Probing the Top-Higgs Yukawa CP Structure in dileptonic $t \bar t h$ with $M_2$-Assisted Reconstruction

Constraining the Higgs boson properties is a cornerstone of the LHC program. We study the potential to directly probe the Higgs-top CP-structure via the $t\bar{t}h$ channel at the LHC with the Higgs boson decaying to a bottom pair and top-quarks in the dileptonic mode. We show that a combination of laboratory and $t\bar{t}$ rest frame observables display large CP-sensitivity, exploring the spin correlations in the top decays. To efficiently reconstruct our final state, we present a method based on simple mass minimization and prove its robustness to shower, hadronization and detector effects. In addition, the mass reconstruction works as an extra relevant handle for background suppression. Based on our results, we demonstrate that the Higgs-top CP-phase $(\alpha)$ can be probed up to $\cos\alpha<0.7$ at the high luminosity LHC.


Introduction
After the discovery of the Higgs boson at the Large Hadron Collider (LHC) [1,2], the determination of its properties has become a prominent path in the search for physics beyond the Standard Model (SM) [3][4][5]. So far, measurements based on the Higgs signal strengths conform to the SM predictions [6,7]. However, the tensor structure of the Higgs couplings to other matter fields remains relatively unconstrained. A particularly interesting option is that the Higgs interactions present new sources of CP-violation, which could be a key element in explaining the matter-antimatter unbalance in the Universe [8,9].
CP-violation in the Higgs sector has been searched for at the LHC mostly via Higgs couplings with W ± and Z gauge bosons throughout the Higgs decays h → W + W − and ZZ [10][11][12][13][14][15][16][17][18][19]. However, these possible CP-violating interactions are one-loop suppressed, arising only via operators of dimension-6 or higher [20,21]. On the other hand, CP-odd Higgs fermion interactions could manifest already at the tree level, being naturally more sensitive to new physics [22? ? ? ? ? ? ? -33]. Of special interest is the Higgs coupling to top quarks, as y SM t ∼ 1. Relevant constraints to the CP-structure of the top-Higgs coupling can be indirectly probed via loop-induced interactions in electric dipole moment (EDM) experiments and gluon fusion hjj production at the LHC [13,[34][35][36]. While electron and neutron EDM can set very stringent bounds on CP-mixed top Yukawa, it critically assumes the Yukawa coupling with the first generation fermions the same as in the SM, and that new CP-violating interactions are limited to the third generation. A minor modification on the strength and CP-structure of the Higgs interactions to first generation can considerably degrade these constraints [34].
Analogously to the direct (model independent) measurement of the top Yukawa strength, the direct measurement for its CP-phase also has the pp → tth channel as its most natural path. Going beyond the signal strength analysis for this channel becomes even further motivated given i) the recent CMS result, showing observation for the tth signal with 5.2σ observed (4.2σ expected) [43,44]; and ii) the High-Lumi LHC (HL-LHC) projections, indicating that this channel will be measured with a very high precision, δy t < 10% [45]. Hence, that is the approach which we follow in the present study, exploring the spin correlations in the top pair decays.
The different Higgs-top CP-structure affects the top-spin correlation, that can propagate to the top quark decay products. The most natural channel to perform such a study is the dileptonic top decay, as the spin analyzing power for charged leptons is maximal. Spin correlations can be enhanced looking at the tt rest frame, however the large experimental uncertainties at hadron collider due to top reconstruction and frame change make this measurement challenging. We will present a method for the top reconstruction that will address these issues, allowing the construction of relevant CP observables at tt rest frame.
The aim of this paper is twofold. First, we will study direct Higgs-top CP measurement via the tth production, exploiting full kinematic reconstruction in the dilepton channel. For this purpose we adopt a kinematic reconstruction method presented in Ref. [46]. Second, since this reconstruction method was studied only at the parton-level, we would like to investigate its performance further beyond the parton-level, including more realistic effects such as parton-shower, hadronization and detector resolution. Although this reconstruction method was initially presented for the top quark pair production tt, we will show that it can be easily adopted to the tth channel. This paper is structured as follows. In section 2, we will present our setup and the kinematic observables to access the CP-phase. In section 3, we will discuss the method for kinematic reconstruction of the dileptonic tops. In section 4.1, we show that the angular correlations can be obtained via this method, presenting the results at the parton level, while in section 4.2, we perform a full signal and background analysis, including parton-shower, hadronization and detector effects, and discuss the prospects of the CP measurement in the tth channel with dileptonic top-quarks and h → bb decays.

Setup and angular observables
We start with the following Lagrangian containing the top Yukawa coupling where v = 246 GeV is the SM Higgs vacuum expectation value, K is a real number and α represents the Higgs-top CP-phase. Hence, the SM Higgs-top interaction is represented by the pure CP-even coupling (K, α) = (1, 0), while (K, α = π/2) parametrizes a pure CP-odd Higgs boson. Various observables have been explored in the literature to access the Higgs-top CP-phase in tth events, e.g., total cross-section, transverse Higgs momentum, invariant tt mass, and spin correlations in the top quark decay products [22][23][24][25][26][27][28][29][30][31]. The latter is specially interesting as it can accurately probe the Higgs-top interaction, exploring the spin polarization of the tt pair via a shape analysis.
While at hadron colliders the top quarks are unpolarized, the top and anti-top pair are highly correlated. This fact can be experimentally revealed by spin correlations between the top decay products [47]. The top-quark spin polarization is transferred to the top decays, t → W + b with W + → + ν or d + u, where the spin analyzing power is maximal for the charged lepton + and the down quark d. Exploring this, Ref. [23] demonstrates that the difference in azimuthal angle between the leptons ∆φ lab (from top decays) in the laboratory frame can directly reveal the CP-structure of the Higgs-top interaction with the sensitivity of the measurement substantially enhanced in the boosted Higgs regime, as shown in the left panel of Fig. 1. This study shows that the Higgs-top coupling strength and the CP structure can be directly probed with achievable luminosity at the HL-LHC, using boosted Higgs substructure in the dileptonic channel.
In the present paper, we would like to include observables in the center-of-mass frame of tt system, exploiting novel kinematic reconstruction methods. Among several distributions studied in the tt differential cross-section measurements, we find that the production angle θ * in the Collins-Soper reference frame brings an interesting correlation, as shown in Fig. 1 (middle). This θ * is a collision angle of the top with respect to a beam axis in the tt centerof-mass frame and therefore the two top quarks have equal and opposite momenta, with each making the same angle θ * with the beam direction [48]. See Ref. [29] for a recent application of a similar observable which probes the spin and parity of a new light resonance.
All these variables, including ∆φ lab and θ * , are sensitive only to the square terms cos 2 α and sin 2 α (CP-even observables), providing only an indirect measure of CP-violation, missing the interference term between CP-even and odd couplings, cos α sin α, that can capture a relative coupling sign. To define CP-odd observables, we have to further explore the spin polarization of the tt pair. Remarkably, tensor product relations of the top-pair and the final state particles, that follow from totally antisymmetric expressions (p a , , are examples of such observables. In the present work, we will focus on a relevant tensor product that has information on the top and anti-top and the charged leptons from top-quark decays, maximizing the spin analyzing power: (p t , p t , p + , p − ). In general, this expression leads to several terms, making it difficult to define an observable that extracts all its information. However, this relation opportunely simplifies at the tt center of mass (CM) frame, resulting in a single triple product provided that we can fully reconstruct the tt CM frame. We further explore this relation to define our CP-odd observable that is defined in the [−π, π] range. In Fig. 1 (right), we display the ∆φ tt distributions at the parton-truth level for different CP hypotheses α. The CP-mixed cases α = π/4 from −π/4 display different distribution shapes, confirming that ∆φ tt is a truly CP-odd observable.
One may quantify these differences via an asymmetry, comparing the number of events with positive and negative ∆φ tt [25]: where A ∈ [−1, 1]. While the asymmetry A results in deviations from the SM hypothesis of at maximum O(4%) (for α ≈ ± π 4 ), ∆φ tt presents parameter space regions that can reach up to O(10%) of difference in ratio d∆φ tt , as shown in the subfigure of the right plot. The latter leads to a potentially stronger distinguishing power that can be explored via a shape analysis. Due to difficulty in event reconstruction to go to the tt rest frame, the ∆φ tt observable has not been investigated in a realistic analysis so far. In this study, we shall attempt to reconstruct the θ * and ∆φ tt variable at hadron-level including detector resolution. We will then examine how these two observables (∆φ tt and θ * ) would improve the existing analysis with the laboratory angle (∆φ lab ). We will make a brief comment on the sign of CP angle as well.

Brief review of kinematic reconstruction
In this section, we briefly review the reconstruction method that we adopt. Our algorithm is entirely based on mass minimization. Thus, it is more flexible for new physics analyses and robust for our spin-correlation study 1 . The event topology considered in this paper is shown in Fig. 2, together with three possible subsystems. The blue dotted, the green dot-dashed, and the black solid boxes indicate the subsystems (b), ( ), and (b ), respectively. We consider that the Higgs (denoted as h) is fully reconstructed, in which case the only source of the missing transverse momentum is two neutrinos from the top decays.
In the presence of two missing particles at the end of a cascade decay, M T 2 provides a good estimate of mass information in the involved decay [49,51,53,58]. Following notations and conventions of Ref. [46], we define M T 2 as follows: where M T P i (i = 1, 2) is the transverse mass of the decaying particle in the i-th side andm is a test mass, which we set to zero in our study. q iT is the unknown transverse momentum of the i-th missing particle, which is a neutrino in this case. Individual values ( q 1T and q 2T ) are unknown and only their sum ( q 1T + q 2T ) is constrained by the total missing transverse momentum, / P T .
Another mass-constraining variable is the M N [46,53,59], which is the (3+1)-dimensional version of Eq. (3.1): where the actual parent masses (M P i ) are considered instead of their transverse masses (M T P i ). Note that the minimization is now performed over the 3-component momentum vectors q 1 and q 2 [53]. In fact, at this point the two definitions (3.1) and (3.2) are equivalent, in the sense that the resulting two variables, M T 2 and M 2 , will have the same numerical value [53,54,60]. However, M 2 begins to differ from M T 2 when applying additional kinematic constraints beyond the missing transverse momentum condition q 1T + q 2T = / P T . Then, the M 2 variable can be further refined and one can obtain non-trivial variants as shown below [54]: is the mass of the parent (relative) particle in the i-th decay chain and a subscript "C" indicates that an equal mass constraint is applied for the two parents (when "C" is in the first position) or for the relatives (when "C" is in the second position). A subscript "X" simply means that no such constraint is applied. Note that M 2XX in Eq.
More specifically, in the tt-like production (tt + X where X is fully reconstructed), we could use the experimentally measured W -boson mass, m W , and introduce the following variable: Similarly, taking the mass m t of the top quark in the minimization, we can define a new variable in the ( ) subsystem: Although these mass-constraining variables are proposed for mass measurement originally, one could use them for other purposes such as measurement of spins and couplings [61]. In our study, we use these variables to fully reconstruct the final state of our interest, with the unknown momenta obtained via minimization procedure. These momenta may or may not be true particle momenta but they provide important non-trivial correlations with other visible particles in the final state, which helps reconstruction.
Based on Ref. [46], we define the following parameter space: where m 2Ct , leading to positive x, y, and z. On the other hand, the wrong pairing could give either sign. Finally, by requiring that the partition which gives more "plus" sign as the "correct" one, we can resolve two-fold ambiguity. Then we treat the corresponding momenta of two missing particles (which are obtained via the minimization procedure) as "real" momenta of two missing neutrinos. If both partitions give the same numbers of positive and negative signs (called "unresolved case"), we discard those events. From Ref. [46], the efficiency of this method is known to be about 88%, including unresolved events with a coin flip, 50% probability of picking the right combination. Since we ignore those events to obtain a highpurity sample, the corresponding efficiency becomes 83%. We also note that we assign the parton level (resolved) negative sign for a partitioning, if a viable solution is not found during minimization. This is because the wrong pairing would fail more often than the correct paring. With the obtained neutrino momenta, now we can reconstruct momenta of W s and top quarks for the CP measurement of the top-Yukawa coupling.

Top-Higgs Yukawa coupling with M 2 -assisted reconstruction
We show our parton-level results in section 4.1, and detector-level (including parton-shower, hadronization, and detector resolution for signal and backgrounds) in section 4.2. For our parton-level study, we assume that the Higgs is fully reconstructed. We separate these semirealistic effects to better examine the capability and feasibility of reconstruction methods in the dileptonic tth production. Throughout our study, we use OPTIMASS [55] to obtain momenta of two invisible neutrinos, following the reconstruction method described in the previous section.

Parton-level analysis
Parton level events are generated at leading order by MadGraph5 aMC@NLO [62] in chain with FeynRules package [63] without any generation level cuts. We use the default NNPDF2.3QED parton distribution function [64] with dynamical renormalization and factorization scales set to m 2 T (transverse mass of the visible system) at the 14 TeV LHC. In this section, we focus on comparison between Monte-Carlo truth and parton-level results without worrying about effects of hadronization and parton-shower, which will be the topic in the next section. Performing the procedure described in the previous section, we obtain the momenta of two neutrinos and also resolve two fold ambiguity in the dilepton final state, which allows full reconstruction of the final state. the purity of the samples is known to be 96% [46]. Note that, throughout this paper, all plots are generated with the "resolved" events, after discarding "unresolved" ones. We find that the efficiency of our method is = 81.38%, which is consistent with 83% as in Ref. [46]. The resolved events contain both correct and wrong combinations and the fraction of the correct combination out of the resolved events is defined as purity.
To examine performance of momentum reconstruction, we show in Fig. 4 correlations between ∆p x ≡ p x,true − p x and ∆p z ≡ p z,true − p z , and between the difference in magnitude | p | − | p true | and the direction mismatch ∆R( p, p true ) for M (b ) 2CW for the SM case (α = 0). Other CP angles show similar results. Here p true is the true momentum of a neutrino and p is the momentum from the minimization using OPTIMASS. In the upper panel, the scatter plots are generated without any cuts, while a mass cut (165 GeV < M As shown in Ref. [23], the difference in azimuthal angles of two isolated leptons in the laboratory frame ∆φ lab provides a good discrimination of different CP angles at the boosted regime. We reproduce this result as already shown in the left panel of Fig. 1. Once the cuts of p T (h) > 200 GeV and m > 75 GeV are applied, the distributions acquire high distinguishing power, as shown in the figure. Thanks to the fact that it depends only on the leptons, and it is reconstructed at the laboratory frame, this observable displays small uncertainties.
Having reconstructed full four-momenta of each top, we form θ * shown in Fig. 5, which is the production angle in the Collins-Soper reference frame [48]. This distribution exhibits very little sensitivity to the adopted reconstruction procedure and retains the corresponding shape at Mone-Carlo truth (see the middle plot in Fig. 1 for comparison). This is partially due to a much simpler structure of θ * as compared to the shape of other distributions such as ∆φ tt .
In Fig. 6, we present ∆φ tt in the center-of-mass frame of the tt system (see Eq. 2.3) for various values of α. While Fig. 1 assumes prior knowledge (parton-truth) of correct final state particles pairs, Fig. 6 is obtained via the M 2 reconstruction. This distribution gets degraded as shown in the left panel of Fig. 6, once we include all the resolved events (admixture of both correct and wrong combinations). However, one can make an improvement with a mass cut on M 2CW < 175 GeV, and restore their original shapes, as shown in the right panel of Fig. 6.
In the case of CP mixed eigenstate (e.g. α = ±π/4), the ∆φ tt distributions are asymmetric with respect to ∆φ tt = 0. On the other hand, θ * distributions are symmetric. Numerical values of ∆φ tt asymmetry are summarized in Table 1. A (α = 0, ±π/2) = 0 is expected but we obtain nonzero values due to statistical uncertainties. We observe that the wrong combinatorics can be further suppressed with the M  closer to the idealistic parton-truth asymmetries.

Detector level analysis and LHC sensitivity
After proving that our top mass reconstruction method dovetails nicely with CP-sensitive observables at the tt rest frame, we perform a full Monte Carlo study, including the Higgs boson decay to a pair of b-quarks. We require four bottom tagged jets and two opposite sign leptons in our signal. The major backgrounds for this signature in order of relevance are ttbb and ttZ. Both signal and background events are showered and hadronized by PYTHIA 6 [68]. Jets are clustered with the FastJet [69] implementation of the anti-k T algorithm [70] with a fixed cone size of R = 0.4 (1.2) for a slim (fat) jet. We include simple detector effects based on the ATLAS detector performances [71], and smear momenta and energies of reconstructed jets and leptons according to their energy values. See Appendix A for more details.
In the phase space where the Higgs is kinematically boosted, its decay products are collimated in the same direction. In this regime, the Higgs can be better reconstructed using a single fat jet evading its possible intervention to the tt-system. Therefore, our previous method of resolving a combinatorial problem can be repeatedly applicable in the boosted Higgs configuration.
The boosted Higgs jet with a two-pronged substructure is a rare feature that the SM backgrounds retain. Thus, it delivers a further handle to disentangle the backgrounds from our signal events. The first demonstration of the use of a jet substructure technique in the dileptonic tth(bb) channel can be found in Ref. [23], where it effectively kills both ttbb and ttZ backgrounds. Here we follow similar steps, employing the TemplateTagger v.1.0 [72] implementation of the Template Overlap Method (TOM) [73,74] as a boosted Higgs tagger, due to its robustness against pile-up contaminations.
We first require at least one R = 1.2 fat jet with p J T > 200 GeV, and |η J | < 2.5.
For a fat jet to be tagged as a Higgs, we demand a two-pronged Higgs template overlap score We require exactly one Higgs-tagged fat jet that passes the cuts in Eqs. (4.3-4.4) and has 2b-tagged slim jets inside 2 :   Additionally, we require at least two slim jets that are isolated from the Higgs-tagged fat jet p j T > 30 GeV, and |η j | < 2.5, (4.6) in which we require exactly two b-tagged slim jets. We demand exactly two isolated leptons passing the cuts in Eq. (4.2) and where p Σ T is the sum of transverse momenta of final state particles (including a lepton) within ∆R = 0.3 isolation cone.
In Fig. 7 (upper-left), we show the reconstructed invariant mass distributions for Higgstagged fat jet, laid out with the dominant ttbb background. The distributions are insensitive to different CP structures, but provide more separation from the background. Hence, we 2CW becomes broader due to parton shower, hadronization and detector resolution effects, compared to parton-level results in Fig. 3, but the basic shape remains the same.
We resolve the combinatorial ambiguity of the two b-lepton pairs based on the prescription in Eq. (3.10). The efficiency of the method for our signal is 82% (comparable to the efficiency at parton level), yet at the same time ttbb and ttZ backgrounds are cut down to 64% and 70%, respectively. Hence, the top mass reconstruction method works as an extra relevant handle in the background suppression, eliminating wrong combinations from b-jets that are not from the top decays. (1/σ) dσ/dφ lab α = 1 2 π α = 1 4 π α = 0 α = − 1 4 π α = − 1 2 π Figure 9: Distributions of ∆φ lab , after resolving the combinatorial problem and 4b-tagging, without (left) and with (right) an additional m > 75 GeV selection.
Momentum reconstructions of two neutrinos are displayed in Fig. 8. The level of accuracy in reconstructing neutrino momenta also degrades to some extent, where the uncertainty in p z direction is greater than the transverse components. Additional mass cut 155 GeV < M (b ) 2CW < 180 GeV reduces the reconstruction efficiency to = 32%, but would increase the purity of the sample and improve the momentum resolution. We observe that the reconstruction method is robust to parton-shower, hadronization, and detector resolution effects, presenting similar efficiencies to the parton level analysis. Our reconstruction is better than (or comparable to) existing results. For example, Ref. [77] performs a conventional kinematic mass reconstruction with the missing transverse momentum and attempts resolving the two-fold sign ambiguity using a likelihood based on transverse momenta of the involved particles. This method leads to 62% efficiency with 50% purity for signal, and 51% efficiency for backgrounds. Since our method is purely based on mass minimization, it is less sensitive to new physics modifications and is a suitable element for a robust spin-correlation analysis. We note that one can further improve the efficiency of our method by utilizing those discarded "unresolved" events and deploying a hybrid method [46] together with M 2 reconstruction.
We acknowledge that there is a certain degree of uncertainty in the precision compared to parton-level results in Fig. 4, where the peaks are broadened. We attribute this change to contaminations in the total missing transverse momentum where additional neutrinos from h → bb system, via the semi-leptonic decays of the b-hadrons, can disrupt the relations in Eqs. (3.8)-(3.9), in combination with detector effects. Nevertheless, overall net shapes stay the same showing its resilience over the procedures.
Distributions of ∆φ lab , ∆φ tt , and θ * are presented in Figs. 9 and 10. The θ * and ∆φ lab distributions remain very similar to those at parton level ( Fig. 1 and Fig. 5), while ∆φ tt distribution gets more distorted (see Fig. 6). Table 2 summarizes the impact of a series of cuts for the signal (α = 0) and background cross sections. In the last column, we show the significances (σ), which are calculated for a , with L(x|n) = x n n! e −x , (4.9) where S and B are the expected number of signal and background events, respectively [78]. We find that our results are roughly in agreement with those from Ref. [23]. Although we obtain high significance as shown in the first row of Table 2, we would impose more stringent cuts for high-purity sample of tth production. We obtain σ = 8.1 with the resolved combinatorics. For an additional mass cut, we could retrieve even higher purity but we would suffer from statistics. In the following analysis, we do not impose this mass cut but instead require the dilepton invariant mass cut, m > 75 GeV. The asymmetry results at detectorlevel are summarized in Table 3   In Fig. 11 (left panel) we display the 95% C.L. bound to distinguish the CP-α Higgs-top interaction from the SM via tth production. Our limits are based on a binned log-likelihood analysis invoking the CL s method for (∆φ lab , θ * ) (blue dashed), and (∆φ lab , θ * , ∆φ tt ) (blue full) [79]. The bounds are obtained, including backgrounds, parton-shower, hadronization and semi-realistic detector effects. To illustrate the robustness of the top reconstruction method when going from the parton to the detector level, we also show the bounds using the parton-level distributions (∆φ lab , θ * ) with the rates rescaled to the full detector analysis (black full). The red-solid curve, labelled as "(∆φ lab , ∆Φ jj )", was extracted for comparison from Ref. [23], which runs a different analysis. To focus only on measurement of the CPphase, we fix the number of signal tth events to the SM prediction α = 0, comparing only the shapes between the null and pseudo-hypotheses. We note that the top reconstruction in the dileptonic channel, where the top spin analyzing power is maximal, results in relevant sensitivity improvements for the direct Higgs-top CP-phase measurement. While the lab-observables (∆φ lab , ∆φ jj ) result in the limit cos α < 0.5 at 95% CL for the high-lumi LHC with 3 ab −1 , the addition of our observables defined at the top pair rest frame in two scenarios (∆φ lab , θ * ) and (∆φ lab , ∆φ tt , θ * ), result in relevant improvements of cos α < 0.65 and cos α < 0.7, respectively.  Figure 11: Left: Luminosity required to distinguish an arbitrary CP-α state from the SM Higgs via tth production. Our limits are based on a binned log-likelihood analysis for (∆φ lab , ∆φ jj ) (red full), (∆φ lab , θ * ) (blue dashed), and (∆φ lab , θ * , ∆φ tt ) (blue full), accounting for the full detector level analysis. To illustrate the robustness of the top reconstruction method when going from the parton to the detector level, we also show the bounds using the parton-level distributions (∆φ lab , θ * ) with the rates rescaled to the full detector analysis (black full). Right: CL s as a function of the luminosity to distinguish CP(π/4) from CP(−π/4) state, based on ∆φ tt distribution.

CP-phase
As we are able to probe ∆φ tt , that is sensitive to the sign of α, we can go beyond and inquire if the LHC will be able to capture also the CP-phase sign. In Fig. 11 (right panel), we show the luminosity needed to disentangle the CP(α = π 4 ) from the CP(α = − π 4 ) state based on ∆φ tt distribution. We chose ± π 4 for an illustration, since they give the largest difference. The observation of the sign for the maximal CP violation case requires at least 8 ab −1 of data at the 14 TeV LHC even at 1σ-level.

Summary
Characterizing the Higgs boson is a critical component of the LHC program. In this paper, we have studied the direct Higgs-top CP-phase determination via the tth channel with Higgs decaying to bottom quarks and the top-quarks in the dileptonic mode. Although this tt decay mode leads to maximal spin analyzing power, it always accompanies two neutrinos in the final state, making the analysis and reconstruction challenging.
We show that kinematic reconstruction can be obtained via the M 2 algorithm. This method is entirely based on mass minimization, being more flexible for new physics studies and robust for our spin-correlation analysis. We expanded the previous M 2 -assisted reconstruction studies, investigating effects of parton-shower, hadronization and detector resolution. We found that the algorithm performance in resolving two fold ambiguity still remains superior despite the slightly worse momentum reconstruction when compared to the parton level. We prove however that an additional mass selection on M (b ) 2CW can efficiently improve the reconstruction efficiencies.
We then studied the Higgs-top CP-phase discrimination via a realistic Monte Carlo analysis. We show that the CP sensitivity of the azimuthal angle between two leptons in the laboratory frame ∆φ lab can be relevantly enhanced when combined with tt rest of frame observables: top quark production angle θ * and ∆φ tt , where the latter is a truly CP-odd observable, sensitive to the sign of the CP-phase. Including the relevant backgrounds, we have performed a binned log-likelihood analysis and computed the luminosity required to distinguish the SM Higgs from an arbitrary CP-phase at 95% confidence level. Based on our results, the Higgs-top CP-phase can be probed up to cos α < 0.7 at the high luminosity LHC.

A Parameterization of detector resolution effects
The jet energy resolution is parametrized by a noise (N ), a stochastic (S), and a constant (C) terms where in our analysis we use N = 5.3, S = 0.74 and C = 0.05 respectively [71]. The electron energy resolution is based on the parameterization The muon energy resolution is derived by the Inner Detector (ID) and Muon Spectrometer (MS) resolution functions where σ ID = E a 2 1 + (a 2 E) 2 (A.4) We choose a 1 = 0.023035, a 2 = 0.000347, b 0 = 0.12, b 1 = 0.03278 and b 2 = 0.00014 in our study [71].