# Graviton Signals in Central Production at the LHC

Authors: Rahul Basu; Tanumoy Mandal
Journal: Advances in High Energy Physics
 (2013)

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## Abstract

We study central production, in the inclusive case, to look for graviton signals in a large extra dimensional model using dilepton and diphoton channels. We carefully analyze signal
and possible standard model background processes and study the feasibility of such new physics searches in a relatively clean environment as in central production where the proton fragments are mostly emitted in the forward direction, and there is a clear rapidity gap between them and the centrally produced system. Our analysis shows that the LHC with 14 TeV center of mass energy and 100 fb−1 (300 fb−1) of integrated luminosity can probe the effective gravity scale up to 3.6 TeV (4.4 TeV) in both the dilepton and diphoton channels.


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## Body

## 1. Introduction

The standard model (SM) has been extremely compatible with all the experimental tests so far. However, there are many theoretical attempts to go beyond the SM in order to answer some fundamental issues in the SM, namely, the hierarchy problems, number of fermion generations. Theories with extra spatial dimensions have been proposed to answer the hierarchy problems of the SM [1, 2]. In what follows, in this paper, we look for the graviton signals as predicted in the large extra dimensional model (proposed by Arkani-Hamed et al. [1]) in the central diffractive processes at the LHC.Forward physics has been used with great success in studying the (SM) physics at colliders. In particular, hadron-electron ring accelerator (HERA) has used forward detectors to greatly enhance our knowledge of perturbative quantum chromodynamics (QCD) and its effects in deep inelastic scattering (DIS) experiments. Moreover, the observation of diffractive events, those with large rapidity gaps between the final state particles, have been one of the most interesting aspects of HERA physics.In the last decade, the importance of forward physics has been recognized for  Large Hadron Collider (LHC) physics too. This has resulted in a proposal to install forward particle detectors at ATLAS and CMS in order to detect protons emitted in the forward direction, implying the existence of a centrally produced system with a rapidity gap between it and the protons [3, 4]. More specifically, we are talking of a process of the kind p+p→p+M+p, also known as Central Exclusive Production (CEP). In this case, the outgoing protons are emitted with barely any loss of energy (typically less than 2% of their longitudinal momenta) along with a centrally produced system M with a rapidity gap between it and the outgoing protons on either side. This is a clean production of the central system since it corresponds to just two forward protons in the final state along with the decay products used to identify the central particle M and no hadronic activity between them. This has therefore been described as being like a vacuum fluctuation as the two protons pass each other, producing the central particle. Some good review on the phenomenology of exclusive processes can be found in [5–7]. Recently, in [8] a general framework of exclusive double diffractive processes and its prospects are discussed.One of the main aim of the forward physics at the LHC is to look for the exclusive Higgs production events. First in [9], it was pointed out that Higgs can be produced in diffractive processes with rapidity gaps on either side at hadron-hadron colliders. Later, this interesting scenario has been discussed in a series of papers [10–18] by several authors. Recently, to compute the background for Higgs searches, in [19], authors have estimated the exclusive bb- pair production cross-section at the LHC. In exclusive processes, Higgs would be produced almost at rest through gluon-gluon fusion. The final state contains two protons and a Higgs and, since the process is exclusive, the invariant mass of the Higgs is directly related to the energy loss of the outgoing protons [20]. In exclusive production, measuring the energy loss of the protons, one can determine the mass of the central system without looking at its decay products.It was discussed in [21], if the outgoing protons scatter through small angles, the two-gluon system is in a Jz=0, C-even, P-even state, where the z-axis is the proton beam axis. This means that any new resonance must carry the 0++ quantum number in CEP. In other words, this enables a clean determination of the quantum numbers of any new resonance [22].With the possibility of tagging the forward outgoing protons, the LHC can be turned into an effective gluon-gluon, photon-proton, and photon-photon collider, giving rise to a major QCD and electroweak physics program [23, 24]. In addition, the possibility of producing quarkonium states like χ, J/ψ, is something being envisaged at the ALICE detector. As discussed in [25, 26], the measurement of the two-body decay channels of χc0 to light mesons in an exclusive process can be used to study the dynamics of heavy quarkonia and to test the QCD framework of CEP.However, all these studies require a QCD based model that allows us to couple the digluon system to the protons. The preferred model to describe that this is the socalled Durham model which we briefly describe in the next section. Before we do that however, we should point out that various other processes in the CEP scenario have recently been observed in the Tevatron at CDF which have given physicists the confidence that the Durham model is on the right track. Even though the Durham model was proposed almost a decade ago, it was not until 2006 that CDF saw diphoton production in the central rapidity region which was consistent with the gluon-gluon fusion Durham model [27]. Subsequently, CDF also found another exclusive process—e+e- and μ+μ- production—produced by two photons [28]. Here, the Tevatron (and in future the LHC) acts as a photon-photon collider. These processes also allow the calibration of the forward proton detectors proposed by CMS and ATLAS. Quarkonium production of J/ψ and ψ (2S) as well as χc0 have also been observed through their decay products [29]. Exclusive dijet production has been observed, at CDF [30] and D0 [31] in line with the predictions of the Durham model. These processes already seen at the Tevatron have given confidence that we can use digluon fusion in  accordance with the Durham model to observe the signatures of new physics.It was indicated in [32] that new physics like SUSY, extra dimensions, and so forth can be searched for in exclusive processes. In the exclusive configuration, various BSM signatures, namely, MSSM Higgs [33], charged Higgs [34], triplet Higgs [35], radions [36, 37], massive gravitons [37], long lived gluinos [38], effects of quantum gravity [39], and so forth, have been discussed in the literature. In this work, we study inclusive double diffractive process as a probe of large extra dimensions (the ADD model) using dilepton and diphoton channels via the exchange of KK graviton.In Section2, we briefly introduce the ADD model. In Section 3, we discuss diffractive processes and summarize the Durham model. In Section 4, we consider dilepton and diphoton production via KK graviton. We discuss important SM backgrounds in Section 5. In Section 6, we summarize our numerical results and present LHC discovery potential of extra dimensions. Finally, in Section 7, we offer our conclusions.


## 2. The ADD Model

In this section, we give a very brief introduction of the ADD model [1]. This model assumes that space is 4+n dimensional where n is the number of extra spatial dimensions. All the SM particles are confined to the usual (3+1)D spacetime which is called “brane,” whereas gravity can propagate in the extra dimensions. In this model, the 4D Planck scale (MPl~1019 GeV) is a derived scale which is related to the fundamental Planck scale (MS~TeV) by
(1)MPl2=VnMS2+n,Vn=(2πR)n,
where Vn is the extra dimensional volume and R is the compactification radius. An important consequence of the ADD model is the appearance of a tower of Kaluza-Klein (KK) modes as a solution to the linearized Einstein equation in 4+n dimensions. These KK modes are almost degenerate and separated in mass by 𝒪(1/R) (1/R~10-4 eV to ~100 MeV for n= 2–7) terms. After KK decomposition, we have massive spin-2 KK gravitons (hμνk) which have interactions with the brane localized SM states via the energy momentum tensor Tμν of the SM
(2)ℒ=-κ2∑kTμν(x)hμνk(x),
where κ=16π/MPl and the summation runs over all KK modes. The ADD model has been studied extensively both theoretically as well as experimentally. Recently, the extra dimensions are being searched for using dilepton and diphoton channels at the LHC, both by ATLAS [40, 41] and CMS [42, 43]. These searches have already put the lower bound on MS quite high.


## 3. Diffractive Processes

We consider two types of double diffractive (DD) mechanisms at the LHC as follows:(1)
central exclusive process (CEP):pp→p+M+p as shown in Figure 1(a);(2)
central inclusive process (CIP):pp→X+M+Y as shown in Figure 1(b).Here, M denotes the centrally produced system (we also denote the invariant mass of the central system with the same notation “M”) and the “+” signs denote the presence of rapidity gaps between the system M and the outgoing protons (in exclusive process) or proton dissociated products X, Y (in inclusive process). The differential cross-sections for exclusive and inclusive DD processes shown in Figure 1 can be expressed in the folllowing factorized form  [32]:
(3)M2d2σdydM2=ℒgg(M2,y)σ^(M2),
where σ^ is the cross-section of the hard subprocess which produces the color singlet system of invariant mass M (gg→M) and ℒgg is the effective luminosity for the production of a system of invariant mass M at rapidity y. The total cross-section σ(pp→X+M+Y) can be calculated using
(4)σ=∫‍dydM21M2ℒgg(M2,y)σ^(M2).Double diffractive production of a system of massM with rapidity gap Δη on either side via (a) the central exclusive process and (b) the central inclusive process at the LHC.
(a)
(b)In our calculation, we keepℒgg and σ^ in a factorized form as the effective luminosity is independent of the subprocess, and for different processes, we need to compute just the subprocess cross-sections. Although we keep ℒgg and σ^ in a factorized form, we must remember that there might exist specific selection rules for different configurations. In the exclusive configuration, the fusing gg state obeys a special selection rule in the limit that the protons scatter through zero angle. The z-component of the angular momentum of a centrally produced system vanishes as the incoming state which consists of the fusing hard gluons has Jz=0 with positive C and P parity [32]. For inclusive production on the other hand, there is no such selection rule, and therefore, the production rate is larger than that for the exclusive production. Although the signals are very clear for CEP, the luminosity and the event rates are very small due to the restricted kinematics. A much larger phase space is available due to the dissociation of the incoming protons in the inclusive DD case. The luminosities for exclusive and inclusive processes can be computed using the known parton distribution functions (PDF) of the protons.


### 3.1. The Durham Model

To estimateℒgg, we will use what is known as the “Durham model,” described in [14, 15, 18, 32]. The ℒgg depends on off-diagonal or skewed gluon distribution functions (off-diagonal, since we need to consider the coupling of two gluons with different momentum fractions, xi and xi′, with a proton). However, as we see, for xi′≪xi and kit≈Qt, the relevant kinematic region for CEP, it is possible to approximate the off-diagonal distributions using the integrated gluon distribution function [44]. For CIP, the dominant (leading logarithm) contribution comes from the asymmetric configuration, Qt2≪kit2. At the partonic level, the inclusive production is equivalent to the exclusive production, and the unintegrated gluon distributions in partons may be calculated perturbatively in terms of nonforward BFKL amplitudes. The effective luminosity depends also on two survival probabilities of the rapidity gaps—one to the QCD radiation and another to the nonperturbative soft rescattering of the protons. The first is expressed as a Sudakov factor which ensures that the fusing gluons remain intact up to the hard scale M/2. The second factor is included as an explicit multiplicative factor 𝒮2, known as the “gap survival factor.” It accounts for the probability that apart from the perturbative processes, no other particle is produced via soft interactions between the protons [45–48]. In general, 𝒮2 is expected to depend on the kinematics of the process and can be calculated using various QCD based models [47–52]. Typically, for LHC energies, 𝒮2 for CEP is estimated to be very small [47, 48] (e.g., in [32] authors found 𝒮2=0.020(0.026) for 14 TeV (8 TeV) LHC). For CIP, relatively smaller absorption cross-section leads to a larger 𝒮2. For simplicity, in our analysis, we keep 𝒮2=0.1 for CIP, as a constant multiplicative factor.We use the MSTW2008 LO parton density [53] in our computation. Since MSTW parametrization for the gluon distribution function G(x,Q)=xg(x,Q) does not go below Q=1 GeV, for Q≤1 GeV, we take the following extrapolation function:
(5)G(x,Q)=α(x)Q[2+{β(x)-2}Q],
so that for Q2→0, G(x,Q)~Q2 [18]. Here, α and β are the two functions of x and can be computed using the following relations:
(6)β(x)=1(1+lnQ0)(G′(x,Q0)G(x,Q0)-2Q0)+2,α(x)=G(x,Q0)Q0[2+{β(x)-2}Q0],
where G′=∂G/∂Q and G, G′ are evaluated at Q0=1 GeV. To compute the Sudakov factor, we use the LO αS (strong coupling) with ΛQCD=220 MeV and Nf=5. The full formalism to calculate effective luminosity for exclusive and inclusive configuration is given in [32]. In Appendix A, we briefly present the computation of ℒgg for CIP.


## 3.1. The Durham Model

To estimateℒgg, we will use what is known as the “Durham model,” described in [14, 15, 18, 32]. The ℒgg depends on off-diagonal or skewed gluon distribution functions (off-diagonal, since we need to consider the coupling of two gluons with different momentum fractions, xi and xi′, with a proton). However, as we see, for xi′≪xi and kit≈Qt, the relevant kinematic region for CEP, it is possible to approximate the off-diagonal distributions using the integrated gluon distribution function [44]. For CIP, the dominant (leading logarithm) contribution comes from the asymmetric configuration, Qt2≪kit2. At the partonic level, the inclusive production is equivalent to the exclusive production, and the unintegrated gluon distributions in partons may be calculated perturbatively in terms of nonforward BFKL amplitudes. The effective luminosity depends also on two survival probabilities of the rapidity gaps—one to the QCD radiation and another to the nonperturbative soft rescattering of the protons. The first is expressed as a Sudakov factor which ensures that the fusing gluons remain intact up to the hard scale M/2. The second factor is included as an explicit multiplicative factor 𝒮2, known as the “gap survival factor.” It accounts for the probability that apart from the perturbative processes, no other particle is produced via soft interactions between the protons [45–48]. In general, 𝒮2 is expected to depend on the kinematics of the process and can be calculated using various QCD based models [47–52]. Typically, for LHC energies, 𝒮2 for CEP is estimated to be very small [47, 48] (e.g., in [32] authors found 𝒮2=0.020(0.026) for 14 TeV (8 TeV) LHC). For CIP, relatively smaller absorption cross-section leads to a larger 𝒮2. For simplicity, in our analysis, we keep 𝒮2=0.1 for CIP, as a constant multiplicative factor.We use the MSTW2008 LO parton density [53] in our computation. Since MSTW parametrization for the gluon distribution function G(x,Q)=xg(x,Q) does not go below Q=1 GeV, for Q≤1 GeV, we take the following extrapolation function:
(5)G(x,Q)=α(x)Q[2+{β(x)-2}Q],
so that for Q2→0, G(x,Q)~Q2 [18]. Here, α and β are the two functions of x and can be computed using the following relations:
(6)β(x)=1(1+lnQ0)(G′(x,Q0)G(x,Q0)-2Q0)+2,α(x)=G(x,Q0)Q0[2+{β(x)-2}Q0],
where G′=∂G/∂Q and G, G′ are evaluated at Q0=1 GeV. To compute the Sudakov factor, we use the LO αS (strong coupling) with ΛQCD=220 MeV and Nf=5. The full formalism to calculate effective luminosity for exclusive and inclusive configuration is given in [32]. In Appendix A, we briefly present the computation of ℒgg for CIP.


## 4. Diffractive Production

With diffractive processes being dominated by two-gluon exchange as shown in Figure1, it is obvious that these processes would be observed only for the final states with a substantial coupling to a gluon pair. In this work, we consider the central production of KK gravitons (G) via DD processes. The spin-2 gravitons can have three possible spin projections Jz=0, 1, and 2. Due to the presence of special Jz=0 selection rule in the exclusive configuration, graviton cannot be produced via leading order (LO) exclusive processes (although there is no Jz=0 point-like gg coupling to a 2+ graviton, it can still be produced at next to LO (NLO) in the exclusive configuration.) [32]. In the unitary gauge, the coupling of the spin-0 projection of G with two gluons is zero as the LO coupling of spin-0 component with any two vector bosons is proportional to the square of the mass of the vector boson, and gluons are massless in this case [54]. By the Landau-Yang theorem [55, 56], it is impossible to produce a spin-1 particle via the fusion of two on-shell vector bosons, but the production is not forbidden if those vector bosons are off-shell. Though the gluons coming from protons are not purely on-shell, the degree of virtuality of the gluons is very small. Thus, the contribution in any process from spin-1 projection of graviton is subdominant [57]. Thus, the Jz=2 is the only possible spin projection that can couple to a gluon pair at LO. Therefore, in this paper, we discuss the LHC signatures of G in inclusive configuration. In what follows, we analyze the diphoton and the dilepton channels via the exchange of G arising in ADD type models [1] as a signal of extra dimension. We carefully consider these signal processes and the relevant background processes for them and look for regions of parameter space where the signal would dominate. Since these processes can only occur in inclusive configuration, the event rates could be substantial to search for at the LHC. Moreover, the nature of the intermediate particle and the coupling with SM particles reflect in the angular distribution of the final state particles.


### 4.1. Dilepton Production

We consider the process where dilepton pair is produced from gluon fusion via the exchange ofG as shown in Figure 2. The Feynman rules for this process are taken from [54] where one can find definitions of all the terms which appear here. We also show these Feynman rules in Appendix B. The matrix element for this process is given by
(7)iℳab=(-iκ2δab)ϵ1α(k1)ϵ2β(k2)Vμν;αβ×(i/2)Bμν;μ′ν′P2-MG2+iε(-iκ8)u-(k3)Γμ′ν′v(k4),
where the coupling κ is related to the Newton constant GN as κ=16πGN. Since the reduced Planck mass MPl*=1/8πGN (MPl*≈2.4×1018 GeV), each KK mode coupling to the SM particles is Planck mass suppressed. A summation over high multiplicity of KK modes lying below the UV cutoff scale MS compensates the suppression and gives rise to a substantial effective coupling strength. Therefore, we replace the graviton propagator in (7) by the following effective propagator:
(8)𝒟eff(s^)=∑k‍i[s^-(MG2)k+i(ΓG)k(MG)k],
where k sums over all KK towers below MS and ΓGMG=ε and “hat” notation is used for subprocess quantities. Here, s^=Mll is the invariant mass of the lepton pair. Since, KK modes are quasicontinuous, this summation can be done by defining KK state density as shown in Appendix B [54]. For n number of extra dimensions, considering the contributions from resonant and nonresonant KK states, the 𝒟eff is given by
(9)𝒟eff(s^)=16πs^n/2-1κ2Γ(n/2)MSn+2[π+2iI(MSs^)],
where the real part comes from the summation over all resonant contributions below MS and the imaginary part is the summed contribution coming from all the nonresonant states. The definition of the I function can be found in Appendix B. After summing over the spins of the final state leptons, the effective squared matrix element takes the following form:
(10)|ℳ|2=(κ41024)(𝒟eff)2(ϵ1α1(k1)ϵ1*α2(k1))×(ϵ2β1(k2)ϵ2*β2(k2))Vμ1ν1;α1β1Vμ2ν2;α2β2×Bμ1ν1;μ1′ν1′Bμ2ν2;μ2′ν2′×tr[(u-(k3)Γμ1′ν1′v(k4))(v-(k4)Γμ1′ν1′†u(k3))]δabδab.Figure 2
The subprocess Feynman diagram for dilepton production.In the zero mass limit of the produced lepton, the angular dependence of|ℳ|2 takes a very simple form as follows:
(11)|ℳ|2=δabδabκ464(𝒟eff)2s^4(1-cos4θ),
where θ is the scattering angle of the leptons in the center of mass (CM) frame of the G. Averaging |ℳ|2 over eight colors and two polarizations of the initial gluons, one can evaluate the subprocess differential cross-section after including the phase space factor as
(12)dσ^(gg→l+l-)d|cosθ|=(132πs^)·(182)·(122)·8·κ464(𝒟eff)2×s^4(1-cos4θ).If we consider that two types of leptons (i.e., electron and muon) are contributing in the dilepton final state, we should multiply the previous differential cross-section by an extra factor of two.


### 4.2. Diphoton Production

We consider the process where a photon pair is produced from gluon fusion via the exchange ofG as shown in Figure 3. As mentioned earlier, the Feynman rules for this process are taken from [54] where one can find definitions of all the terms which appear here and also can be found in Appendix B. The matrix element for this process is given by
(13)iℳab=(-iκ2δab)ϵ1α(k1)ϵ2β(k2)Vμν;αβ(i/2)Bμν;μ′ν′P2-MG2+iε×(-iκ2)Vμ′ν′;α′β′ϵ3*α′(k3)ϵ4*β′(k4).
After summing over all KK states up to MS contributing to a physical process and summing over two polarizations of the final state photons, the effective squared matrix element takes the following form:
(14)|ℳ|2=(κ464)(𝒟eff)2(ϵ1α1(k1)ϵ1*α2(k1))(ϵ2β1(k2)ϵ2*β2(k2))×(ϵ3*α1′(k3)ϵ3α2′(k3))(ϵ4*β1′(k4)ϵ4β2′(k4))×Vμ1ν1;α1β1Vμ1′ν1′;α1′β1′Vμ2ν2;α2β2×Vμ2′ν2′;α2′β2′Bμ1ν1;μ1′ν1′Bμ2ν2;μ2′ν2′δabδab.
After doing some tedious algebra, the angular dependence of |ℳ|2 takes the following form:
(15)|ℳ|2=δabδabκ464(𝒟eff)2s^4(1+6cos2θ+cos4θ),
where θ is the scattering angle of the photons in the CM frame of the G. Averaging |ℳ|2 over eight colors and two polarizations of the initial gluons, one can evaluate the subprocess differential cross-section after including the phase space factor as
(16)dσ^(gg→γγ)d|cosθ|=12·(132πs^)·(182)·(122)·8·κ464(𝒟eff)2×s^4(1+6cos2θ+cos4θ).
Here, we have included an extra 1/2 factor because of the presence of two identical particles in the final state.Figure 3
The subprocess Feynman diagram for diphoton production.


## 4.1. Dilepton Production

We consider the process where dilepton pair is produced from gluon fusion via the exchange ofG as shown in Figure 2. The Feynman rules for this process are taken from [54] where one can find definitions of all the terms which appear here. We also show these Feynman rules in Appendix B. The matrix element for this process is given by
(7)iℳab=(-iκ2δab)ϵ1α(k1)ϵ2β(k2)Vμν;αβ×(i/2)Bμν;μ′ν′P2-MG2+iε(-iκ8)u-(k3)Γμ′ν′v(k4),
where the coupling κ is related to the Newton constant GN as κ=16πGN. Since the reduced Planck mass MPl*=1/8πGN (MPl*≈2.4×1018 GeV), each KK mode coupling to the SM particles is Planck mass suppressed. A summation over high multiplicity of KK modes lying below the UV cutoff scale MS compensates the suppression and gives rise to a substantial effective coupling strength. Therefore, we replace the graviton propagator in (7) by the following effective propagator:
(8)𝒟eff(s^)=∑k‍i[s^-(MG2)k+i(ΓG)k(MG)k],
where k sums over all KK towers below MS and ΓGMG=ε and “hat” notation is used for subprocess quantities. Here, s^=Mll is the invariant mass of the lepton pair. Since, KK modes are quasicontinuous, this summation can be done by defining KK state density as shown in Appendix B [54]. For n number of extra dimensions, considering the contributions from resonant and nonresonant KK states, the 𝒟eff is given by
(9)𝒟eff(s^)=16πs^n/2-1κ2Γ(n/2)MSn+2[π+2iI(MSs^)],
where the real part comes from the summation over all resonant contributions below MS and the imaginary part is the summed contribution coming from all the nonresonant states. The definition of the I function can be found in Appendix B. After summing over the spins of the final state leptons, the effective squared matrix element takes the following form:
(10)|ℳ|2=(κ41024)(𝒟eff)2(ϵ1α1(k1)ϵ1*α2(k1))×(ϵ2β1(k2)ϵ2*β2(k2))Vμ1ν1;α1β1Vμ2ν2;α2β2×Bμ1ν1;μ1′ν1′Bμ2ν2;μ2′ν2′×tr[(u-(k3)Γμ1′ν1′v(k4))(v-(k4)Γμ1′ν1′†u(k3))]δabδab.Figure 2
The subprocess Feynman diagram for dilepton production.In the zero mass limit of the produced lepton, the angular dependence of|ℳ|2 takes a very simple form as follows:
(11)|ℳ|2=δabδabκ464(𝒟eff)2s^4(1-cos4θ),
where θ is the scattering angle of the leptons in the center of mass (CM) frame of the G. Averaging |ℳ|2 over eight colors and two polarizations of the initial gluons, one can evaluate the subprocess differential cross-section after including the phase space factor as
(12)dσ^(gg→l+l-)d|cosθ|=(132πs^)·(182)·(122)·8·κ464(𝒟eff)2×s^4(1-cos4θ).If we consider that two types of leptons (i.e., electron and muon) are contributing in the dilepton final state, we should multiply the previous differential cross-section by an extra factor of two.


## 4.2. Diphoton Production

We consider the process where a photon pair is produced from gluon fusion via the exchange ofG as shown in Figure 3. As mentioned earlier, the Feynman rules for this process are taken from [54] where one can find definitions of all the terms which appear here and also can be found in Appendix B. The matrix element for this process is given by
(13)iℳab=(-iκ2δab)ϵ1α(k1)ϵ2β(k2)Vμν;αβ(i/2)Bμν;μ′ν′P2-MG2+iε×(-iκ2)Vμ′ν′;α′β′ϵ3*α′(k3)ϵ4*β′(k4).
After summing over all KK states up to MS contributing to a physical process and summing over two polarizations of the final state photons, the effective squared matrix element takes the following form:
(14)|ℳ|2=(κ464)(𝒟eff)2(ϵ1α1(k1)ϵ1*α2(k1))(ϵ2β1(k2)ϵ2*β2(k2))×(ϵ3*α1′(k3)ϵ3α2′(k3))(ϵ4*β1′(k4)ϵ4β2′(k4))×Vμ1ν1;α1β1Vμ1′ν1′;α1′β1′Vμ2ν2;α2β2×Vμ2′ν2′;α2′β2′Bμ1ν1;μ1′ν1′Bμ2ν2;μ2′ν2′δabδab.
After doing some tedious algebra, the angular dependence of |ℳ|2 takes the following form:
(15)|ℳ|2=δabδabκ464(𝒟eff)2s^4(1+6cos2θ+cos4θ),
where θ is the scattering angle of the photons in the CM frame of the G. Averaging |ℳ|2 over eight colors and two polarizations of the initial gluons, one can evaluate the subprocess differential cross-section after including the phase space factor as
(16)dσ^(gg→γγ)d|cosθ|=12·(132πs^)·(182)·(122)·8·κ464(𝒟eff)2×s^4(1+6cos2θ+cos4θ).
Here, we have included an extra 1/2 factor because of the presence of two identical particles in the final state.Figure 3
The subprocess Feynman diagram for diphoton production.


## 5. SM Backgrounds

In the diffractive configuration, there are possibilities of producing a central system fromgg, γγ, qq, or WW fusion processes. In a same kinematic region, the effective luminosity for the gg fusion (ℒgg) is the largest at the LHC among all the alternatives, whereas the effective luminosities for γγ, qq, or WW fusion processes are much smaller compared to ℒgg. Estimations of effective luminosities for the gg, γγ, and WW can be found in [32] and for the qq in [58]. While computing the SM backgrounds for the dilepton and the diphoton signal channels, we can sometimes neglect γγ, qq, and WW initiated background processes due to the small luminosities of the fusing particles.


### 5.1. Dilepton Backgrounds

In Figure4, we show the Feynman diagrams of some important background subprocesses for the dilepton channel proceed through gg, γγ, qq, and WW initial states. When one considers lepton pair production within the SM in the diffractive configuration, one would not expect a significant rate for a lepton pair unaccompanied by other particles (like radiation  jets/photons or other SM particles). Although there is always a chance to miss those extra particles other than the lepton pair or to misidentify other particles as leptons, in our background computation, we do not include those reducible backgrounds as these are expected to be very small. Using the Landau-Yang theorem, dual considerations of angular momentum conservation and Bose symmetry prevent a pair of gluons couple to an on-shell γ/Z (via a quark loop, see Figures 4(a) and 4(b)) or a WW pair couple to an on-shell γ/Z (see Figures 4(g) and 4(h)). While such a coupling, although very small, is indeed permitted for an off-shell γ/Z. The pieces in the corresponding vertex function are proportional to the degree of virtuality of the initial particles or to the momentum of the γ/Z itself. Moreover, gg→ll processes involve a quark loop, and WW→ll processes are suppressed due to very low WW luminosity. Because of these reasons, we are not including gg and WW initiated processes in our computation. We also neglect qq initiated processes in Figures 4(d) and 4(e) due to very low luminosity for qq. Consequently, these processes lead only to subdominant contributions.The subprocess Feynman diagrams for dilepton channel.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)The dominant SM background for the dilepton channel comes from the inelastic photoproduction of the lepton pair as shown in Figure4(c) where photons are emitted from the quarks inside protons. This contribution can be very large in the kinematic region where the invariant mass of the lepton pair is small. This is because the collinear emission of equivalent photons from quark lines can give large contribution. The inelastic pp→ll cross-section has been computed in [59] for the Weizsäcker-Williams photon pairs, and an outline of the computation is presented in Appendix C. The contributions from the interference terms among various background processes might be important at low energies. Since we are only interested in the high energy regions, we do not include them for simplicity.


### 5.2. Diphoton Backgrounds

In Figure5, we show possible background subprocesses for the diphoton channel initiated from gg, γγ, qq, and WW initial states. The dominant background for the diphoton channel comes from the gg→γγ box diagram (via quark loop) shown in Figure 5(a), and cross-section is proportional to αS2αem2 (αem is the QED coupling). There are other higher order diagrams that contribute to gg→γγ process as shown in Figures 5(b) and 5(c) where Higgs is involved. The Higgs is produced from gg fusion via a top quark loop and then decayed to γγ via another top quark or a W loop. There are also Delbruck type (light-by-light scattering) backgrounds possible shown in Figures 5(d) and 5(e). In this case, quarks from the dissociated protons radiate two photons which then give two final state photons via a fermion or W in the loop. This contribution is much suppressed as cross-section is proportional to αem4. The other backgrounds which are initiated from qq (see Figure 5(f)) and WW (see Figures 5(g) and 5(h)) initial states are negligible as the corresponding effective luminosities are very low. We note that all the gg and γγ initiated background processes occur only via loop diagrams, and they are usually very small. If the signal rate is substantial in the diphoton channel, searching the signatures of extra dimensions in the diphoton channel might be very promising.The subprocess Feynman diagrams for diphoton channel.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)We estimate the dominantgg→γγ box diagram background cross-section using γγ→γγ helicity amplitudes taken from [60]. Relevant formulae are given in Appendix D. At low energy, the fermion loop contribution in the box diagram dominates, but above a few hundred GeV, this contribution starts falling rapidly, whereas the W loop contribution dominates in the total cross-section of the γγ→γγ process at high energies. Other higher order γγ→h→γγ processes similar to Figures 5(b) and 5(c) are not considered here. We do not include qq initiated process in our background computation as the contribution originates from qq-  t-channel exchange in Figure 5(f) is roughly two order of magnitude lower than the gg contributions [58]. As mentioned earlier, we neglect WW initiated processes for low WW luminosity and all background interference terms for simplicity.


## 5.1. Dilepton Backgrounds

In Figure4, we show the Feynman diagrams of some important background subprocesses for the dilepton channel proceed through gg, γγ, qq, and WW initial states. When one considers lepton pair production within the SM in the diffractive configuration, one would not expect a significant rate for a lepton pair unaccompanied by other particles (like radiation  jets/photons or other SM particles). Although there is always a chance to miss those extra particles other than the lepton pair or to misidentify other particles as leptons, in our background computation, we do not include those reducible backgrounds as these are expected to be very small. Using the Landau-Yang theorem, dual considerations of angular momentum conservation and Bose symmetry prevent a pair of gluons couple to an on-shell γ/Z (via a quark loop, see Figures 4(a) and 4(b)) or a WW pair couple to an on-shell γ/Z (see Figures 4(g) and 4(h)). While such a coupling, although very small, is indeed permitted for an off-shell γ/Z. The pieces in the corresponding vertex function are proportional to the degree of virtuality of the initial particles or to the momentum of the γ/Z itself. Moreover, gg→ll processes involve a quark loop, and WW→ll processes are suppressed due to very low WW luminosity. Because of these reasons, we are not including gg and WW initiated processes in our computation. We also neglect qq initiated processes in Figures 4(d) and 4(e) due to very low luminosity for qq. Consequently, these processes lead only to subdominant contributions.The subprocess Feynman diagrams for dilepton channel.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)The dominant SM background for the dilepton channel comes from the inelastic photoproduction of the lepton pair as shown in Figure4(c) where photons are emitted from the quarks inside protons. This contribution can be very large in the kinematic region where the invariant mass of the lepton pair is small. This is because the collinear emission of equivalent photons from quark lines can give large contribution. The inelastic pp→ll cross-section has been computed in [59] for the Weizsäcker-Williams photon pairs, and an outline of the computation is presented in Appendix C. The contributions from the interference terms among various background processes might be important at low energies. Since we are only interested in the high energy regions, we do not include them for simplicity.


## 5.2. Diphoton Backgrounds

In Figure5, we show possible background subprocesses for the diphoton channel initiated from gg, γγ, qq, and WW initial states. The dominant background for the diphoton channel comes from the gg→γγ box diagram (via quark loop) shown in Figure 5(a), and cross-section is proportional to αS2αem2 (αem is the QED coupling). There are other higher order diagrams that contribute to gg→γγ process as shown in Figures 5(b) and 5(c) where Higgs is involved. The Higgs is produced from gg fusion via a top quark loop and then decayed to γγ via another top quark or a W loop. There are also Delbruck type (light-by-light scattering) backgrounds possible shown in Figures 5(d) and 5(e). In this case, quarks from the dissociated protons radiate two photons which then give two final state photons via a fermion or W in the loop. This contribution is much suppressed as cross-section is proportional to αem4. The other backgrounds which are initiated from qq (see Figure 5(f)) and WW (see Figures 5(g) and 5(h)) initial states are negligible as the corresponding effective luminosities are very low. We note that all the gg and γγ initiated background processes occur only via loop diagrams, and they are usually very small. If the signal rate is substantial in the diphoton channel, searching the signatures of extra dimensions in the diphoton channel might be very promising.The subprocess Feynman diagrams for diphoton channel.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)We estimate the dominantgg→γγ box diagram background cross-section using γγ→γγ helicity amplitudes taken from [60]. Relevant formulae are given in Appendix D. At low energy, the fermion loop contribution in the box diagram dominates, but above a few hundred GeV, this contribution starts falling rapidly, whereas the W loop contribution dominates in the total cross-section of the γγ→γγ process at high energies. Other higher order γγ→h→γγ processes similar to Figures 5(b) and 5(c) are not considered here. We do not include qq initiated process in our background computation as the contribution originates from qq-  t-channel exchange in Figure 5(f) is roughly two order of magnitude lower than the gg contributions [58]. As mentioned earlier, we neglect WW initiated processes for low WW luminosity and all background interference terms for simplicity.


## 6. Numerical Results

In all our numerical computations, we use the MSTW2008 LO parton densities to obtain the unintegrated parton distributions. Here, we once again give the numerical values of some quantities which are used. To compute the Sudakov form factors, we use NLOαS with ΛQCD=220 MeV and number of “active” flavor Nf=5. We take a fixed value of the “gap survival factor,” 𝒮2=0.1 in our analysis. Our results depend on two model parameters, the number of extra dimensions n and the ultraviolet cutoff MS of the theory, and four kinematical variables, invariant mass M and rapidity y of the centrally produced system, rapidity gap Δη between the central system and the outgoing protons or proton dissociated products, and the CM energy S of two colliding protons at the LHC. The cutoff scale MS is of the order of few TeV for low scale gravity theories. The lower limit of MS is bounded from experiments, and the bounds are already quite high as stated in Section 2. If we increase MS, the signal cross-sections decrease as usual. In our case, the signal falls off very rapidly with increasing MS because of the presence of MS8 in the denominator of the signal cross-sections (see (12) and (16)). This makes the ADD model very difficult to search for experimentally.In Figure6(a), we show the dependence of the effective luminosity ℒgg on the invariant mass M of the central system produced at rapidity region y=0 at the 14 TeV LHC. The ℒgg shows a decreasing nature with increasing M since it is harder to produce more massive objects while keeping other parameters fixed. In Figure 6(b), we plot the dependence of ℒgg on y with M=500 GeV at the 14 TeV LHC. In the diffractive processes, it is more likely to produce an object centrally, that is, near y=0 region. Thus, a system which is produced away from the central region is less probable, and we see a decreasing behavior of ℒgg with increasing  y.(a) The effective luminosityℒgg as a function of the invariant mass M of the central system produced at y=0 at the 14 TeV LHC and (b) ℒgg as a function of y for the production of a system with mass M=500 GeV at the 14 TeV LHC. For both plots we choose four values of the rapidity gap, that is, Δη= 1.5, 2.0, 2.5, and 3.0.
(a)
(b)In Figure7, we show the total signal cross-section in the dilepton (σll where l={e,μ}) channel as a function of S. In Figure 7(a), we show σll for different Δη taking n=2 and MS=2 TeV. The cross-section increases as we increase S as expected. If we increase Δη, the σll decreases as the effective luminosity decreases with increasing Δη (see Figures 6(a) and 6(b)). In Figure 7(b), we show the σll for different n varied from two to seven. We see that as we increase n, the σll decreases. This is because κ2|𝒟eff|~2/(n-2) for n>2, in the limit MS2≫s^ (see (B.9)). Here, we compute the total cross-section after applying the following selection cuts:
(17)|yψψ|≤2,|cosθψψ|≤1,100GeV≤Mψψ<MS-10GeV,
where θ is the scattering angle of ψ (where ψ=l, γ) in the rest frame of the centrally produced system and Mψψ is the invariant mass of the ψψ pair. We have collected events with the rapidity of the central system |yψψ|≤2. The upper limit of Mψψ can go to MS up to which the theory is valid. Here, we have taken the upper limit on Mψψ slightly smaller than MS as the I function in (9) diverges at MS. The cross-sections are only few fb, and we need higher CM energy at the LHC to observe these events.The total signal cross-section (pp→X+ll+Y) in dilepton channel (σll) as a function of LHC CM energy. In (a), we plot σll for Δη= 1.5, 2.0, 2.5, and 3.0 for n=2 and MS=2 TeV. In (b), we plot σll for n= 2–7 for MS=2 TeV and Δη=2. In both plots, σll's are computed after applying the cut defined in (17).
(a)
(b)In Figure8, we show the total signal cross-section in the dilepton (σll) channel as a function of MS at the 14 TeV LHC. In Figure 8(a), we show σll for different Δη taking n=2, and in Figure 8(b), we show σll for different n taking Δη=2. Here, we compute the total cross-section after applying the kinematical cuts defined in (17). The cross-section decreases rapidly as we increase MS since MS8 is present in the denominator of the total cross-section.The total signal cross-sections (pp→X+ll+Y) in dilepton channel (σll) as a function of MS at the 14 TeV LHC. In (a), we plot σll for Δη= 1.5, 2.0, 2.5, and 3.0 for n=2. In (b), we plot σll for n= 2–7 for Δη=2. In both plots, σll's are computed after applying the cut defined in (17).
(a)
(b)In Figure9(a), we show signal and background invariant mass distributions (dσll/dMll) of the lepton pair after applying the selection cuts defined in (18) at the 14 TeV LHC. To compute dσll/dMll, we have not integrated cosθψψ in the full range from -1 to 1 because the background cross-section diverges as |cosθψψ|→1 (see (C.5)). We plot signal dσll/dMll for MS= 1.5, 2.0, and 2.5 TeV taking n=2 and Δη=2 for both signal and background. The signal dσll/dMll is a monotonically increasing function of Mll (Mll2=s^) because the subprocess cross-section increases roughly as  s^3 (see (12)). The background cross-section is computed only considering the dominant γγ→ll channel. For small values of Mll, the background is quite large but falls off rapidly as we increase Mll. Thus, to observe an excess over the background one should collect lepton pairs with sufficiently high Mll:
(18)|yll|≤2,|cosθll|≤0.8.(a) The invariant mass distributions (dσll/dMll) for signal and background (pp→X+ll+Y) of the lepton pair after applying the cuts defined in (18) at the 14 TeV LHC. (b) The angular distributions (dσll/dcosθll) for signal and background of the lepton pair after applying the cuts defined in (19) at the 14 TeV LHC. For both plots, we take MS= 1.5, 2.0, and 2.5 TeV and n=2 for signal and Δη=2 for both signal and background.
(a)
(b)In Figure9(b), we show signal and background angular distributions (dσll/dcosθll) of the lepton pair after applying the selection cuts defined in (19) at the 14 TeV LHC. To compute dσll/dcosθll, we apply a very high invariant mass cut on the lepton pair to reduce large background in the small Mll region. We show signal dσll/dcosθll for MS= 1.5, 2.0, and 2.5 TeV taking n=2 and Δη=2 for both signal and background. The angular distribution carries spin information of the intermediate particle. For dilepton production, the angular distributions for signal and background show a very contrasting behavior. For signal dσll/dcosθll~(1-cos4θll) (see (12)) which attains its maximum at cosθll=0. On the other hand, background attains its minimum at cosθll=0 since it goes as (1+cos2θll)/sin2θll and diverges when |cosθll|→1 (see (C.5)). This contrasting feature can be used as a unique signature of the extra dimensions
(19)|yll|≤2,750GeV≤Mll<1250GeV.In Figure10, we show the total signal cross-section in the diphoton channel (σγγ) as a function of S after applying the cut defined in (17). In Figure 10(a), we show σγγ for different Δη taking n=2 and MS=2 TeV. In Figure 10(b), we show σγγ for different n varied from two to seven. In Figure 11, we show the σγγ as a function of MS at the 14 TeV LHC. In Figure 11(a), we show σγγ for different Δη taking n=2, and in Figure 11(b), we show σγγ for different n taking Δη=2. Here, we compute the σγγ after applying the kinematical cuts defined in (17). The behavior of these plots is very similar to the corresponding plots for dilepton channel, and we are not repeating those features here. An interesting point to notice is that σll and σγγ are similar even quantitatively. This is because surprisingly σll and σγγ are equal after cosθ integration from -1 to 1 as follows:
(20)∑l=e,μ‍∫-11‍d(cosθ)dσ^(gg→l+l-)d|cosθ|=∫-11‍d(cosθ)dσ^(gg→γγ)d|cosθ|.The total signal cross-sections (pp→X+γγ+Y) in diphoton channel (σll) as a function of LHC CM energy. In (a), we plot σll for Δη= 1.5, 2.0, 2.5, and 3.0 for n=2 and MS=2 TeV. In (b), we plot σll for n= 2–7 for MS=2 TeV and Δη=2. In both plots, σll's are computed after applying the cut defined in (17).
(a)
(b)The total signal cross-sections (pp→X+γγ+Y) in diphoton channel (σγγ) as a function of MS at the 14 TeV LHC. In (a), we plot σγγ for Δη= 1.5, 2.0, 2.5, and 3.0 for n=2. In (b), we plot σγγ for n= 2–7 for Δη=2. In both plots, σγγ's are computed after applying the cut defined in (17).
(a)
(b)In Figure12(a), we show signal and background invariant mass distributions (dσγγ/dMγγ) of the diphoton pair after applying the selection cuts defined in (21) at the 14 TeV LHC:
(21)|yγγ|≤2,|cosθγγ|≤1.
We plot signal dσγγ/dMγγ for MS= 1.5, 2.0, and 2.5 TeV taking n=2 and Δη=2 both for signal and background. The signal dσγγ/dMγγ is a monotonically increasing function of Mγγ (Mγγ2=s^) because the subprocess cross-section increases roughly as  s^3 (see (16)). The background cross-section is computed including gg and γγ initiated processes as shown in Figure 5. Although the background in Figure 12(a) can beat signal in the small Mγγ region, it dies out very rapidly in the high Mγγ region. This is because the diphoton background goes roughly as 1/Mγγ2 and becomes almost negligible at large Mγγ. In Figure 12(b), we show signal and background angular distributions (dσγγ/dcosθγγ) of the diphoton pair after applying the selection cuts defined in (22) at the 14 TeV LHC:
(22)|yγγ|≤2,250GeV≤Mγγ<1250GeV.(a) The invariant mass distributions (dσγγ/dMγγ) for signal and background (pp→X+γγ+Y) of the photon pair after applying the cuts defined in (18) at the 14 TeV LHC. (b) The angular distributions (dσγγ/dcosθγγ) for signal and background after applying the cuts defined in (19) at the 14 TeV LHC. For both plots, we take MS= 1.5, 2.0, and 2.5 TeV and n=2 for signal and Δη=2 for both signal and background. The background in (b) is shown after multiplying by a factor of 50.
(a)
(b)We see that diphoton signal and background angular distributions behave just in the opposite way to the dilepton signal and background angular distributions, respectively. The signaldσγγ/dcosθγγ~(1+6cos2θ+cos4θ) has a minimum at cosθ=0 and attains its maximum value at |cosθ|=1, whereas the dσγγ/dcosθγγ for the dominant gg→γγ background attains its maximum value at cosθ=0 as shown in Figure 12(b). This is because of the nature of angular dependent part in (D.1). The similar angular behavior is true for subdominant  γγ→γγ background also. Whereas, there is no angular dependency of other subdominant gg→h→γγ backgrounds because of the spin-0 nature of the intermediate Higgs.


### 6.1. LHC Discovery Potential

We define the luminosity requirement for the discovery of KK gravitons at the LHC as follows:(23)LD=Max{L5,L10},
where L5 denotes the luminosity required to attain 5σ statistical significance and L10 is the luminosity required to observe 10 signal events. We compute LD after applying some kinematical cuts which we call the “discovery cuts” as defined in the following.


#### 6.1.1. Discovery Cuts

Motivated by the invariant mass and angular distributions in Figures9 and 12, we construct some kinematical cuts to separate the signal from the background in the dilepton and diphoton channels as follows:  (1)
dilepton channel:|yll|≤2; |cosθll|≤0.8; MS/2≤Mll<MS-10GeV;(2)
diphoton channel:|yγγ|≤2; |cosθγγ|≤1; 250GeV≤Mγγ<MS-10GeV.We call these cuts as the “discovery cuts” for the discovery of KK graviton at the LHC. In Figure 13, LD goes as L10 for both dilepton and diphoton channels in the whole parameter space we have displayed. In case of the diphoton channel, the background is already quite small compared to the signal, whereas for the dilepton channel, background becomes under control after the “discovery cuts.” With the “discovery cuts,” one can probe MS roughly up to 3.6 TeV (4.4 TeV) with 100 fb−1 (300 fb−1) integrated luminosity at the 14 TeV LHC.The required luminosity (LD) for the discovery of KK graviton in (a) dilepton and (b) diphoton channels as a function of MS at the 14 TeV LHC with “discovery cuts” (see text for the definitions of the cuts). The LDll and LDγγ are computed for n= 2–7 with Δη=2 at pp→X+ψψ+Y level where ψ={l,γ}.
(a)
(b)


## 6.1. LHC Discovery Potential

We define the luminosity requirement for the discovery of KK gravitons at the LHC as follows:(23)LD=Max{L5,L10},
where L5 denotes the luminosity required to attain 5σ statistical significance and L10 is the luminosity required to observe 10 signal events. We compute LD after applying some kinematical cuts which we call the “discovery cuts” as defined in the following.


### 6.1.1. Discovery Cuts

Motivated by the invariant mass and angular distributions in Figures9 and 12, we construct some kinematical cuts to separate the signal from the background in the dilepton and diphoton channels as follows:  (1)
dilepton channel:|yll|≤2; |cosθll|≤0.8; MS/2≤Mll<MS-10GeV;(2)
diphoton channel:|yγγ|≤2; |cosθγγ|≤1; 250GeV≤Mγγ<MS-10GeV.We call these cuts as the “discovery cuts” for the discovery of KK graviton at the LHC. In Figure 13, LD goes as L10 for both dilepton and diphoton channels in the whole parameter space we have displayed. In case of the diphoton channel, the background is already quite small compared to the signal, whereas for the dilepton channel, background becomes under control after the “discovery cuts.” With the “discovery cuts,” one can probe MS roughly up to 3.6 TeV (4.4 TeV) with 100 fb−1 (300 fb−1) integrated luminosity at the 14 TeV LHC.The required luminosity (LD) for the discovery of KK graviton in (a) dilepton and (b) diphoton channels as a function of MS at the 14 TeV LHC with “discovery cuts” (see text for the definitions of the cuts). The LDll and LDγγ are computed for n= 2–7 with Δη=2 at pp→X+ψψ+Y level where ψ={l,γ}.
(a)
(b)


## 6.1.1. Discovery Cuts

Motivated by the invariant mass and angular distributions in Figures9 and 12, we construct some kinematical cuts to separate the signal from the background in the dilepton and diphoton channels as follows:  (1)
dilepton channel:|yll|≤2; |cosθll|≤0.8; MS/2≤Mll<MS-10GeV;(2)
diphoton channel:|yγγ|≤2; |cosθγγ|≤1; 250GeV≤Mγγ<MS-10GeV.We call these cuts as the “discovery cuts” for the discovery of KK graviton at the LHC. In Figure 13, LD goes as L10 for both dilepton and diphoton channels in the whole parameter space we have displayed. In case of the diphoton channel, the background is already quite small compared to the signal, whereas for the dilepton channel, background becomes under control after the “discovery cuts.” With the “discovery cuts,” one can probe MS roughly up to 3.6 TeV (4.4 TeV) with 100 fb−1 (300 fb−1) integrated luminosity at the 14 TeV LHC.The required luminosity (LD) for the discovery of KK graviton in (a) dilepton and (b) diphoton channels as a function of MS at the 14 TeV LHC with “discovery cuts” (see text for the definitions of the cuts). The LDll and LDγγ are computed for n= 2–7 with Δη=2 at pp→X+ψψ+Y level where ψ={l,γ}.
(a)
(b)


## 7. Conclusions

In this paper, we have discussed the possibility of looking for new physics, in particular, the signatures of large extra dimensions, in diffractive processes at the LHC. We have concentrated on the central inclusive production where the outgoing protons breakup, but the fragments are mostly emitted in the forward direction. We have studied in detail the signal of KK gravitons via the dilepton and the diphoton channels. From angular momentum conservation, the spin-2 graviton cannot be produced at LO in exclusive processes as discussed in the text, but it can be produced in an inclusive configuration. Although the backgrounds are larger for inclusive production, the larger cross-section and event rate for signals make the collider search for extra dimensional theories very promising. Since the intermediate particle is spin-2 in nature, we also get a unique angular distribution which can be used to distinguish signals from backgrounds. We have shown that it is very unlikely to produce a lepton or a photon pair in the SM with very high invariant mass in the inclusive configuration. Thus, experimentally, if we find a reasonable number of lepton or photon pairs with high invariant mass, it would clearly indicate the signature of new physics possibly the signature of large extra dimensions.In this work, we have indicated the possibility of using dilepton and diphoton in the final state to signal the presence of extra dimensions. We have carefully estimated the sizes of the signal and the background and found that the signal rates are not too big. Nevertheless, it is possible within reasonable parameter ranges as suggested by present day studies to use central production, with forward detectors for the proton fragments, to look for KK gravitons as a signal for ADD-like theories. The great advantage of using such channels for the study of new physics is that they are clean, and the signals are easily distinguished from the backgrounds. On the flip side, the event rates are considerably smaller than other standard new physics searches. This can be compensated by runs at higher energies and greater luminosities at some future date. There is another general issue with high luminosity run at the LHC—the presence of huge “pile-up” background. This background can overwhelm the rapidity gap signatures. If we consider inclusive processes and sacrifice the forward proton tagging (applicable only for exclusive processes), we can detect rapidity gap events at the LHC [8].All higher dimensional models are valid up to a cutoff scale. In our case, the signal cross-sections depend on the eighth power of1/MS (MS is the cutoff scale of the theory). Thus, numerical results are very sensitive to the UV cutoff. The experimental lower bound of MS≈3 TeV for n=2. Future experiments can push up the lower bound and make the signatures less visible. We show that LHC with S=14 TeV and 100 fb−1 (300 fb−1) of integrated luminosity can probe MS up to 3.6 TeV (4.4 TeV) in both the dilepton and the diphoton channels.



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*Source: 652714-2013-07-01.xml*