Large extra dimension effects through lightbylight scattering at the CERN LHC
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Abstract
Observing lightbylight scattering at the large hadron collider (LHC) has received quite some attention and it is believed to be a clean and sensitive channel to possible new physics. In this paper, we study the diphoton production at the LHC via the process \({{pp}}\rightarrow {{p}}\gamma \gamma {{p}}\rightarrow {{p}}\gamma \gamma {{p}}\) through graviton exchange in the large extra dimension (LED) model. Typically, when we do the background analysis, we also study the double Pomeron exchange of \(\gamma \gamma \) production. We compare its production in the quark–quark collision mode to the gluon–gluon collision mode and find that contributions from the gluon–gluon collision mode are comparable to the quark–quark one. Our result shows, for extra dimension \(\delta =4\), with an integrated luminosity \(\mathcal{L} = 200\,\mathrm{fb}^{1}\) at the 14 TeV LHC, that diphoton production through graviton exchange can probe the LED effects up to the scale \({M}_{S}=5.06 (4.51, 5.11)\,\mathrm{TeV}\) for the forward detector acceptance \(\xi _1 (\xi _2, \xi _3)\), respectively, where \(0.0015<\xi _1<0.5\), \(0.1<\xi _2<0.5\), and \(0.0015<\xi _3<0.15\).
Keywords
Large Hadron Collider Large Extra Dimension Central Exclusive Production Forward Detector Large Extra Dimension1 Introduction
The large hadron collider (LHC) at CERN generates high energetic proton–proton (\({{pp}}\)) collisions with a luminosity of \(\mathcal{L}=10^{34}\,\mathrm{cm}^{2}\,\mathrm{s}^{1}\) and provides the opportunity to study very high energy physics. At such a high energy, most attention is usually paid to the central rapidity region where most of the particles are produced and where most of the high \({{p}}_{T}\) signal of new physics is expected. Indeed, the CDF collaboration has already observed such a kind of interesting phenomenon including the exclusive lepton pairs production [1, 2], photon–photon production [3], dijet production [4] and charmonium (\(J/\psi \)) meson photoproduction [5], etc. Now, both ATLAS and CMS collaborations have programs of forward physics which are devoted to studies of high rapidity regions with extra updated detectors located in a place nearly 100–400 m close to the interaction point [6, 7, 8, 9]. Technical details of the ATLAS forward physics (AFP) projects can be found, for example, in Refs. [10, 11]. The physics program of this new instrumentation covers interesting topics like elastic scattering, diffraction, lowx QCD, central exclusive production (CEP), and the photon–photon (\(\gamma \gamma \)) interaction, the last two being the main motivation for the AFP project.
The simplest exclusive production is due to the exchange of two photons: \({pp}\rightarrow {p}\gamma \gamma {p}\rightarrow {pXp}\) where X is the centrally produced system. In such production at the LHC, the invariant mass of the photons can span up to 1 TeV scales, high enough to reach scales of possible new physics. In addition, the production of these processes mainly through the QED mechanisms which are well understood and their predictions have a very small uncertainty. These make the twophoton exchange physics particularly interesting. Therefore, we can use this kind of production mechanism to determine the luminosity at the LHC precisely [12], to study the interaction of electroweak bosons with overconstrained kinematics, to test the standard model (SM) at high energies or to study the new production channels that could appear, i.e., SUSY [13, 14, 15, 16, 17, 18], anomalous gauge couplings [19, 20, 21, 22, 23, 24], unparticle [25], and extra dimensions [26, 27], etc.
Observing lightbylight scattering at the LHC has received quite some attention [28] and it is believed a clean and sensitive channel to possible new physics. In this paper, we study the diphoton signal from graviton exchange in the large extra dimension (LED) model via the main reaction \({pp}\rightarrow {p}\gamma \gamma {p}\rightarrow {p} {G}_\mathrm{kk} {p}\rightarrow {p}\gamma \gamma {p}\) where \({G}_\mathrm{KK}\) is the KK graviton in LED. A similar study has been performed in Ref. [27] where the authors study the diphoton signal in both the LED and Randall–Sundrum (RS) models and take \(\gamma \gamma \) SM production as the corresponding background. In our study we also consider the double Pomeron exchange (DPE) production of the diphoton and present their cross section dependence on the energy loss of the proton \(\xi \) and compare its production separately in the quark–quark collision mode to the gluon–gluon collision mode. Our paper is organized as follows: we build the calculation framework in Sect. 2 including a brief introduction to the central exclusive diphoton production and equivalent photon approximation (EPA), the general diphoton exchange process cross section and a brief introduction to the LED model. Section 3 is arranged to present the input parameters and numerical results of our study. Typically we present a discussion of DPE diphoton production. Finally we summarize our conclusions in the last section.
2 Calculation framework
2.1 Central diphoton exchange at the LHC and EPA
2.2 LED and light–light scattering through graviton exchange
The hierarchy problem strongly suggests the existence of new physics beyond the SM at TeV scale. The idea that there exist extra dimensions (ED) which was first proposed by ArkaniHamed, Dimopoulos, and Dvali [32, 33], might provide a solution to this problem. They proposed a scenario in which the SM field is constrained to the common \(3+1\) spacetime dimensions (“brane”), while gravity is free to propagate throughout a larger multidimensional space \({D}=\delta +4\) (“bulk”). The picture of a massless graviton propagating in D dimensions is equal to the picture that numerous massive Kaluza–Klein (KK) gravitons propagate in four dimensions. The fundamental Planck scale \({M}_{S}\) is related to the Planck mass scale \({M}_\mathrm{Pl}={G}_{N}^{1/2}=1.22\times 10^{19}\,\mathrm{GeV}\) according to the formula \({M}^2_\mathrm{Pl}=8\pi {M}^{\delta +2}_{S} {R}^\delta \), where R and \(\delta \) are the size and number of the extra dimensions, respectively. If R is large enough to make \({M}_{S}\) on the order of the electroweak symmetry breaking scale (\(\sim \)1 TeV), the hierarchy problem will be naturally solved, so this extra dimension model is called the LED model or the ADD model. Postulating \({M}_{S}\) to be 1 TeV, we get \({R}\sim 10^{13}~\mathrm{cm}\) for \(\delta =1\), which is obviously ruled out since it would modify Newton’s law of gravity at solarsystem distances; and we get \({R}\sim 1~\mathrm{mm}\) for \(\delta =2\), which is also ruled out by torsionbalance experiments [34]. When \(\delta \ge 3\), where \({R} < 1~\mathrm{nm}\), it is possible to detect a graviton signal at high energy colliders.
At colliders, the exchange of a virtual KK graviton or the emission of a real KK mode could give rise to interesting phenomenological signals at TeV scale [35, 36]. The virtual effects of the KK modes could lead to the enhancement of the cross section of pair productions in the processes, for example, dilepton, digauge boson (\(\gamma \gamma \), \({ZZ}\), \({W}^+{W}^\)), dijet, \({t}\bar{t}\) pair, HH pair [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61], etc. The real emission of a KK mode could lead to large missing \({E}_{T}\) signals viz. mono jet, mono gauge boson [35, 36, 62, 63], etc. The CMS collaboration has performed a lot of research for LED on different final states at \(\sqrt{{s}}=7\) TeV [64, 65, 66], and they set the most stringent lower limits to date to be \(2.5~\mathrm{TeV} < {M}_{S} <3.8~\mathrm{TeV}\) by combining the diphoton, dimuon, and dielectron channels.
3 Numerical results
3.1 Input parameters and kinematic cuts

CMSTOTEM forward detectors with \(0.0015<\xi _1<0.5\);

CMSTOTEM forward detectors with \(0.1<\xi _2<0.5\);

AFPATLAS forward detectors with \(0.0015<\xi _3<0.15\),
3.2 Background analysis
Our signal topology is simply that of two photons in the final states excited by graviton exchange. The main background comes from two sources: one is the background coming from SM \({pp}\rightarrow {p}\gamma \gamma {p}\rightarrow {p}\gamma \gamma {p}\) production through oneloop contributions. The other comes from diffractive DPE [or Central Exclusive Diffractive (CED) production] of the diphoton.
Let us first consider the SM \(\gamma \gamma \rightarrow \gamma \gamma \) oneloop production. Though there is no tree level contribution to \(\gamma \gamma \rightarrow \gamma \gamma \), it is still important to include loop effects of its contributions. The precise determination of this cross section has a special importance to test the renormalization procedure of the parts of the SM containing W gauge bosons. Moreover, as in our case, this loop process becomes a background for new physics searches through \(\gamma \gamma \) scattering. Oneloop diagrams involve charged fermions and the W bosons rotate in loop. Here we include all these contributions and perform the calculation with the FFL package. The calculation can also be found in Ref. [27].
Background contribution for diphoton production in different parton collision modes before and after taking into account the survival probability factor
\(\sigma \) (fb)  Background contribution for diphoton production  

\(({S}_\mathrm{DPE},{S}_{\gamma \gamma })\)  \({u}\bar{u}\)  \({d}\bar{d}\)  gg  \(\mathrm{SM}_\mathrm{loop}\)  Total 
(1, 1)  8.5792  1.0724  4.49159  0.1415  14.2846 
(0.03, 0.9)  0.2574  0.0322  0.1347  0.1273  0.5516 
3.3 Signal boundary at future LHC
4 Summary
A lot of theoretical work has been done to study the LED effects. Even if a process can be traced back to a definite set of operators, it is rarely the case that a particular collider signature can be traced back to a unique process. For this reason many different, complementary measurements are usually required to uncover the underlying new physics processes. Observing lightbylight scattering at the LHC has recently received much more attention [28]. It is believed to be a clean and sensitive channel to possible new physics. In this paper, we calculate the diphoton production at the LHC via the process \({pp}\rightarrow { p}\gamma \gamma {p}\rightarrow {p}\gamma \gamma {p}\) in the SM and LED. Typically, when we do a background analysis, we also study the DPE of \(\gamma \gamma \) production. We present their cross section dependence on the energy loss of the proton \(\xi \) and compare its production separately in the quark–quark collision mode to the gluon–gluon collision mode. We conclude that the contribution from the gluon–gluon collision mode are comparable to the quark–quark collision mode. A \({p_{T}}^\gamma > 300\ \mathrm{GeV}\) cut can suppress the DPE background efficiently. However, if there are no kinematic cuts taken into account, especially in the low \(\xi \) range, they should better be studied and considered. Finally, we present the \({M_{S}}\) bounds for the \(3\sigma \) and \(5\sigma \) deviations from the total backgrounds as functions of the luminosity \(\mathcal{L}\) with extra dimensions \(\delta =4\) for different choices of the forward detector acceptance \(\xi \). Concerning the criteria, for a statistical significance of \(\mathrm{SS} > 5\), with an integrated luminosity \(\mathcal{L} = 200\,\mathrm{fb}^{1}\), \({pp}\rightarrow {p}\gamma \gamma {p}\rightarrow {p}\gamma \gamma {p}\) production through graviton exchange can probe the LED effects up to the scale \({M_{S}}=5.06(4.51,5.11)\, \mathrm{TeV}\) for \(\xi _1(\xi _2,\xi _3) \), respectively, where \(0.0015<\xi _1<0.5\), \(0.1<\xi _2<0.5\), and \(0.0015<\xi _3<0.15\).
Notes
Acknowledgments
Project supported by the National Natural Science Foundation of China (No. 11205070), Shandong Province Natural Science Foundation (No. ZR2012AQ017) and by the Fundamental Research Funds for the Central Universities (No. DUT13RC(3)30).
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