Probing the nonstandard top-gluon couplings through $t\bar{t}\gamma\gamma$ production at the LHC

In this paper, we investigate the anomalous chormo-electric and chormo-magnetic dipole moments of top quark through the top pair production in association with two photons at the LHC. We present first the strategy to reconstruct this process assuming different source of background processes. Then we focus on the existing constraints from inclusive top pair production from Tevatron and LHC, adding the new LHC measurement. Afterwards, we introduce the new cross section ratio $R_{2\gamma/\gamma}=\sigma_{t\bar{t}\gamma\gamma}/\sigma_{t\bar{t}\gamma}$ and show the usefulness of this ratio to cancel most of the systematic uncertainties and its special functionality to constrain dipole moments. At the end, we use the scaler sum of the transverse momentum of jets, $H_{T}$, in order to define a signal dominated region and to obtain the limits on these anomalous top couplings using the different amount of expected data from LHC.


Introduction
Top quark is the heaviest elementary particle which has been discovered till now [1].Therefore from theoretical point of view it plays an important role in the electroweak symmetry breaking (EWSB) mechanism as it has the largest Yukawa coupling among all other fundamental particles.Furthermore, top sector is considered as one of the most likely places that the new physics can be probed.There are several models that predict the existence of new particles which are expected to couple to the top quark preferentially.Another attractive aspect of top quark is CP properties of its interactions with the SM fields.The CP violation has a tiny contribution in the SM model through the complex phase of CKM matrix which is not big enough to explain the observed matter anti-matter asymmetry in the universe and need a new source of CP violation which should come from beyond SM.The CP violating terms in the top quark interactions from BSM can apear as electric dipole moment (EDM), chormo EDM (CEDM), and weak EDM (WEDM) terms.Therefore, precise measurement of these moments will pave the path for finding the effect of new physics.
The first and second runs of Large Hadron Collider(LHC) with the center of mass energies of 7, 8, and 13 TeV confirmed the SM model of particle physics by discovering the long soughtafter Higgs boson [2,3] and no hint from the BSM has been found.However, there are many SM properties which is not yet measured accurately.Therefore, one of the missons for phase II upgrade of LHC is to make these measurements precise by providing the unprecedented amount of data which is expected to be 3 ab −1 integrated luminosity (IL), ultimately.In this context many SM rare processes becomes accesible such as multi-boson processes like VVV, VVVV as well as associate productions of top quark pair with multi-boson like t t+VV processes where, V stands for W, Z, and γ.These processes with multiple fermion and boson degrees of freedom are providing a rich ground for testing the fermion gauge-boson as well as triple and quartic gauge boson couplings predicted within the SM, also BSM [4,19].Even though the production phase space of these processes are limited due to higher energy threshold which leads to lower cross section.On the other hand, they are benefited from multiplications of final state particles which reduce the contributions of background massively.It should be mentioned that the cross section measurement of t tW , t tZ, and t tγ processes have been performed in the CMS and ATLAS collaborations [7][8][9][10].
The aim of this paper is to study how well the chormo-electric and magnetic dipole moments of top quark throughout the top quark pair production in association with two photons, t tγγ, can be measured.As these dipole moments are absent in tree level and they can only show up at higher order corrections, they turn out to be very small in the SM.Therefore, any deviation could indicate the presence of new physics, on the contrary, consistency with the SM values could constrain the new couplings which can contribute in this process.
The paper is organized as follow.In section 2, we describe effective field theory approach and define the top quark CEDM and CMDM in this context and then translation of these moments to the dimension-six operators is presented.In section 3, the t tγγ production at LHC within the SM framework is explained and then the implementation of dimension-six operators via the effective Lagrangian approach to calculate the cross section is presented.In section 4, the strategy to select signal process and consideration of related background processes are explained.Section 5, is dedicated to discuss the current constraint on d g V and d g A from inclusive top pair production then we introduce the new ratio of R 2γ/γ = σ t tγγ /σ t tγ to constrain the anomalous couplings.In section 6, we employe scaler sum of jet's transverse momentum distribution to define a signal dominated region and using the single bin experiment to extract the limit on the d g V and d g A respectively.Finally, in section 7, we summarise the results and conclude the paper.

gt t effective coupling
Effective field theory is a remarkable framework to describe the effects of physics at a high energy scale Λ, which is necessarily higher than the energy scale of the experiment.Essentially when the heavy degrees of freedom from high energy physics can not be directly produced, one can integrating them out resulting to new terms which are added to the SM Lagrangian.These new terms are composed from higher dimension operators suppressed with inverse power of Λ, and respect the Lorentz invariance, SM gauge symmetries, and Baryon, and lepton number conservations.Thus SM effective Lagrangian up to the dimension-six operators can be written as follow: where, L SM shows the SM Lagrangian.O (6) i are the dimension-six operators that have the dominant contribution in the experimental observables and c i 's are unknown dimensionless coefficients which show the strength of the new physics coupling to the SM particles.After the EWSB, the integrated out terms will produce the new couplings which does not exist at tree level in SM such as, electric and magnetic dipole moments, as well as couplings which correct the SM interactions.The most general form of gt t coupling assuming up to the dimensions-six operators can be depicted as follows: where, g s , λ a , and G a µν are strong coupling constant, Gell-Mann matrices, and gluon field strength tensor, respectively.The d g V and d g A are real parameters which represent the top quark chormo-magnetic and chormo-electric dipole moments.The first term is the SM interaction, while the rest terms contain the gt t and ggt t interactions and are generated from dimension-six operators based on the convention used in [11,12] which has the following form: where, qL3 and t R are the weak doublet of left-handed quark field and the right-handed top quark field respectively.φ is weak doublet of Higgs field and φ = iτ 2 φ * .The relation between the dimension-six operator in equation 3 and chormo-moments of the top quark after the symmetry breaking can be written as: where, m t is top quark mass and v is vacuum expectation value of Higgs field.The chormoelectric dipole moment (CEDM) and chormo-magnetic dipole moment (CMDM) are related to the real and imaginary part of O 33  uGφ and both are considered in this study.In the SM, CMDM of top quark (d g V ) can be generated via one loop QCD and electroweak diagrams.There are two types of Feynman diagrams which contribute to the QCD part.First diagram is the one which external gluon emitted from the internal top quark and in the second diagram external gluon is coming from the exchanged gluon due to non-abelian properties of strong interaction.The total amount of QCD contribution is d g V = −0.008[13] which is dominated SM loop contribution.In the electroweak loop diagrams W ± , Z, and Higgs can be exchanged while the gluon coming from the internal quark.This tiny contribution is about 12% of QCD part but with the opposite sign.Finally, the total amount of SM loop correction is d g V = −0.007[13].CEDM contribution in the SM arises from the three loop diagrams and shown to be very small [13].
Direct bounds on the CMDM and CEDM from inclusive and differential measurements of t t process in the Tevatron and LHC can be obtained [14-16, 18, 25].Also with the considerable amount of the data that LHC in its upgraded phase will collect, the SM rare processes such as t t in association with two heavy gauge bosons and multi top quark productions are shown to be sensitive to these anomalous interactions of top and gluon [6,19].In addition, CMS experiment has obtained the limits on these dipole moments via the measurement of t t spin correlation using the √ s = 8 TeV data [20].Moreover, it has been shown that there is a large sensitivity to probe the CMDM and CEDM in the high invariant mass of top pair process where, the top quarks are highly boosted [21].Single top tW production is also shown to be sensitive to top quark chormo-moments via its cross section and top quark polarization [22,23].
In addition to the direct bounds, there are also indirect bounds on the top quark dipole moments from low energy measurements which are known to be the stringent limits up to now.For example, from measurement of rare B-meson decays b → sγ, top quark chormo-magnetic moment constrains at 95% confidence level (CL) with −3.8 × 10 −3 < d g V < 1.2 × 10 −3 [24].Also measurement of neutron electric dipole moment could constrain the top quark chormo-electric dipole moment by |d g A | ≤ 0.95 × 10 −3 at 90% of CL [25].In the next sections, we examine the potential of t tγγ process to probe the top quark CMDM and CEDM.

t tγγ production at proton-proton collisions
Top pair production in association with two photons within the SM framework can occur through the gluon-gluon fusion or quark antiquark annihilation at the LHC.The Feynman diagrams with the dominant contribution for the process of t tγγ are shown in the Figure 1.The reason that the dominant production mode for t tγγ is from q q annihilation comes from the fact that photons can radiate either from top quarks or initial state quarks while it is not the case for gluon-gluon fusion mode production.For instance, the calculated contribution of q q production mode at LO with √ s = 13 TeV for t t, t tγ, and t tγγ processes are 13%, 32%, and 66%, respectively.In order to calculate the cross sections as well as event generation for the signal and relevant backgrounds, MadGraph5 aMC@NLO package [26] is used.The total cross section is calculated assuming the top quark mass m t = 172.5 GeV, W boson mass m W = 80.37 GeV and G F = 1.16639 × 10 5 GeV 2 .The NNPDF3 PDF is used as parton distribution functions [27].The values of factorization scale (µ F ) and renormalization scale (µ R ) are calculated event by event and considered to be µ , where the sum is over the visible final state particles.Top quark and W boson decays are considered in the narrow width approximation and spin correlation in the top quarks decay is considered.
To calculate the cross section of t t+X including the chormo-moments of top quark the effective Lagrangian is imported via the FeynRules package [28] and the obtained UFO model [29] is linked to the MadGraph5 aMC@NLO in order to generate events and calculate the cross section.The total calculated cross section at leading order arising from dimension-six operators in the equation 3, including the CMDM and CEDM of top quark are parametrised as: Figure 1: Dominant Feynman diagrams for t t in association with two photons process within the SM framework.
where, the σ SM is the SM cross section.The second term is the interference between the SM and real part of O 33  uGφ operator which has 1 Λ 2 contribution.The third and forth quadratic terms correspond to pure real and imaginary part of O 33  uGφ which have the contributions of order of 1 Λ 4 .It should be mentioned that dimension eight operators also generate additional terms in the order of 1 Λ 4 but we drop those terms as we only considered the dimension-six operators in this analysis.In the equation 5, there is no linear d g A term as the cross section must be a CP-conserving observable.In addition to the signal process, we generate several reducible background processes such as t tγ, W γγ+jets, single top+γγ, Zγγ+jets, diboson+γγ including the WWγγ, WZγγ and ZZγγ and finally γγ+jets as well as an irreducible background which is the SM t tγγ with the MadGraph5 aMC@NLO .All the generated samples are passed to the Pythia 8 [30] in order to perform the parton showering and hadronization.The Jet clustering is performed using the antik t algorithm [32] implemented in the FastJet package [33] using the radius parameter of R=0.5.B-tagging and miss-tagging efficiencies for the jets which are originated from the hadronization of b-quark is considered [34].These efficiencies are parametrized based on the transverse momentum of the jets.In this analysis fast detector response estimated using the Delphes 3.4.1 package [35] based on the similar condition of CMS detector.

Analysis strategy
In this section we present the analysis strategy to select the t tγγ signal events.We also discuss the relevant background processes and estimation of their contribution in this final state.As a result, one can obtain the potential power of this process to probe the chormo-moments of top quark which is going to be discussed in the next sections.In this analysis we consider the semi-leptonic decay mode of t tγγ process as this decay mode has the large contribution as well as the fact that presence of one lepton along with the two photons will help suppress the background processes effectively.
In order to select signal events we require to have exactly two isolated photons with the transverse momenta p T > 25 GeV and pseudorapidity of |η| < 2.5.We also demand to have a lepton (electron or muon) with the same p T and η cut values as photon.Moreover, we veto events containing any other leptons in order to suppress the backgrounds including Z bosons such as Zγγ+jets.The requirements for the jet selection are p T > 40 GeV, |η| < 5 and for the btagged jets are p T > 40 GeV |η| < 2.5.In order to suppress the backgrounds which does not contain a W boson we require the missing transfers energy (MET) to be greater than 30 GeV.In addition to the mentioned cuts, in order to have well isolated objects we require the angular separation between the two photons as well as between the photons and other objects to be ∆R(γ, X) = ∆φ 2 + ∆η 2 > 0.5 where X=e, µ, jets, b-jets, γ.On top of the other requirements, we ask the events to have H T > 300 GeV where this variable is defined as H T = Σ p T , and the sum is performed over the transverse momentum of jets within the defined acceptance region.The higher value of H T corresponds to the heavier mass final states which is t t in the case of our signal and could suppress the processes with lower mass and no mass states such as W+jets+γγ and γγ+jets respectively.Table 1 shows the expected yields for the two signal samples d g V =0.2, and d g A =0.2 as well as the SM backgrounds after applying each set of selection cuts.It should be mentioned that the expected yields for the signal samples comprise the contribution of anomalous top quark dipole moments, SM t tγγ contribution, and their interference.
Apart from the background processes with two real photons there is a contribution from the t tγ process.At first it should be mentioned that t tγ is a different process from t tγγ as the former has two photons in the matrix elements while the earlier has one.However, events from t tγ process may have overlap with t tγγ when the showered photon by Pythia lands into the generator acceptance of t tγγ.Due to high value cut applied for ∆R between the photons and other objects one would expect this overlap to be small.However, we have subtracted this contribution in order to be precise in our background estimation.The total obtained yield for t tγ after applying all the selection cuts found to be 14 for 100 f b −1 .
In addition to the above background processes, in the real experiment there is a probability that the jets are misidentified as a photon.The reason behind this misidentification is that inside a jet there are considerable amount of neutral hadrons such as pions which promptly decay into the two photons in the boosted topology.Therefore, produced shower of these two close by photons will overlap inside the electromagnetic calorimeter and misidentified as a photon which so called fake photon.As a result, in a real detector, processes such as W/Z+jets, W/Z+jets+γ, multijet+γ, and multijet which have large cross sections may pass our selection criteria due to this mis-reconstruction of jets.The probability of this misidentification in the current real experiments such as CMS and ATLAS are varied between 10 −3 − 10 −5 depending on the transverse momentum of a photon.We have estimated the contribution of these processes by applying the selection cuts explained in the previous section except the photon.The resulting cross section for the discussed processes are laying below 10 3 pb.Therefore, applying the fake photon probability will brings their contribution into the negligible level.However, precise estimation of fake photons is usually performed using the data driven techniques and full simulation of detector components which is beyond the scope of this analysis.

t tγγ role to constrain strong dipole moments of top quark
In this section we explain how the t tγγ process can play a complementary role to constrain the chormo-moments of top quark.At first we discuss the current bounds which one can obtain from the inclusive cross section measurements of t t+X where, X=γ, jets.Then in the second part the constraints from a new defined ratio of σ t tγγ /σ t tγ and the possible improvements with respect to inclusive t t cross section measurements will be discussed.

Constraints from t t+X production measurements
In order to obtain the stringent bounds on d g V and d g A one could combine results from different experiments.In this section we consider the measurements on the inclusive cross sections of t t in Tevatron from pp collisions at √ s=1.96TeV [36], combined measurements of CMS and ATLAS with pp collision at √ s=8 TeV [37] and two other recents measurements of CMS on the cross section of t tγ at √ s=8 TeV [10] and cross section of t t at √ s=13 TeV [38].In order to obtain the experimental bounds, one needs to drive the functionality of the total cross section to the anomalous couplings based on the hadrons that collide and the center of mass energy that the collisions occur.Exploiting the method explained in section 3, we evaluated the total cross sections including the leading order contribution of top quark chormo-moments.Table 2 shows the obtained values for each coefficient belong to the linear and quadratic terms for each measurement.Then the constraints obtained using the measured values for the total cross sections along with the precise available cross sections that SM predicts at next-to-leading order (NLO) or next-to-next-leading order (NNLO) calculated with Top++ [39]. Figure 2 (left) depicts the two dimensional bounds on d g V and d g A for each measurements separately and the right one shows the overlap region of all measurements in the zoomed view.The total colorful area is the bound that obtained from Tevatron and LHC8 which is compatible with the results of Refs [15,21].The pink colored area is the one obtained adding CMS13 t t cross section measurements with 2.2 f b −1 integrated luminosity and t t + γ measurement at CMS at center of mass energy of 8 TeV.As it can be seen the improvement in the bounds is not significant and it is only on the d g V coupling.The t t + γ measurement also does not produce tighter bounds.As t t inclusive cross section measurement at CMS13 is systematically dominated, adding more data recorded by CMS in 2016 will not increase the precision on the measurements by large value and consequently no big improvement in the top quark dipole moments bounds is expected.Moreover, one can show that considering better precision on the inclusive cross section only leads to obtain the better bounds on d g V .Therefore, we introduce a new observable in the selected phase space which provide the different functionality and can be used to tighten the current bounds especially on CP violating coupling.

Cross section ratio
As it was discussed in the previous section the current cross section measurements of the top quark pair production has a limited power to tighten the current bounds on top quark chormo-moments.Therefore, we propose a new observable in order to constrain the current allowed phase space of these anomalous couplings which is the ratio of the cross section of t tγγ to the t tγ within the selected phase space and defined as: Using the ratio has the advantage of cancelling the systematic uncertainties.From the theoretical point of view, uncertainties from parton distribution function and α s can be reduced assuming the leading order or higher order corrections.Apart from that several systematic uncertainties arising from luminosity, jet energy scale, b-jet tagging, and lepton identification can be canceled out.Especially using the proposed R 2γ/γ will reduce effectively the photon identification uncertainties as well.
There are several studies which are shown the idea of using the cross section ratio in order to reduce the uncertainties.For instance in the Ref [40], authors shows that using the ratio of σ t t+H /σ t t+Z , top Yukawa coupling can be measured with 1% precision assuming the proton-proton collision data with center of mass energy of 100 TeV.In another study it was shown that at the LHC the cross section ratio of single top quark production in association with a photon over the single top quark production, σ tjγ /σ tj is a precise observable which can probe the top quark electric and magnetic dipole moments [41].Also it has been presented that using the σ t t+γ /σ t t and σ t t+Z /σ t t, several sources of uncertainties cancel and they could be more sensitive observables to the electroweak dipole operators of the top quark [42].The available measurements on the cross section ratio of σ t t+γ /σ t t at the Tevatron and LHC and the measured cross section of single top quark in association with a photon are in Refs.[9,10,43,44].
We have tested R 2γ/γ against the variation of renormalization and factorization scales by generating the dedicated samples considering the µ f = µ R and equivalent them once to the 2 × Q 0 and subsequently to Q 0 /2.Then the ratios for each values of µ f = µ R are calculated respectively.The uncertainty due to this scale variation for R 2γ/γ is obtained below ±0.5% while the uncertainty for each total cross section is about 12%.We also evaluated the robustness of defined ratios against the variation of parton distribution functions (PDFs), by generating the different samples for t tγγ and t tγ using the three different PDF sets naming NNPDF3.0 [45], MSTW08 [46], and CTEQ6L1 [47].Then we calculate the R 2γ/γ ratio for each set of PDFs which results an uncertainty about 2%.The stability of ratio against different uncertainties shows that this is a robust experimental observable.
In the following we discuss the effect of these anomalous couplings on the defined ratio.As it was explained in the section 3, the contribution of gluon-gluon fusion in t tγγ is lower than the t t + γ and t t processes, considering the photon radiation from this initial state is forbidden.Thus the ratio R 2γ/γ is benefited from this dissimilar functionality and can probe these anomalous couplings in the regions which is different from the one obtained from the normal inclusive cross section.Considering the high amount of integrated luminosities expected to be delivered by LHC, also the cancelation of different sources of uncertainty, this ratio in the selected phase space can be measured with very good precision.Therefore, We have considered the 5% total uncertainty and have extracted the two dimensional 95% bounds on the d g V and d g A . Figure 3 (left) shows the 95% C.L allowed regions extracted from different measurements with the dashed lines comparing with the blue solid bound which is obtained from the R 2γ/γ , considering 5% uncertainty.Figure 3 right compares the current combined limit obtained from Tevatron and LHC at 8 and 13 TeV shaded gray area, with the bound obtained using the R 2γ/γ in the zoomed view.It can be seen that the new behaviour of this ratio can tighten the current allowed region for both anomalous couplings but especially has a considerable power to constrain the d g A .The obtained bounds from R 2γ/γ for each couplings are −0.0088< d g V < 0.0083 and −0.037 < d g V < 0.037 when one considers only one coupling at a time.

Kinematic handel
In this section, we explore the sensitivity of t tγγ process to probe the top quark CMDM and CEDM by looking into the kinematic distribution of final state particles.Equation 2 indicates that additional terms originating from dimension-six operators have different Lorentz structure as well as particular dependence on the fields momentum.Thus, one expects that the rate and kinematic distribution of final state particles alter due to presence of such anomalous couplings.
Figure 4 shows some normalized kinematic distributions which compares the expected SM t tγγ process with the same process when we apply only one of the d g V =0.3 or d g V =0.3 each time.Top left plot is the H T distribution and the top right and bottom plots show the missing transverse energy and invariant mass of two photons, respectively.Figure 4 indicates that including the new terms in the effective Lagrangian modifies the shape of these distributions especially in the tail of distributions where, the process is happening in the higher energy scale and shows the momentum dependence of these anomalous couplings.It should be mentioned that these plots include the effect of showering, hadronization, object clustering and detector effects.
We use H T distribution as a sensitive observable to find potential upper limit on the cross section of t tγγ in presence of d g V and d g A and then using this upper limit to obtain the constraint on these coupling assuming no any deviation from the SM is observed.We use the single bin counting experiment over the H T distribution in the signal region which is the region with high value of H T .Essentially this signal region have to be optimised for the best cut value of H T .The conventional criteria is to obtain the value which results the lowest limit on the cross section or in the other word the best power to bound the d g V and d g A .Therefore, one needs to minimize the 95% expected limit on the signal cross section in order to find the optimized H T value.It is worth mentioning that in the procedure of optimisation one needs only to consider the statistical uncertainty and no any systematic uncertainty is applied.The statistical procedure to extract the expected limit is presented in the following.The probability for measuring the N events in the signal region is given by Poisson distribution: where σ sig , L, ε, and B are signal cross section, integrated luminosity, signal efficiency and number of expected background events, respectively.Except the signal cross section which is the parameter of interest the rest of parameters are known.Signal efficiency in the signal region is defined as the number of events passing our selection cuts explained in the section 4 and certain cut value of H T over the total number of events which only pass the H T cut.Exploiting Bayesian approach one can extract the 95% C.L upper limit on the signal cross section in the signal region by integrating over the posterior probability defined as: The explained statistical tool is employed to find the optimized cut value for H T .Therefore, the 95% C.L expected limits on the cross section for different values of H T are calculated which start from 400 to 1200 GeV in 100 GeV step.The optimization is done separately when one of the couplings is considered while the other coupling is set to zero.This procedure is also preformed for different values of each coupling to see if any dependency on the parameter of coupling exists.Figure 5 shows the 95% expected limit as a function of H T for d g V = 0.1, 0.3 considering the 100 f b −1 integrated luminosity.
The minimum expected limit is obtained for the H T =1000 GeV.The same procedure is implemented for d g A = 0.1, 0.3 and the same optimized value is obtained.Therefore, we consider the  We find the limits on the d g V and d g A by comparing the expected limit on the cross section with the theoretical cross section in the signal region considering 100 and 300 f b −1 at √ s= 13 TeV and 3000 f b −1 at √ s= 14 TeV.It should be mentioned that the compared theoretical cross section curves in the signal region is subtracted from the SM value to consider the pure non-SM cross sections originated by dimension-six operators.The results obtained for different integrated luminosities and different center of mass energies are shown in the table 3.
Figure 6 shows the upper limits on the d g V (left) and d g A (right) considering the 300 f b −1 integrated luminosity which are compared with the theory curves.The obtained bounds from H T distribution shows very good improvement using the 3000 f b −1 expected amount of data especially on the d g A coupling.It should be mentioned that generally, the optimized cut value changes when one assumes the different integrated luminosities.Thus, in order to obtain the limit for each considered amount of data, the optimization procedure is performed separately.

Summary
For the first time rare SM top quark pair in association with two photons production at the LHC is considered to investigate the prospects of constraining the top quark chormo-moments.In the SM, these dipole moments are produced through the higher QCD, electroweak loop corrections which results to tiny values and any deviation from SM values would be a hint for new physics.In addition, using the process with high particle multiplicity helps reduce the number of backgrounds effectively.The analysis is performed based on the effective Lagrangian approach where, the dimension-six operators induced modification to the gt t coupling.We considered the semi-leptonic decay of top quark pair and defined a set of selection cut to reconstruct this final state effectively.
In the next part, a new cross section ratio in the selected phase space as R 2γ/γ = σ t tγγ /σ t tγ , is introduced.This ratio is important in two aspects in dealing with the top quark couplings.First, In this observable a considerable amount of theoretical and experimental uncertainties cancel out.In addition to the conventional reduction of uncertainties, the one related to the photon identifications could be reduced due to presence of photon in both numerator and denominator.Second, due to different contribution of gluon-gluon production mode in the t tγγ and t tγ, the functionality of the ratio can probe the different phase space of top quark couplings and let to constrain especially the CP-violating coupling, d g A , effectively.Considering a 5% precision on this ratio measurement, we obtained the −0.0088 < d g V < 0.0083 and −0.037 < d g V < 0.037 limits for each coupling.
We also explored different kinematic distributions of final state particles which include the effect of parton showering, hadronization, jet clustering and detector simulation.We selected the distribution of scaler sum of jets transverse energy, H T .The contribution of these non-SM couplings in the higher value of H T is pronounced with respect to the pure SM contribution due to the dependency of new couplings to the momentum.We have optimized the H T cut value in order to define a signal region where, the best power to probe these couplings is obtained.Finally, we  used a counting bin experiment method based on Bayesian approach to find the upper limit on the signal cross section in the signal region.By comparing the theoretical cross section and upper limit in the defined signal region we have extracted the −0.006 < d g V < 0.03 and −0.014 < d g A < 0.014 bounds using the 3 ab −1 integrated luminosity.Figure 7 shows the summary of the limits for the d g V (left) and d g A (right) obtained with different observables introduced in this analysis assuming the different integrated luminosities and the combined results from Tevatron and LHC8.

Figure 2 :
Figure 2: Two dimensional allowed regions for d g V and d g A using the different measurements which has been performed so far.The left one shows each expriment bounds and the right one depicts the overlap region in the zoomed view.

Figure 3 :
Figure 3: Comparison the current obtained bounds from Tevatron, and LHC at 8 and 13 TeV using the inclusive top pair production with the extracted 95% C.L allowed region obtained from R 2γ/γ ratio in the selected phase space is shown in the left plot.The right one illustrates the zoomed view in the overlap region and shows the improvement in the obtained constraints from the R 2γ/γ .

Figure 4 :
Figure 4: Normalized distributions of H T , missing transverse energy, and invariant mass of two photons.The plots compare the SM t tγγ with the same process when only one of the d g V , d g A are applied.

Figure 5 :
Figure 5: The 95% expected limit on the cross section as a function of H T for two different values of d g V is shown.The optmized H T value found to be 1000 GeV considering the 100 f b −1 integrated luminosity.

Figure 6 :
Figure 6: 95% C.L expected upper limits on the signal cross section in the signal dominated region compare with the theoretical cross sections of signal for 300 f b −1 integrated luminosity.

Figure 7 :
Figure 7: The summary of the limits for the d g V (left) and d g A (right) obtained different observables introduced in this analysis assuming the different integrated luminosities and the combined results from Tevatron and LHC8 are illustrated.

Table 1 :
Expected number of events for the two signal samples and backgrounds after apply the selection cuts for the 100 f b −1 Integrated luminosity (IL).