly the observation of a Higgs boson at mass around 125 GeV as reported by the ATLAS and CMS collaborations [16,17]. With this major discovery and the excellent per-  of the coupling between Y 2 and the quarks/gluons (κ q,g ). While previous searches typically assume more "natural" (SM-like) couplings (i.e. κ q,g = 1), the lack of a strong excess thus far opens up the possibility that κ q,g is significantly smaller, in which case the Y 2 may have eluded discovery. If κ q,g is too small to provide large enough cross-section via the traditional gg → Y 2 or qq → Y 2 production mechanisms, another technique must be devised to probe In this analysis, we propose a search for a heavy spin-2 resonance produced through vector boson fusion (VBF) processes and decaying to a pair of photons (Fig. 8). The Y 2 production cross section from VBF processes is independent of κ q,g . The identification of events produced via VBF processes has been a key experimental tool to the discovery of the Higgs boson [27]. The VBF topology has also been proposed as an effective tool for dark matter [28,29], supersymmetry [30,31,32,33,34], Z [35], and heavy neutrino searches at the LHC [36] due to the natural collinear logarithmic enhancement obtained in the production cross section at high mass values, as well as the significant reduction of SM backgrounds.
The Y 2 → γγ decay channel is motivated by its relatively clean experimental signature with localized diphoton mass spectrum. Furthermore, while spin-1 Z and spin-2 Y 2 bosons can both result in dilepton, dijet, and ZZ/W W channels, an excess in the γγ final state would rule out a Z .
To allow for a generic and model independent approach, we consider an effective field theory (EFT) consisting of three terms in the Lagrangian: (i) kinetic term representing the Y 2 interactions with the SM gauge (matter) fields V (f ) and where T V,f µν is the energy-momentum tensor of V or f ; (ii) Y 2 interaction with the SM Higgs doublet where T FP µν is the energy-momentum tensor of the FP ghost field. In the above Lagrangian equations Λ represents the cut-off scale, the gauge fields V are the SM electroweak gauge bosons or the gluon, and the matter fields f are quarks, leptons, and left-handed neutrinos. This particular implementation also allows for scenarios with non-universal couplings to be studied at NLO accuracy [37].  Signal and background samples were generated with MadGraph5 aMC (v2.6.4) [38], considering proton-proton (pp) beams with √ s = 13 TeV. In the case of the spin-2 signal samples, the model files were generated using the FeynRules package [39] and obtained from Ref. [40].
The dominant contributions to the total Y 2 decay width are from the massive SM final , with a dependence given by where l is the angular momentum quantum number, m(X) is the mass of the heavy particle X, and κ X the coupling of X to Y 2 . The term (1 − 4 m(X) 2 m(Y 2 ) 2 ) (2l+1)/2 represents the kinematically allowed phase space, i.e. 4 m(X) 2 m(Y 2 ) 2 < 1 and thus m(Y 2 ) > 2m(X). Therefore, since we allow the possibility that Y 2 couples to all the heavy SM particles, we consider m(Y 2 ) values above 2m(t) ≈ 350 GeV.
To illustrate the unitarity violating phase space (to be defined below), we consider two benchmark scenarios: (i) standard couplings to the fermions, gluons, and Higgs boson and (ii) suppressed couplings to the gluon and light quarks q = u, d, s, c, b ( κq,g Λ = 0), but with free parameter κ V . The latter case represents a proxy for our main interest in this paper, where the lack of a strong excess in gg → Y 2 and qq → Y 2 searches thus far motivates the possibility that κ q,g is small. This scenario makes VBF an important mode for discovery.
On the other hand, it is important to point out that even if κ q,g ≈ 1 (or larger), a VBF Y 2 search is still relevant to establish the coupling of Y 2 to the vector bosons of the SM, which is important to assess the correct physics model that best fits the observed data should there be evidence for discovery. To preserve unitarity, we require that the total decay width of Y 2 (calculated from Ref. [40]) cannot exceed the mass of Y 2 . Fig. 9 shows the unitarityviolating phase space (i.e, where the total decay width of Y 2 exceeds m(Y 2 )) and the Y 2 → γγ branching ratio, as a function of m(Y 2 ) and κ V , for the benchmark case where we assume Figure 9: Y 2 → γγ branching ratio as a function of m(Y 2 ) and κ V , for the benchmark case where κ f,g,H = 1. The gray shaded region represents the unitarity-violating phase space. κ f,g,H = 1. Fig. 10 shows the unitarity-violating phase space and the Y 2 → γγ branching ratio, as a function of m(Y 2 ) and κ V , for the benchmark case where we assume κ q,g = 0.
In the scenario with more natural couplings to the light quarks and gluon, the unitarity acceptable region extends to m(Y 2 ) ≈ 3.6 (3.2) TeV for κ V = 0.1 (1.0). The theoretically allowed region can be as large as m(Y 2 ) ≈ 8.4 (5.0) TeV for κ V = 0.1 (1.0) when κ q,g = 0.
For this reason we generate signal samples with m(Y 2 ) values up to 8.4 TeV. The diphoton branching ratio B(Y 2 → γγ) is approximately 10 (4)% for κ q,g = 0 (1) and κ V = 1.0, but can be as high as about 20% for large κ V values.
The signal samples were produced considering electroweak production of Y 2 with two associated jets and suppressed QCD coupling (i.e. pp → jjY 2 with α 0 QCD ). Fig. 11 shows the VBF Y 2 production cross section as a function of m(Y 2 ) for κ V = 0.1, 1.0, and 5.0.
As expected, the cross section scales as κ 2 V . Fig. 12 shows the Y 2 → γγ decay width as a

Event selection criteria
Although VBF processes are characterized by relatively low production cross sections (compared to DY and gluon-gluon fusion processes), the unique topology of VBF compensates for   Criterion The values of N S and N B in the optimization process are derived within a diphoton mass window m(Y 2 ) − 2Γ < m γγ < m(Y 2 ) + 2Γ, where Γ is the Y 2 → γγ decay width. We note these particular definitions of N S , N B , and significance are used only for the purpose of optimizing the selections. We propose to determine final discovery potential with a shape based Figure 14: m γγ distributions for the main backgrounds and various signal benchmark points. Simulated events populating these distributions have satisfied the requirements of at least two jets and two photons. A comparison of the signal and background distributions indicate the need to apply more stringent VBF selections for the low-mass signal benchmark points than the high-mass scenarios.
analysis to be described later in Section 4.
The optimal selection cut for the pseudorapidity gap |∆η jj | depends on m(Y 2 ). The signal benchmark points with high m(Y 2 ) values, on the other hand, lie in the tail of the reconstructed m γγ background distribution, thus requiring a less stringent |∆η jj | cut. Figure 15: The normalized signal significance S Smax as a function of the lower bound imposed on |∆η jj |. The critical point at 6.0 for m(Y 2 ) = 350 GeV motives us to apply a "Tight" selection cut of |∆η| > 6.0 to maximize discovery potential for low mass signal models. Similarly, the critical point at 4.0 for m(Y 2 ) = 1 TeV motives us to apply a "Loose" selection cut of |∆η| > 4.0 to maximize discovery potential for high mass (TeV scale) signal models.  |∆η jj | > 6.0, while |∆η jj | > 4.0 provides the best discovery potential for the higher mass signal point m(Y 2 ) = 1 TeV. We hence define a "Tight" and "Loose" signal region with pseudorapidity gap requirements of |∆η jj | > 6.0 and |∆η jj | > 4.0, respectively, in an attempt to maximize the sensitivity to low and high mass signatures. The results shown in Section 4 are obtained by applying both "Tight" and "Loose" criteria and choosing the one that gives the largest signal significance for a given m(Y 2 ) value.
In addition to the VBF selections, we select two γ candidates, requiring that p T (γ) > 30 GeV and |η(γ)| < 2.5 for both photons with p lead T (γ) > 60 GeV for the leading photon. Figure 17: The normalized signal significance S Smax as a function of the lower bound imposed on p lead T (γ). The signal significance is maximized at around around 60 GeV for both benchmark points with m(Y 2 ) = 350 GeV and m(Y 2 ) = 1 TeV, which motives a selection cut at p lead T (γ) > 60 GeV.
The signal and background p T distributions (normalized to unity) of the leading photon are shown in Fig. 16, while Fig. 17 shows the normalized signal significance S/S max as a function of p lead T (γ) cut value, assuming an integrated luminosity of 100 fb −1 . The signal significance is maximized at approximately 60 GeV for both the m(Y 2 ) = 350 GeV and the m(Y 2 ) = 1 TeV benchmark points, which supports our choice of selection cut at p lead T (γ) > 60 GeV. By a similar methodology, we determined the optimal threshold for the p T of the sub-leading photon to be p T (γ) > 30 GeV.
Finally, in addition to the VBF dijet and diphoton selections, simulated events in the proposed search region are required to have zero jets tagged as b-quarks and no recon- in comparison to the electron/muon thresholds, is due to the experimentally more challenging nature of τ h and b-jet reconstruction. The event selection criteria used in the γ 1 γ 2 j f j f "Tight" and "Loose" signal regions are summarized in Table 3. Fig. 18 shows the signal and background m γγ distributions, after applying the "Loose" event selection criteria as listed in Table 3 with |∆η| > 4.0. Fig. 19 is similar but with the "Tight" |∆η| requirement of 6.0. Again, the bulk of the (now largely reduced) background distribution lies at relatively low reconstructed diphoton mass values, while the signal bumps dominate at the tails of the m γγ distribution. Depending on the ∆η cut value, the contributions of the γγ+jets backgrounds are reduced by approximately 4-5 orders of magnitude, while the signal acceptance is 12-58% depending on m(Y 2 ). Figure 18: m γγ distribution for the main backgrounds and various signal benchmark points, after applying the event selection criteria as in Table 3 with |∆η| > 4.0. Figure 19: m γγ distribution for the main backgrounds and various signal benchmark points, after applying the event selection criteria as in Table 3 with |∆η| > 6.0.
We use the full range of the reconstructed diphoton mass distribution to perform a shape based analysis of the discovery potential, following a profile binned likelihood approach to define the test statistic, using the ROOFit [44] toolkit. Systematic uncertainties are incorporated into the calculation as nuisance parameters in order to obtain an experimentally realistic estimate of the signal significance. A 15% systematic uncertainty related with γ identification efficiency, based on [21,22], has been included, considering 100% correlation between the two photons and 100% correlation among signal and background processes. In addition, a 12% uncertainty in the signal and background yields due to the choice of parton distribution function (PDF) included in the simulated signal samples is evaluated based on the PDF4LHC recommendations [45]. This is consistent with the 15% uncertainty from the CMS VBF SUSY and VBF dark matter searches [29,34]. The effect of the chosen PDF set on the shape of the m γγ distribution is negligible. Finally, we have included a 20% uncertainty related with the experimental difficulties involved with reconstructing, identifying, and calibrating forward jets at the LHC. This 20% effect is categorized as an overall uncertainty on the efficiency of the VBF selection criteria, based on Refs. [29,34]. A local p-value is calculated as the probability under a background only hypothesis to obtain a value of the test statistic as large as that obtained with a signal plus background hypothesis. The signal significance S is then defined as the value at which the integral of a Gaussian between S and ∞ results in a value equal to the local p-value.
The expected signal significance has been calculated considering different scenarios of integrated luminosity at the LHC, ranging from 100 to 3000 fb −1 (based on the current and  The expected signal significance was calculated performing a profile binned likelihood of the diphoton mass distribution, assuming an expected luminosity of 3000 f b −1 . The black dashed line encloses the region with 5σ discovery potential.
The main result of this paper is that probing heavy spin-2 bosons Y 2 produced through VBF processes can be a key methodology to complement current searches for TeV scale particles at the LHC. In the context of a generic and model independent approach via an effective field theory, both standard and non-universal couplings for Y 2 to the SM particles can be studied. Of particular interest is that there has been no evidence for a TeV scale Y 2 at the LHC to date. The Y 2 boson may have failed to be discovered in searches within the CMS and ATLAS experiments thus far because κ q,g is small. Thus, the Y 2 would not be discoverable by the "standard" searches via gluon-gluon fusion or quark-antiquark annihilation currently conducted at the LHC. In addition, even if a Y 2 were to be discovered with gg → Y 2 or qq → Y 2 , a VBF Y 2 search remains a key part of the Y 2 search program at the LHC in order to establish the couplings κ V of the Y 2 to the SM vector bosons. We consider Y 2 decays to γγ to show that the requirement of a diphoton pair combined with two high p T forward jets with large separation in pseudorapidity and with large dijet mass is effective in reducing contributions from QCD multijet, γ+jets, γγ+jets, and other SM backgrounds. Dilepton, dijet, and ZZ/W W channels can all result from spin-1 Z or spin-2 Y 2 production. However, an excess in the γγ final state would rule out Z . In keeping within the EFT in this analysis, various values of κ V have been studied, and effects of varying κ V on the branching ratio and decay width for Y 2 have been considered. These considerations related to κ V have been made with particular attention to the theoretically allowed phase space for determining discovery potential. Assuming proton-proton collisions at √ s = 13 TeV, the proposed VBF Y 2 → γγ search is expected to achieve a discovery reach with signal significance greater than 5σ for Y 2 masses up to 4.4 TeV and κ V couplings down to 0.5.