Searching for anomalous top quark interactions with proton tagging and timing detectors at the LHC

We study the LHC sensitivity to new broad neutral resonances produced in two-photon fusion and decaying to a top quark pair, $\gamma\gamma \to t\bar{t}$. This is probed in central exclusive $t\bar{t}$ production in proton-proton collisions, $pp \to p t\bar{t} p$. We use the tagging of the intact protons by PPS (CMS) and AFP (ATLAS) and consider the semi-leptonic $t\bar t$ channel. The sensitivity is also mapped onto a set of dimension-8 $\gamma\gamma t\bar{t}$ operators in the large mass limit. Using the kinematical correlations between the intact protons and the reconstructed $t\bar{t}$ system, we obtain a sensitivity to the couplings of the dimension-8 operators of $1.4 \cdot 10^{-11}~\mathrm{GeV}^{-4}$ at 95% CL. The sensitivity to the anomalous couplings is significantly improved down to about $7\cdot 10^{-12}~\mathrm{GeV}^{-4}$ if the proton time-of-flight is known with a precision of 20 ps in future measurements. The 95% CL sensitivity to broad neutral resonances reaches masses of order $ 1500~\mathrm{GeV} $ when using timing information.


Introduction
Under the hypothesis that new physics with strong interactions exists beyond the Standard Model (SM) of particle physics, it is possible that a new state with broad width lies at the TeV scale. Searching for such broad resonances at the LHC is somewhat challenging since the analyses cannot efficiently rely on standard bump-searching methods. Instead, the search may substantially benefit from observation channels featuring a highly reduced background. The observation channels from central exclusive production (CEP) processes, in which both protons remain intact in the final state, belong to this category and therefore provide an environment favorable to the search for broad resonances.
Among all processes, the CEP topology stands out because it can be efficiently selected using the forward proton detectors built for this purpose in the CMS and ATLAS experiments, namely the Precision Proton Spectrometer (PPS) [1] and the ATLAS Forward Proton detector (AFP) [2], respectively. Forward detectors measure the outgoing intact protons, leading to the reconstruction of the entire final state kinematics of both the proton and central systems. This set of techniques leads to drastic background reduction.
A key example is the pp → γγpp process for which the background for 300 fb −1 drops below one expected event in the high mass region (see e.g. [3]). It was demonstrated in [4] that this channel is an efficient precision probe of broad neutral particles 1 .
The SM central exclusive production of tt has been investigated in recent phenomenological studies [26][27][28]. The process has not been observed experimentally, but a recent search by the CMS Collaboration has set an upper bound on its cross section of σ = 0.59 pb at 95% CL at 13 TeV [29]. It is likely that the SM process could be observed at the high-luminosity LHC [30]. Photoproduction of top quark pairs can be used to constrain the electromagnetic dipole moments of the top quark, as discussed in Ref. [31] for γ-gluon fusion processes, for example.
The goal of the present paper is to expand the prospects of CEP searches to the case of neutral particles coupled to both photons and top quarks. Our focus is on evaluating the sensitivity of the exclusive pp → ttpp process to the presence of (possibly broad) neutral resonances. In the large mass limit the photon-top quark interactions become local and can be described using local dimension-8 effective operators. Thus, the sensitivity to these dimension-8 operators is also studied throughout this paper as a natural extension.
We emphasize that our focus on dimension-8 operators is motivated by the neutral particle scenario. In principle, searching for the dimension-6 top quark dipole operators in the CEP topology is also well-motivated. This interesting case is kept for a separate investigation. In the case of neutral particles, we will verify that the loop-generated contribution to the dipole is negligible in the scope of our study, hence justifying our focus on the dimension-8 operators.
Importantly, the sensitivity to the pp → ttpp process is expected to be substantially enhanced by the use of timing detectors embedded into the forward detectors [32]. These timing detectors provide an independent reconstruction of the primary vertex using intact proton information, improving further the selection of signal events. Our study serves to illustrate the power of these timing detectors in the specific case of broad neutral resonances.
The plan of the paper is as follows. In Section 2 the models for neutral particles are introduced. We also work out the basis of effective operators describing local γγtt interactions. Section 3 provides basics on forward detectors and describes the simulation framework. Section 4 briefly describes the statistical framework. Section 5 describes the search for γγ → tt in the semi-leptonic decay channel. Section 6 presents our results and a summary is given in Section 7.

Effective field theory and neutral particles
Here, we define extensions of the SM which induce anomalous γγ → tt scattering. We start by deriving the relevant basis of higher dimensional operators that contribute to such anomalous processes. The lowest dimensional operators turn out to have dimension eight, and we identify three CP-even and three CP-odd operators. Any new physics model contributing to anomalous tt production via photon fusion can be matched to these operators at low energy. We then introduce generic models of neutral resonances with trilinear couplings to both photons and top quarks. They can themselves be considered subsectors of well-motivated extensions of the SM, such as composite Higgs models, extra dimensions, etc. Moreover, we explicitly provide the matching of these generic models to the aforementioned dimension-8 effective theory. These (effective) models provide the basis for our simulations in the subsequent sections.

Operator basis
The physics candidates probed by our experiment may have a mass scale Λ much higher than the other scales involved in the amplitudes. In such a regime, the amplitudes can be expanded in inverse powers of Λ. Whenever this expansion is possible, the observable effects of the high mass physics can be described by a series of local operators encoded in a low-energy effective Lagrangian, L = L SM + n,i Our interest is in the set of dimension-8 operator (i.e. n = 4) involving two top quarks and two photons. We allow for both CP-even and CP-odd bilinear invariant intt and photon field strength. At a given order in the expansion, the equations of motion can be used to reduce the set of the effective operators. We find an irreducible basis of six operators (omitting the subscript n), Bilinear terms of the formtΓγ µ ∂ µ t, where Γ is an arbitrary Lorentz structure, are reduced by using the top quark equation of motion into other operators from the above basis plus operators involving other fields, which are irrelevant for the process considered. One can also check that F µρF ν ρ = 1 4 g µν FF such that operators of the form F µρF ν ρt Γγ µ ∂ ν t are reduced into O 3,4 using the top quark equation of motion.
The effective Lagrangian description breaks down at momenta of order of the Λ mass scale. In case of strong coupling, this breakdown coincides with the breakdown of the perturbative expansion in the effective couplings. It also roughly coincides with violation of unitarity, signalling the necessity of a UV completion.
We parametrize the coefficients of the basis of operators shown in Eq. (2.1) as

Neutral particles
Neutral particles with non-renormalizable couplings to SM operators are present in common extensions of the SM. Such theories often contain scalar, pseudo-scalar and spin-2 particles, respectively denoted by ϕ,φ and h µν . Examples include the Peccei-Quinn axion [33], the Kaluza-Klein (KK) graviton and the radion in warped extra dimensions [34], the dilaton in theories of strongly coupled electroweak breaking [35], Goldstone bosons of extended composite Higgs models [36], mesons and glueballs of strongly-coupled theories [37], extra scalars breaking the global symmetry of composite Higgs models [38][39][40], Higgs portal models [41], and many more. Independently of the model they originate from, their leading couplings to photons and quarks can be can be classified in terms of CP quantum numbers and written as where ϕ is the CP-even scalar, a the CP-odd scalar, and h µν the CP-even spin-2 field. The couplings f X appearing in Eq.(2. 3) e (2.4) are typically restricted by unitarity to Let us note that in some models that address both the hierarchy and flavor problems of the SM (such as warped extra-dimensions with SM fermions in the bulk), it is common that the heavy neutral resonances couple more strongly to the top quark than to the lighter quarks. The partial width of both the CP-even and CP-odd scalar into γγ is (2.6) The partial width for the CP-even and CP-odd scalar into tt are respectively

Matching to dimension-8 operators at tree-level
When any of these particles is heavy, it contributes to the effective EFT operators classified in Eq. (2.1). The matching is as follows, depending on which of the particles is integrated out • Spin-0, CP-even scalar φ • Spin-0 CP-odd scalarφ • Spin-2 field h µν This EFT regime typically applies in our context whenever m 2.8 TeV as the experimental acceptance is very low beyond this scale and a heavier resonance cannot be resolved, leaving only the imprint in the higher dimensional operators.

Estimate of dipole operator at loop-level
The above couplings of the top quark to the neutral resonance also generate a CP-even dimension-6 dipole operator where a factor of m t arising from electroweak symmetry breaking is shown explicitly and ζ d has a mass dimension of m −2 . This operator modifies the SM top quark coupling to the photon, and hence the γγ → tt production amplitude via the standard t-channel topology. However, the coefficient ζ d is loop suppressed and goes as and even in the strong-coupling scenario in Eq. (2.5), ζ d →  which is of the order of ∼ 10 −6 for a 1 TeV resonance and a typical energy of E =500 GeV. Therefore, such an effect is completely negligible.

Signal modeling
In our setup the anomalous pp → ttpp process (Fig. 1c) is probed in the configuration of forward protons, i.e. in very peripheral proton-proton collisions. In very peripheral collisions, the electromagnetic field generated by the electrically charged protons can be treated as a source of quasi-real photons. These quasi-real photons can then interact to produce the top quark pair system. This photon emission off the proton is treated within the equivalent photon approximation (EPA) [42,43]. In contrast to the standard parton distribution functions used in the quantum chromodynamics (QCD) factorization theorem, the flux and energy spectra of the quasi-real photons are under better theoretical control. This is because they are parametrized with the elastic electric and magnetic form factors extracted from precision electron-proton elastic scattering data. Due to additional soft interactions between the protons, not all of them will remain intact after the quasi-real photon exchange. This means that the cross section for photon-induced processes with intact protons is reduced [44][45][46][47][48]. For our projections, this effect is taken into account by supplementing the cross section calculation with a survival probability factor that accounts for the probability that the protons remain intact after the photon exchange. For our calculations, we assume a survival probability of 90%. The signal process originates from the squared anomalous amplitude plus the interference with the SM exclusive production of tt. The SM exclusive production of tt mainly happens via photon-initiated interaction (Fig. 1a), while the amplitude for gluon initiated CEP (Fig. 1b), which can be calculated with the perturbative QCD Durham model [49], is at least two orders of magnitude lower, thus negligible.
In the present study the SM cross section at √ s = 14 TeV, ∼ 0.35 [27,50], is between one and two orders of magnitude lower than its anomalous counterpart when considering coupling values equal to the predicted sensitivity. This difference is further enhanced when applying the selection criteria. The fact that the square SM amplitude is smaller than the square BSM amplitude necessarily implies that the latter dominates the signal while the interference is subleading (see [51]). Anticipating the final sensitivity, we can thus neglect beforehand the interference between anomalous and SM amplitudes.
The anomalous central exclusive production of tt via γγ interaction ( Fig. 1c) is generated with the Forward Physics Monte Carlo (FPMC) event generator [52], which implements the EPA approach. The scattering amplitudes were computed using MadGraph [53], and implemented in FPMC.

Background modeling
The present study focuses on the reconstruction of anomalous exclusive tt production in the semi-leptonic decay channel. The dominant background components to tt exclusive production, in high-pileup conditions, are processes with final states similar to tt semileptonic decays, in coincidence with intact outgoing protons coming from soft diffractive pileup events. A next-to-leading order cross section of 903 pb for QCD tt production at 14 TeV with resummation at next-to-leading logarithmic accuracy is considered following Ref. [54].
Soft diffractive reactions at 14 TeV are expected to have a production cross section of the order of 20 mb. During the CERN LHC Run 2, average simultaneous interactions (pileup) in the 30-50 range were reached at the ATLAS and CMS interaction points. This high number of interactions, combined with the large soft single and central diffractive cross section yields a significant amount of forward protons coming from pileup collisions. Even if kinematic constraints between forward protons and the central system measurement can be exploited to tame this background component, as shown in the later sections, it still represents the main challenge when searching for tt exclusive production.
To take into account this effect, a conservative average number of concurrent interactions of 50 is considered. In each tt event, the number of pileup interactions is sampled from a Poisson distribution. For each pile up vertex, 0, 1 (in one detector arm) or 2 protons (in both arms) are assigned. The probability per-pileup vertex of having protons in the forward detectors is calculated using the Pythia8 event generator [55]. Then, the ξ distribution for these intact protons is sampled from a 1/ξ distribution, which is an approximation to the expected ξ distribution of soft diffractive interactions. The proton fractional momentum loss is considered in the range between 0.015 and 0.2 for our projections. A 2% Gaussian smearing is applied on ξ to mimic detector resolution effects.
The main background component is given by QCD tt + jets production. Simulated events for this process are generated with MadGraph and matched to parton showers and hadronization with Pythia8. A secondary background contribution is the QCD W W + jets production in coincidence with pileup protons from soft diffraction. In this case the cross section considered is 131.3 pb, following Ref. [56].
Another background contribution might arise from single-diffractive tt production in coincidence with pileup protons. The process cross section is expected to be O(1) pb. However, even though one of the intact protons might be kinematically correlated to the central system, the second pileup proton will not. Hence, it is effectively suppressed by exploiting this kinematical correlation, making it negligible.
In double-pomeron exchange, not all of the energy of each exchanged pomeron goes into the production of the tt system. This means that the invariant mass of the tt system reconstructed with the intact protons information heavily underestimates the true tt mass (see for example the diffractive mass fraction reported by CDF in [57] or Figure 3 of Ref. [28]). This process is therefore suppressed in the selection process.
CEP of tt by color-singlet two-gluon exchange, which is an irreducible background component, is suppressed at high tt masses. This is because the cross section needs to be supplemented with a Sudakov form factor that accounts for the probability that there is no initial-state radiation that could spoil the exclusivity of the process. The probability that there are no gluon emissions decreases rapidly with the mass of the central system, since there is more phase-space available for them. No such Sudakov form factor is present in calculations with two-photon fusion processes. This has been shown explicitly in Refs. [3,48].

Detector simulation
The detector simulation is performed with the Delphes package, tuned with the CMS datacard [58]. Detector efficiencies and energy/momentum smearings are parametrized as a function of the particle kinematics (pseudo-rapidity, transverse momentum for tracking detectors, pseudo-rapidity and energy for calorimeters) [59,60]. Jets are clustered with the FastJet package [61], using the anti-k t algorithm [62] with a distance parameter R = ∆φ 2 + ∆y 2 = 0.5, and transverse momentum p T > 20 GeV. b-tagging is included following Ref. [63] and takes into account both the tagging efficiency and the misidentification rate. Leptons are reconstructed within the pseudo-rapidity range |η| < 2.5, and jets for |η| < 5. Missing transverse energy is computed in a particle-flow approach.
To account for the proton measurement resolution, a 2% Gaussian smearing on the proton fractional momentum loss (ξ = (p i − p f )/p i ) is applied and only protons with 0.015 < ξ < 0.20 are considered, to match the typical forward detectors acceptance.
The longitudinal position of primary vertices is randomly sampled from a Gaussian distribution of 5 cm RMS, according to the reported CMS observations [64]. Timing detector resolution effects are included by applying Gaussian smearings on the proton time of arrival, assuming a 200 m distance of forward detectors from the interaction point. Timing resolutions of 20 and 60 ps are considered, the former, being compatible with the design scenario presented in [1], and the latter accounting for performance already achieved today.

Statistical framework
For our projections, we need to assume a set of observed data. As commonly done, we assume that no statistical fluctuations are present in these pseudo-data, which are usually dubbed "Asimov" data and that we denote here with a prime. As mentioned before, the integrated luminosity is chosen to be L = 300 fb −1 , which is about the expected integrated luminosity to be taken by CT-PPS and AFP in Run-3 (in Run-2, CMS and ATLAS collected about 100 of data with forward detectors at 13 TeV).
The observed events follow a Poisson distribution and for this kind of analysis we can safely neglect the systematic uncertainties. The statistics for the events together with the prediction for the event rates sets the likelihood function needed for our analysis, where b is the expected number of events from the background. In our study, depending on the cases, b may be much larger than 1 or O(1). In order to draw projected exclusion contours, we take the background-only hypothesis for the Asimov data, Our method to obtain the projected exclusion contours is the following. We define the posterior probability density for σ as L(σ)π(σ) where the prior is π(σ) = 1 if σ > 0 and 0 otherwise. The highest posterior density region at 1 − α credibility level is solved analytically and is simply given by where Γ(x, y) is the incomplete Gamma function. The credibility regions for different values of α amount respectively to exclusion at 2σ, 3σ, 5σ in terms of standard statistical significance 2 . The projected sensitivity to the signal that we quote is the value of σ satisfying Eq. (4.3) for a given statistical significance.
5 Anomalous γγ → tt in the semi-leptonic decay channel Since each of the top quarks decays to a W boson and a b quark, events can be classified depending on the W boson decays. Events in which both W boson decays are leptonic are called fully-leptonic. When one W boson decay is hadronic and other is leptonic the event is called semi-leptonic. When two hadronic W boson decays take place, events are called fully-hadronic.
Fully-leptonic decays generally present lower backgrounds, but have a low branching fraction of the order of 10%, and the presence of two neutrinos in the final state lowers the precision of the tt system mass measurement, effectively reducing the background rejection provided by the measurement of the leading protons. Fully-hadronic decays on the other hand have the highest branching fraction. They are however strongly impacted by QCD jets backgrounds, so they represent a challenging environment for exclusive tt measurements. For the present study, the event selection and reconstruction was therefore tuned for semileptonic events, as they represent a good compromise under all the above-mentioned aspects.
Throughout this section the signal is taken to be generated from the basis of ttγγ dimension-8 operators (see Eq. (2.1)). The analysis is applied to signal events from neutral particles in the next section.

Event selection and reconstruction
Exclusive semi-leptonic tt events are selected in three steps: pre-selection, central selection and matching and eventually timing. A pre-selection is applied to select events with at least one lepton in the final state, two b-tagged jets, two non b-tagged jets, and one tagged proton per detector side. Furthermore, a missing energy transverse E miss T > 20 GeV is required. EFT operators yield tt mass distributions that can be grouped into two families: O 5 and O 6 , which contain an additional derivative, produce cross sections that grow faster with m tt , compared to O 1 ,O 2 ,O 3 ,O 4 . The two families are thus studied in parallel, and O 1 and O 5 are shown as their representatives. 2 The standard statistical significance is given by . We can also notice that for b 1, upon approximating Γ(x, y) ∼ y x−1 e −y and expanding in small s b we obtain  Non-diffractive tt Anom. tt 1 = 10 11 GeV 4 Anom. tt 2 = 10 11 GeV 4 Anom. tt 3 = 10 11 GeV 4 Anom. tt 4 = 10 11 GeV 4 Anom. tt 5 = 10 11 GeV 4 Anom. tt 6 = 10 11 GeV 4 Figure 2: Mass of the tt system at generator level (stable-particle level). All histograms are normalized to unity.
As illustrated in Fig. 2, anomalous tt events are expected to show mass distributions peaked towards higher values with respect to SM tt. The two b-tagged jets and non btagged jets with the largest transverse momenta are therefore chosen, as well as the largest p T lepton.
The mass of the central system can be expressed in relation to the proton measurement with: with ξ + and ξ − being the fractional momentum losses of the protons measured in the two proton detectors. The proton with the largest ξ is chosen to enhance the event selection efficiency of anomalous tt exclusive events in case of multiple protons on each detector side. After the pre-selection is performed, each top quark is reconstructed from its decay product. In the following, t h refers to the top quark that decays into hadrons, while t refers to the one decaying into leptons.
To assign the b-tagged jets to their respective top (anti)quark, the mass of the system formed by the two non b-tagged jets and a b-tagged jet is computed. The b-jet assigned to t h is thus the one yielding a mass measurement closest to the top quark mass. The other b-jet is consequently assigned to t . t is reconstructed together with the highest p T lepton and missing transverse energy. In order to improve the t reconstruction, the longitudinal component of the neutrino four-momentum (p ν z ) is estimated. The value of p ν z is computed analytically based on the relation of the four-momentum of the lepton-neutrino system and the W boson mass, where the lepton kinematics are measured, p ν T = E miss T , and the neutrino mass is neglected. The solution that minimizes |p ν z − p z | is chosen, and in case of imaginary solutions only the real part is considered. With both t h and t reconstructed, further selection is performed based on their kinematics. As shown by Fig. 3, the top quark p T spectrum in anomalous tt exclusive production is broader with respect to the SM, and higher values are more frequent. A selection of p T > 425 GeV for both t h and t is therefore applied.
A similar approach is applied to m tt (Fig. 4), the mass measured by the central detector, selecting m tt > 960 GeV. A mass spectrum shifted towards higher values is indeed characteristic of anomalous exclusive processes. With this mass selection, the SM CEP of tt is strongly suppressed, making the interference with BSM production negligible.
Since no further radiation is expected in the final state, the tops are produced back-toback in the transverse plane. Selecting events with acoplanarity |1 − |φ t h −φ t | π | < 0.09, as Fig. 5a illustrates, thus favors anomalous production with respect to SM tt+jets production. Further exploiting the fact that top quarks are balanced in the transverse plane, we require the ratio of their transverse momenta p t h T /p t T > 0.88 (see Fig. 5b). In exclusive events, tt pairs are also produced in a narrower rapidity range (see Fig. 6), therefore we require |y tt | < 0.72.
Finally, a selection on the sum of the transverse momenta of the decay products H T is performed. H T is computed as where j indicates the non b-tagged jets used for reconstruction and j b indicates the btagged ones. As Fig. 7 shows, selecting high H T values above 1100 GeV suppresses the SM tt background while retaining anomalous exclusive tt events. The final selection step is performed by comparing the mass and rapidity of the final state reconstructed in the central detector from the decay products with the measurements that can be obtained from proton tagging. As shown in Eq. system can be measured via the fractional momentum losses of the protons. Similarly, the rapidity of the central system can be computed from the proton kinematics: where ξ + is the fractional momentum loss of the outgoing proton with positive p z , and ξ − the one of the proton with negative p z . In background events, pileup protons are uncorrelated with the processes observed in the central system. Mass and rapidity measurements done with outgoing protons are thus expected to be uncorrelated with the same measurements given by the tt system reconstructed from its central decay products. This is reflected in variables such as the mass match ratio and ∆y tt , defined as follows: Pre-selection Central selection Proton matching Timing Table 1: Summary of the analysis sequential cuts applied at each selection stage.
where the c index indicates reconstructed quantities from decay products measured in the central detector.
As Fig. 8 illustrates, signal events are expected to show a narrow distribution around zero, while background events form a broader one. This is due to the uncorrelated nature of the two pileup protons selected in background events. Since pileup protons follow a 1/ξ momentum loss distribution, the mass computed with a random combination peaks at lower values with respect to m tt , so negative mass match ratios are favored. Event candidates are classified as signal when | ∆m tt m p tt | < 0.08 and |∆y| < 0.05.
Finally, a selection based on the proton time of arrival is applied. The longitudinal vertex position reconstructed by the central tracking detectors (z c ) is required to be compatible with the one reconstructed from timing measurements (z p ), which is computed as where c denotes the speed of light and t + (t − ) indicates the time of arrival of the proton with positive (negative) p z . The distribution of z c − z p is Gaussian in our setup, and only events falling within 1.5σ limits are accepted for maximum significance.
A similar selection is performed on the (t + + t − ) variable, which is expected to be compatible with twice the forward detectors distance from the interaction point, divided by the speed of light, in case of protons originating from the same vertex. Also in this case, a 1.5σ compatibility requirement is applied.
A summary of the cuts applied at each selection stage is given in Table 1.

Results
In this section we first display our results on the ttγγ dimension-8 operator basis, turning on one operator at a time. We then apply the analysis to models with broad neutral resonances. Table 2 summarizes the expected events for 300 fb −1 for both signal and background, along the cut flow established in Table 1.

Sensitivity to dimension-8 operators
The non-diffractive W W background is fully removed by the mass and rapidity matching of the central event with the proton system. The non-diffractive tt background gives ∼ 100 events without the use of timing detectors. This is in contrast with the case of CEP of electroweak gauge boson pairs (γγ, γZ, W + W − , ZZ), where the non-diffractive backgrounds can be suppressed to just a few event counts [3,24,65,66]. The reason is that non-diffractive tt is dominated by gluon-initiated processes with a partonic cross section that scales with α 2 s , whereas non-diffractive electroweak gauge boson pair production are due to quark-initiated processes with cross sections proportional to α 2 weak at leading order. Furthermore, the tt decay is significantly more challenging to reconstruct, which complicates the use of tighter event selection requirements to suppress the non-diffractive background. Using the timing detectors at the nominal resolutions of 60 ps and 20 ps, this background is reduced by a factor of ∼ 7 and ∼ 60.
We see that, if the timing detectors performance matches expectations, this channel may actually be a precision channel with almost no background, along the same lines as the well-known CEP γγ → γγ channel (see e.g. [3,66]).
The statistical significance is computed using the expression presented in Section 4, and a scan of the dimension-8 EFT operator couplings (ζ 1...6 ) is performed to find the 95% CL limits and the 5σ sensitivities, presented in Table 3. The results are presented for three possible scenarios, considering a 300 fb −1 integrated luminosity: without using information from timing detectors, and using them with nominal resolutions of 60 ps and 20 ps.   Table 3: 95% CL and 5σ projected limits on each of the couplings, setting the other ones to zero. Multiple timing detector performance scenarios are considered: no timing information, timing detector resolution σ t = 60 ps, and timing detector resolution σ t = 20 ps.

Sensitivity to neutral scalars
In this section we consider a model of neutral scalar coupling to photons and top quarks (see section 2). In such a case the direct competition with other channels should be taken into account. We have verified that for any value of mass and coupling, a 5σ discovery of the neutral scalar would first occur in the γγ → γγ channel according to the analysis from [4]. As a result the question that should be raised is the following: In the hypothesis of a discovery of the neutral scalar in the γγ → γγ channel, how well could we measure the scalar's coupling to top quarks? To answer this question, we work at the level of 95% confidence level. We assume two typical values for the coupling to the photons, where we also indicate the value of the partial width into photons. For both scenarios the neutral scalar can be considered as broad since Γ ≥ m. The case of maximally broad width also corresponds to the strongest coupling allowed by EFT validity or unitarity. In Fig. 9 we present the projected sensitivity of our search expressed in the pp → ttpp cross section. The CP-even and CP-odd results are very similar. We can see that in the   Figure 10: Projected sensitivity at 95% CL in the (m φ − f −1 tt ) plane. Regions above the curves are sensitive to our pp → tt pp search. mass range considered, the scenario with moderately broad width has better sensitivity. This is because the width from f γγ = m 4π is so broad that it tends to suppress the total cross section in this mass range.
Importantly, we can see that the use of the timing detectors is key in order to increase the sensitivity of the search. Without timing detectors, the projected sensitivity in the moderately broad case goes only up to 1200 GeV and is vanishing for the maximally broad case over the considered mass range. In contrast, using the nominal performance for the timing detectors, it turns out that the sensitivity in both cases reaches ∼ 1450 − 1500 GeV, a substantial improvement. In Fig. 10 we display the 95% CL sensitivity to the f tt coupling, either with or without timing detectors. We can again see that the timing detectors are key to expand the reach of the measurement.

Summary and perspectives
In this work, we have studied the sensitivity of the central exclusive pp → pp tt process to anomalous interactions between top quarks and photons at √ s = 14 TeV. The intact protons are detected with forward proton detectors -the PPS for CMS and the AFP detector for ATLAS. We focused on the semi-leptonic decay channel of the top quark pair. We considered signals from broad neutral resonances and from ttγγ dimension-8 local operators. Our analysis does not rely on a bump search method nor on shape analysis.
The main background for central exclusive production (CEP) processes consists of quantum chromodynamics (QCD) processes paired with forward protons from uncorrelated pileup interaction. CEP processes are efficiently selected by using the mass and rapidity of the outgoing two-proton system provided by the forward detectors. Furthermore, in the channel under consideration, it turns out that the timing detectors complementing the forward detectors open the possibility of significant, additional background reduction. For example, at L = 300 fb −1 , while the background with no timing information is about 100 events, the background gets reduced to O(1) events when using the timing detectors with nominal resolution of 20 ps. This shows that the timing detectors have the potential to make the CEP γγ → tt process a high precision channel, which can be used to search for physics beyond the Standard Model.
We considered a scenario of broad neutral scalars with either moderately (Γ ∼ m) or maximally (Γ ∼ 4πm) broad width. We find that the timing information is key in order to significantly increase the sensitivity of the channel. For example for resolution of 20 ps we find 95% CL sensitivity up to mass of ∼ 1500 GeV, while the sensitivity is significantly worse if no timing information is used.
An extension of the present work could be to investigate hadronic decays with highly boosted topologies. The kinematics of the new physics processes considered in this study are such that boosted hadronic decays of top quarks can be reconstructed as large radii jets more frequently than in the SM. However, to fully exploit this channel, a judicious choice on jet substructure techniques needs to be taken to separate the boosted top quark topology from the overwhelming background of light-quark and gluon jets. For example, variables that are sensitive to the number of prongs in the large-radius jet, such as N -subjettiness variables, and their ratios, could be used. Also (un)groomed variables could be exploited to separate QCD top quarks, which have contributions from underlying event activity and initial-state radiation effects, from the photon-induced top quark production, which does not. We leave this as possible future work.
The present study was only focused on dimension-8 operators, as motivated by the neutral particle scenario, which generates suppressed dimension-6 operators which have been neglected here. Investigating the sensitivity of CEP tt channels to dimension-6 photontop quark operators (namely the top quark anomalous dipoles) is an interesting direction, especially when the timing information is taken into account. This exciting possibility is left for further investigation.