Identifying a new particle with jet substructures

Journal of High Energy Physics, Jan 2017

We investigate a potential of determining properties of a new heavy resonance of mass \( \mathcal{O}(1) \) TeV which decays to collimated jets via heavy Standard Model intermediary states, exploiting jet substructure techniques. Employing the Z gauge boson as a concrete example for the intermediary state, we utilize a “merged jet” defined by a large jet size to capture the two quarks from its decay. The use of the merged jet benefits the identification of a Z-induced jet as a single, reconstructed object without any combinatorial ambiguity. We find that jet substructure procedures may enhance features in some kinematic observables formed with subjet four-momenta extracted from a merged jet. This observation motivates us to feed subjet momenta into the matrix elements associated with plausible hypotheses on the nature of the heavy resonance, which are further processed to construct a matrix element method (MEM)-based observable. For both moderately and highly boosted Z bosons, we demonstrate that the MEM in combination with jet substructure techniques can be a very powerful tool for identifying its physical properties. We also discuss effects from choosing different jet sizes for merged jets and jet-grooming parameters upon the MEM analyses.

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Identifying a new particle with jet substructures

Received: October Identifying a new particle with jet substructures Chengcheng Han 1 2 4 8 9 10 11 12 13 14 15 Doojin Kim 1 2 4 6 7 9 10 11 12 13 14 15 Minho Kim 1 2 3 4 5 9 10 11 12 13 14 15 Kyoungchul Kong 0 1 2 4 9 10 11 12 13 14 15 g 1 2 4 9 10 11 12 13 14 15 Sung Hak Lim 1 2 3 4 9 10 11 12 13 14 15 h 1 2 4 9 10 11 12 13 14 15 Myeonghun Park 1 2 3 4 9 10 11 12 13 14 15 0 Department of Physics and Astronomy, University of Kansas 1 CH-1211 Geneva 23 , Switzerland 2 Gainesville , FL 32611 , U.S.A 3 Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS) 4 Kashiwa , Chiba 277-8583 , Japan 5 Department of Physics , Postech 6 Department of Physics, University of Florida 7 CERN, Theory Division 8 Kavli IPMU (WPI), The University of Tokyo 9 Open Access , c The Authors 10 291 Daehak-ro , Yuseong-gu, Daejeon, 34141 , Korea 11 Pittsburgh , PA 15260 , U.S.A 12 Department of Physics and Astronomy, University of Pittsburgh 13 Lawrence , KS 66045 , U.S.A 14 Pohang 790-784 , Korea 15 Daejeon , 34051 , Korea 1Corresponding author. particle - states, exploiting jet substructure techniques. Employing the Z gauge boson as a concrete example for the intermediary state, we utilize a \merged jet" de ned by a large jet size to capture the two quarks from its decay. The use of the merged jet bene ts the identi cation of a Z-induced jet as a single, reconstructed object without any combinatorial ambiguity. We nd that jet substructure procedures may enhance features in some kinematic observables formed with subjet four-momenta extracted from a merged jet. This observation motivates us to feed subjet momenta into the matrix elements associated with plausible hypotheses on the nature of the heavy resonance, which are further processed to construct a matrix element method (MEM)-based observable. For both moderately and highly boosted Z bosons, we demonstrate that the MEM in combination with jet substructure techniques can be a very powerful tool for identifying its physical properties. We also discuss e ects from choosing di erent jet sizes for merged jets and jet-grooming parameters upon the MEM analyses. ArXiv ePrint: 1609.06205 1 Introduction 2 3 4 Phase-space reduction Angular correlations among nal state particles Results with jet substructure techniques Event reconstruction Lepton isolation criteria Tagging a merged jet Phase-space distortion from a jet substructure Analysis with matrix element methods Determining the CP property Matrix Element Method A Background consideration in MEM analyses B Phase space restriction from other jet substructure methods Introduction The Large hadron collider (LHC) has played an important role in deepening our understanding of electroweak symmetry breaking by discovering a Higgs particle. As the LHC experiment reaches the energy scale of tera electronvolt (TeV), it is of paramount importance to study potential new physics such as various extended Higgs sectors, existence of other fundamental scalars [1{3], vector resonances under the set-up of composite models [4{9], and so on. We remark that resonances in those new physics models often have sizable branching fractions to heavy SM particles including the weak gauge bosons, the Higgs, and the top quark, if kinematically allowed. As increased center-of-mass energy at the LHC enables us to probe heavier new particles of O(1) TeV, a substantial mass gap between a new particle and a heavy SM state would result in a large boost of the latter, accompanying highly collimated objects along the boost direction of the latter in the nal state. While the leptonic decay products of the above-listed heavy SM particles often carry advantages in conducting data analyses thanks to their cleanness, hadronic decay products are expected to play an important role in not only discovery opportunity but property measurement at the early stage due to their larger branching fractions. However, their jetty nature at the detection level renders associated analyses challenging because of signi cant overlaps between the nal state jets, requiring robust analysis tools to deal with such hadronic objects reliably. A promising venue in developing relevant techniques is the eld of jet substructure [10]. A successful application of the jet substructure techniques is to tag single-jet-looking or single-prong QCD jets [11]. The idea is that one can capture hadrons from the decay of a heavy SM particle, using a single \merged" jet which is de ned by a proper choice of the jet size. An expected bene t from utilizing a resultant (massive) merged jet is mitigation of the systematics which often arises in considering multi-particle (e.g., combinatorial ambiguity), by reducing the number of reconstructed objects. The price for it is the possibility that even a normal QCD jet may acquire a sizable mass in combination with underlying QCD activities including pile-ups.1 In this regard, there are dedicated studies to reduce corruptions from irrelevant hadrons for a given jet [13{16], and to di erentiate a jet resulting from a boosted heavy SM state from an ordinary QCD jet by looking into its substructure [13, 17{25]. Many proposed methods along the line have been successfully implemented for analyzing the LHC data, and they concurrently improve the sensitivities for the high mass region by reducing relevant SM backgrounds e ciently. While tagging a boosted jet by jet substructure techniques is useful for discovery opportunities e.g., heavy resonance searches, the constituent-jet information itself allows to construct various experimental observables for further data analyses. In this context, it is interesting to question how far characteristic features in kinematic distributions are preserved after subjet isolations, if included are various realistic e ects such as parton shower, hadronization/fragmentation, detector response, and jet clustering. We rst point out that rather precise identi cation of the features is viable in some controlled environment, despite the presence of realistic e ects. Motivated by the spin-parity determination of the SM Higgs boson [26] and the diboson resonance [27, 28] through massive bosonic intermediary states in relevant decay processes, gular variables formed with reconstructed subjets. In the case of production of a new, bosonic heavy resonance, the jet substructure techniques are relevant to the channels of W W , ZZ, and Z in which the associated nal state is, at least, partially hadronic. For a su ciently boosted, heavy state V , the angular separation R between its two decay products is given by where mV and PTV denote the mass and the transverse momentum of particle V . Since usual jet substructure techniques begin with identifying a \merged" jet by a fairly large xed cone 1See ref. [12] for the jet substructure techniques alleviating the pile-up contamination. size to capture all constituent jets followed by a declustering procedure to nd subjets, the hardness of PTV is crucial in choosing a reasonable cone size, hence too a successful subjet analysis. Moreover, considering the fact that the generic shape analysis demands global information, we see that a proper de nition of merged jets is a key component for posterior analyses. In particular, the phase-space reduction induced by xing a cone size for merged jets would cause adverse distortions of the kinematic distributions of interest, becoming an obstacle in decoding the physics behind signals. To illustrate these points, we employ two benchmark points for a heavy resonance decaying into a ZZ nal state in order to cover kinematically distinctive regions, one for the moderately boosted Z case and the other for the highly boosted one. We contrast/compare them in terms of the angle particularly sensitive to the CP state of the resonances. We there explicitly show that remarkably, jet substructure techniques preserve useful information quite well. Being con dent of the above single-variable analysis, we then move our focus onto matrix element method (MEM)-based observables which allow us to make full use of all available information encrypted in four-momenta of nal state particles [29{38]. Unlike other statistical methods based on distributions of multiple observables, the MEM is predicated on a straightforward and elegant interpretation on the probability measure P, that is, the quantum amplitude of a given process with hypothesis is schematically given as where M is the matrix element for hypothesis and W is the transfer function introduced to map parton-level momentum vectors (fqg) to reconstruction-level ones (fprecog). Markedly, the usefulness of the MEM has been proven in discriminating di erent spin/CP state hypotheses [26, 29, 30, 34, 35, 39]. In particular, the MEM was a driving force to determine various properties of the SM Higgs particle in the four-lepton channel, which has been considered as one of the most exciting achievements at the LHC. In more detail, by identifying the interaction between the Higgs boson and a Z-boson pair, it has been shown that the Higgs boson is indeed related to the SU(2)L U(1)Y gauge symmetry breaking mechanism. We note that this channel comes with ten degrees of freedom compared to its competing diphoton channel with only four degrees of freedom although the former involves smaller statistics than the latter. Therefore, given low statistics, it is imperative to combine di erent information from various degrees of freedom in an optimized way, for which the MEM is well-suited. We remind that many of the collider studies for the decay of a heavy resonance into the nal state particles via massive SM states often advocate fully leptonic channels in not only search for new particles but measurement of their properties, due to the clean nature of lep nal states even at the reconstruction level. While it is challenging to extract useful information from hadronic decay products unlike leptonic ones, the remarkable discriminating power of the MEM motivates us to construct an MEM-based kinematic discriminant (KD) using four-momenta of subjets. We then investigate how much the discrimination potential is retained in the context of jet substructure techniques again employing the benchmark scalar resonances. To convey our main ideas coherently, we organize this paper as follows. In section 2, we begin with the discussion on the phase-space reduction occurred by the introduction of a xed cone size. In section 3, we provide a brief review on various angular variables for discriminating the spin and the CP states of heavy resonances, and discuss the impact of the phase-space reduction upon kinematic observables, in particular, CP-sensitive ones. In section 4, we con rm the observations made in the two previous sections, using detectorlevel Monte Carlo simulation. We then, in section 5, present our main results obtained from the MEM-based analyses under the circumstance of negligible background contamination, in conjunction with the jet substructure techniques. Our concluding remarks and outlook appear in section 6. Finally, appendices A and B are reserved for the discussion on the MEM-based analyses including backgrounds and the phase-space reduction in other jet substructure techniques, respectively. Phase-space reduction We begin this section by estimating the cone size R for \Merged Jets" (MJ) to capture both of the two visible particles v1 and v2 emitted from a highly boosted massive particle are massless and well-approximated to two subjets j1 and j2 which are the constituents of a merged jet. We de ne PT (MJ) and mMJ as the laboratory-frame transverse momentum and the mass of a merged jet, respectively. With the assumption of PT (MJ) mMJ, simple kinematics in leading-order QCD leads to z) PT (MJ) where z is de ned as min(PT (j1);PT (j2)) , i.e., the fractional transverse momentum of the leading subjet (say, j1) with respect to the total transverse momentum. Here the equality is obtained in the limit of z = 1=2. two subjets which is de ned as We then closely look at the relation between R and the angular separation 12 denote the di erences between the two subjets in pseudorapidity and azimuthal angle in the laboratory frame, respectively. The angular distance between j1 and j2 in the laboratory frame can be expressed in terms of the polar angle azimuthal angle of the leading subjet in the heavy particle rest frame relative to the boost direction to the laboratory frame [40]: R122 = 2 cosh sin sin 2 sinh sin cos has a minimum at = =2 and = 0 for any xed [40]. Therefore, a necessary condition to capture the two subjets for a given is that the cone size R should be greater than the lower limit of R1m2in = 2 csc 1(cosh ) where the last step is done by setting cosh in the transverse plane and taking a large transverse momentum limit. Note that this asymptotic behavior is identical to the estimate in eq. (2.1). Now if we set the cone size to be RMJ, all events with R < RMJ are accepted. We then translate this inequality to the upper bound for the polar angle : This inequality implies that xing the cone size for MJs con nes the polar angle to a certain range, resulting in a reduction of the accessible phase space. To visualize this observation, we exhibit cos distributions of quarks (say, b) from Higgs or Z gauge boson decays. To minimize any e ects on the angular distributions from their production, we assume that a pair of H or Z bosons are produced via the decay of a heavy at distribution. On the other hand, a Z boson has transverse and longitudinal polarization components, and thus its coupling to particle S is described in a somewhat complicated manner. Denoting MZ and as the Z gauge boson mass and a scale parameter, we de ne the interaction Lagrangian between S and Z as Lint = 1 cos2 ) + ( 22 + 32)(1 + cos2 ) + O are the eld strength tensor and the dual eld strength tensor for the Z boson, respectively. In MS MZ limit, the rst term takes care of the interaction of the longitudinal polarization component while the other two describe that of the transverse polarization components [29, 41], and the resulting di erential cross section in cos is Figure 1 displays our numerical results with parton-level Monte Carlo simulation for which the input mass of the heavy resonance S is 1 TeV for illustration. As mentioned above, we take the decay process of H or Z into a bottom quark pair. The upper-left panel shows the unit-normalized distributions of Rbb for the Higgs boson (orange histogram) and the Z gauge boson (blue histogram). The red and the blue dashed lines mark the intuition on what fraction of events are tagged. The other three panels (upper-right for the Higgs boson, lower-left for the longitudinal Z, and lower-right for the transverse Z) demonstrate the unit-normalized cos distributions with R 0:8 (red histogram) and 1:2 (blue histogram) and compare them with the corresponding theory expectations represented by solid black lines. We clearly observe that a xed cone size for MJs distorts −1 R ≤ 0.8 R ≤ 1.2 −1 −1 R ≤ 0.8 R ≤ 1.2 −0.5 R ≤ 0.8 R ≤ 1.2 R = Rpeak R = 0.8 R = 1.2 Theoretical expectation Theoretical expectation Theoretical expectation −0.5 −0.5 1 TeV. The upper-left panel shows unit-normalized Rbb distributions for the Higgs boson (orange histogram) and the Z gauge boson (blue histogram) cases. The red and blue dashed lines mark right for H, lower-left for ZL, and lower-right for ZT ) show unit-normalized cos distributions with cone sizes for MJs R 0:8 (red histogram) and R 1:2 (blue histograms) and compare them with corresponding theory predictions (solid black lines). Dashed vertical lines represent the upper bounds on j cos j for a given RMJ according to eq. (2.5). the shape of di erential distributions. Hence, when investigating physics governing experimental signatures with kinematic distributions including angular observables, one should conduct a careful examination on how much of partonic information would be missing by the introduction of a xed cone size for MJs in reconstructing nal state objects. Angular correlations among nal state particles As in the case of the SM Higgs boson whose rst signature appeared in the nal states with and ZZ, if a heavy new particle X respects the SM electroweak gauge symmetry, it may appear as a resonance in the nal states with ZZ, W W , Z , and . We divide them ` + (the (a) panel), Z (the (b) panel), and ZZ=W +W (the (c) panel) processes. For a su ciently heavy X (i.e., mX 2MZ ), we can neglect the possibility of o -shellness of internal gauge boson propagators. Then the processes in (a), (b), and (c) panels have two, four, and six degrees of freedom, respectively, at the X rest frame. into three categories according to the number of angular degrees of freedom measured in the rest frame of particle X. : two angular degrees of freedom as ( ; (b) X ! Z : four angular degrees of freedom as ( ; We schematically show angular con gurations for three cases in gure 2, matching the item numbers with the panel ones. The decay of X into two gauge bosons V1 and V2 involves two degrees of freedom, polar angle and azimuthal angle of V1 (or equivalently V2) about the beam axis. In a similar manner, each of the two gauge bosons (except the photon) involves two degrees of freedom, polar angle i and azimuthal angle i of one of the decay products relative to the Vi boost direction in the Vi rest frame. Another degree of freedom comes with the rapidity of the whole decay system which encodes the information of initial state partons through the parton distribution functions. However, imposing a rapidity cut on the reconstructed heavy resonance, we anticipate that any of its associated impact upon kinematic observables becomes mild [35]. We begin with the observables related to the decay process of X itself, which are the . They can be evaluated as follows: = p^V1 z^jX ; where jX implies that all relevant physical quantities are measured in the rest frame of particle X. Here z^ lies on the beam direction as usual, while x^ is chosen to be an azimuth 2These angles are not suitable for the spin and parity analysis in X ! W +W because the two neutrinos are not detected. Instead, we can use the azimuthal angle between two leptons, ``, the dilepton invariant mass, m``, and the transverse mass of the dilepton system, mT , to distinguish spin and parity hypotheses [39, 42]. reference direction on the plane perpendicular to z^. The determination of the helicity/spin of X by variable azimuthal angle is closely connected to the production mechanism for it. The carries the helicity information of X, which becomes available if there is interference among di erent helicity states [43]. If X is produced in association with another particle, its helicity state is obtained by a linear superposition of various helicity states with corresponding amplitudes given in terms of relevant Clebsch-Gordan coe cients. Under a spatial rotation around the X momentum axis by say, , each helicity state obtains a phase factor ei denotes the helicity value of the state. Therefore, the sum over various helicity states give rise to non-trivial interference among the corresponding quantum amplitudes in the resulting cross section, which will be imprinted in the distribution. On the other hand, if X is singly produced, its helicity state is uniquely xed by initial partons, rendering the helicity sum incoherent. Thus we do not expect to observe distinctive features in the distribution. When it comes to polar angle spin state of X can be inferred from the distribution in [44]. At the tree level, the matrix element contains a projection of the X helicity onto the beam direction. In more detail, the Wigner d-function, which depends on the net spin between the initial and the nal states, describes the amplitude of this projection whose angle is . Therefore, the distribution can be a good observable for identifying the production mechanism and the spin of X. We next consider angular variables related to the decay of Vi. As we demonstrated explicitly in section 2, the impact of a xed RMJ upon cos i di ers in polarization states (see also the bottom panels in gure 1). This implies that we can infer the Vi polarization from its decaying angles i, which are crucial in understanding the coupling of X-V1-V2, and they are de ned as follows: cos 1 = p^q p^V2 jV1 ; cos 2 = p^`+ p^V1 jV2 ; where the decay products of V1 and V2 are distinguished merely to avoid any potential notational confusion (see also gure 2(c) for relevant decay products). It turns out that the remaining angles i pertain to the CP state, which is one of the highly non-trivial properties to be identi ed in collider analyses. Indeed, the di erence between two azimuthal angles of the V1 and V2 decaying planes, 2, provides the strongest discriminating power between di erent CP states [29, 34, 41],3 and this quantity is evaluated by 2) = In the rest of this paper, we focus on the determination of the CP state of X assuming that X is a scalar S, as other properties such as the spin of X or the interaction to a longitudinal or transverse component of Vi can be measured by other angular variables mostly with the longitudinal polarization vector of gauge bosons through an interaction of HZ Z . explained above. We remark that if there are interactions between CP-even scalar and the longitudinal polarization of Vi through either a tree level coupling SVi Vi or a higher dimensional operator S D HyD H, we can easily distinguish them from the corresponding interactions with CP-odd scalar because the latter mostly interacts with the transverse polarization vector of Vi. We therefore consider only higher dimensional operators of dimension 5, for which identifying the CP state is more challenging. Before the breakdown of the SM electroweak gauge symmetry SU(2)L U(1)Y , relevant Lagrangians for CP-even and CP-odd state scalars are where W a and B are eld strength tensors of SU(2)L and U(1)Y , respectively, while W~ a are their corresponding dual eld strength tensors. After electroweak symmetry breaking, the couplings between S and mass eigenstate vector bosons can be described as where new coupling constants cW W , cZZ , c , and cZ are related to cY , cW , and the Weinberg angle w as follows: cW W = 2 cW ; cZZ = cW cos2 w + cY sin2 w ; = cY cos2 w + cW sin2 w ; cZ = (cW Similarly, we have c~W W , c~ZZ , c~ , and c~Z in terms of c~Y and c~W as in eqs. (3.10) through (3.13). SU(2)L-singlet. As two coupling constants cY and cW determine four decay modes of S, at least two decay channels should be non-vanishing. For example, if the S ! one can expect to observe at least either S ! ZZ or S ! Z channel is observed, channel as well. However, may not be available, as it depends only on cW which could vanish if S were As brie y discussed before, plays an important role in determining the CP state of resonance S. In this sense, Z nal states are irrelevant because they do not involve two decaying planes. In our numerical study, we focus on S ! ZZ which subsequently decay semileptonically, i.e., qq`+` . One reason for this choice is that the nal state is expected to o er a better handle in inferring the underlying decay mode than the fully hadronic decay channel in which there exists non-negligible chance to misidentify observed events as S ! W +W 4One could study the S ! W +W using the energy-momentum conservation. due to the issue of jet mass resolution [28, 45].4 ! qq` channel by reconstructing the four vector of a neutrino ( ) Compared to the fully leptonic channel, the semileptonic channel certainly enjoys higher statistics due to the larger branching fraction of Z into quark pairs, allowing us to have better signal sensitivity. However, in a more realistic situation, this naive expectation is not straightforwardly applied. Once we take SM backgrounds into consideration, we are forced to impose severe cuts to suppress huge backgrounds including Z+jets so that we may end up with a similar order of sensitivity compared to the 4` channel. More speci cally, it turns out that for mS & 700 GeV, the signal sensitivity expected from the semileptonic channel becomes comparable to that from the fully leptonic channel [46, 47]. Remarkably, the jet substructure techniques come into play in this high-mass regime. Note again that a merged jet from major backgrounds contains a single quark together with additional QCD activities from radiation, whereas a signal merged jet consists of two partons. Therefore, jet substructure techniques enable us to reduce SM backgrounds more e ciently, hence get them under control. On top of background rejection, we pro-actively utilize jet substructure methods to extract partonic information from a merged jet initiated by Vi ! qq. As explicitly demonstrated in section 2, the procedures in the methods e ectively restrict relevant phase space of nal states, and in particular, the accessible region in i angles may be signi cantly affected. The coe cients for the di erential distributions in are related to i in the narrow width approximation (NWA) as follows [29]: d cos 1d cos 2d d cos 1d cos 2d / 2 sin2 1 sin2 2 + cosh2(2 )(1 + cos2 1)(1 + cos2 2) cosh(2 ) sin(2 1) sin(2 2) cos + cosh2(2 ) sin2 1 sin2 2 cos(2 ) ; where we average contributions from di erent quark and anti-quark avors as we cannot discern them. Here de nes a Lorentz boost factor as cosh above expressions imply that jet clustering procedures alter = MS=(2MZ ). Certainly, the distributions by limiting i angles. If there were no restrictions on i, integrating i over the full ranges of (0; ) would give rise to di erential distributions in However, as we pointed out in the previous section, xing the angular separation between relevant subjets results in shrinking accessible phase space with respect to i (see also eq. (2.5)), and therefore, to appropriately interpret outputs from any data analyses for discriminating the CP state of S, we should be armed with a solid understanding of relevant We shall closely look at this observation in the next section, taking a couple of benchmark points (BPs) with di erent jet size parameters in Cambridge/Aachen (C/A) algorithm [48, 49]. The following BPs are chosen to cover di erent kinematical regions: one for the moderately boosted Z and the other for a highly boosted kinematics of Z. For the mass choice in BP1, we expect moderately boosted phase space in which the associated merged jet analysis becomes comparable to analyses based on a normal jet size nd that typical Lorentz boost factors in the two BPs are large enough (e.g., cosh for BP1 and cosh ' 8:33 for BP2) to simplify eq. (3.14) as d cos 1d cos 2d / (1 + cos2 1)(1 + cos2 2) + sin2 1 sin2 2 cos(2 ) : Note that the second term in this expression di ers from that of eq. (3.15) by the sign. Denoting two relevant coe cients by C1 and C2, we have d cos 2 (1 + cos2 1)(1 + cos2 2) ; from which we nd where we de ne the ratio of C2 to C1 as R . Hence, a better discriminating power is expected with a larger R . The expressions in eqs. (3.16) and (3.17) suggest that this ratio at the parton level without any restriction on the phase space should converge to a quarter. As discussed in the previous section, nding hadronic decaying Z boson by a merged jet causes a phase space reduction toward the plane orthogonal to the Z boson propagation direction as illustrated in eq. (2.5). In this context, it is interesting to look into the behavior of R as we restrict the phase space. Assigning 1 and 2 to hadronic and leptonic branches, (cos 1)min and 2 is unrestricted for simplicity.5 Noting that the integrands in eqs. (3.19) and (3.20) are even in cos 1, we nd that R can be expressed as 5In more realistic situations, there arises some mild phase space reduction even on the leptonic side. However, we here isolate the e ect induced in jet substructure techniques for developing the relevant insight. line represents the R value in the full phase space limit. space). Figure 3 shows the functional behavior of R over (cos 1)max, wherein R tonically increases as (cos 1)max decreases. This implies that phase space reduction by a xed cone size renders R greater than 1/4 (dashed black horizontal line in remarkably achieving better identi cation on the CP state. In the next section we shall con rm this observation with Monte Carlo simulation at both parton and detector levels. Results with jet substructure techniques In this section, we present our results with jet substructure techniques, using Monte Carlo simulation. For a more realistic study, we consider various e ects such as parton shower, hadronization/fragmentation, and detector responses. To this end, we take a chain of simulation programs. We rst create our model les using FeynRules [52] and plug them into a Monte Carlo event generator MadGraph5 [53] with parton distribution functions parameterized by NN23LO1 [54]. The generated events are further pipelined to Pythia 6.4 [55] for taking care of showering and hadronization/fragmentation, and to Delphes3.3.2 [56] with a CMS detector model for taking care of detector responses. In order to form jets from the nal state particles, we employ the particle- ow algorithm in Delphes-3.3.2 and feed resultant particle- ow objects to FastJet [57, 58]. Event reconstruction As we discussed earlier, for our benchmark points belonging to a high mass regime, Z decay products are likely to be highly collimated. Denoting the angular distance between the two (fermionic) decay products as Rff , its distribution develops a peak as shown in gure 4, which is inherited from a Jacobian peak in the Z-boson transverse momentum distribution. The last statement can be understood by restricting eq. (2.4) into the transverse plane, i.e., ff 2 Rff for MS = 750 GeV (left panel) and MS = 1500 GeV (right panel) for which f denotes any fermionic decay product of the Z gauge boson. We select events with a mass window of jMZ mff j < 15 Z . Dashed black lines mark the expected lower Rff as in eq. (2.4) for which PT of a Z boson is localized at the Jacobean peak of MZ sinh with cosh being a boost factor. where mff is the invariant mass of two decay products. The minimum opening distance is obtained by setting the numerator to be half the mass of S 6Note that csc 1(x) is a monotonically decreasing function in terms of x. Rff Note that mff follows the usual Breit-Wigner distribution around MZ , and therefore, some small fraction of events can populate even below the expected minimum value 2 csc 1 MS=(2MZ ) in the Rff distributions exhibited in gure 4.6 Predicated upon this parton level assessment, we determine an isolation criteria for leptonic decay products of Z bosons in section 4.1.1 and a jet size for clustering merged jets to capture hadronic decaying Z bosons into a single jet in section 4.1.2. Lepton isolation criteria To reconstruct individual Z boson-induced leptons without any confusion with heavy avor quark-induced leptons, we require the following isolation criteria: I = Ri` < Riso and pT;i where ` is a candidate for an isolated lepton, and i's are any particles in the vicinity of the lepton candidate ` which satis es a Z boson decay. Isolation parameters for each benchmark point are tabulated in table 1, for which the values are conventional [59, 60] except that for Riso. We choose Riso so as to have an isolated lepton according to the observation made in gure 4. Tagging a merged jet We begin with applying C/A algorithm to cluster particles from a hadronically decaying Z boson. As this is a sequential recombination algorithm based on the angular separation between two objects, it is useful for us to access sub-clusters by the angular order, in particular, to evaluate the angular variable. The algorithm combines two objects, which have the smallest angular distance, by adding up their momenta. This combining process continues until every clustered object is isolated from the others by an angular distance RMJ. Here RMJ de nes the jet size for a merged jet in the C/A algorithm. In language of the kT algorithm [61], the C/A algorithm is equivalent to the sequential clustering with a metric between objects, dij = diB = 1 ; where B denotes the beam line.7 For each iteration, two objects which have the smallest dij are combined. If diB is smallest, the object i is promoted to a C/A jet and escapes from clustering. The iteration terminates if all objects are identi ed as jets. After completion of clustering, we can obtain an angular hierarchy of sub-clusters by simply rewinding the clustering procedure. We then match sub-clusters to partons from a Z gauge boson, imposing relevant cuts to reduce the possibility of mistagging a QCD jet as a Z-induced one. To achieve this goal, we employ the Mass Drop Tagger (MDT) [13] whose procedure is brie y summarized below. The MDT essentially traces back the clustering sequences of a C/A jet and attempts to nd subjets satisfying the symmetric conditions. (1) Clustering: we cluster energy deposits in calorimeters using the C/A algorithm of a jet radius R = RMJ. (2) Splitting to look into a substructure: we rewind the last clustering sequence of a jet j, labelling two subjets as j1 and j2 with mj1 > mj2 . (3) Checking symmetric conditions: major backgrounds in our case would be Z(! `+` ) + js where a quark-initiated jet appear as a merged one. In this case, most of 7Here B is a legacy notation of kT algorithm, as diB for C/A algorithm does nothing with the beam line and it is just related to the threshold angular scale RMJ. the energy deposits are inclined to be localized along the momentum direction of the initial quark, so that there is a high chance of unbalanced energy sharing between two subjets including mass and transverse momentum. In contrast, a signal MJ consists of two prongs (i.e., two quarks) that ensure democratic energy sharing in two subjets. To quantify this di erence, the MDT demands an upper bound and a lower bound y on MDT parameters and y, respectively: This procedure is useful to discriminate prongs in subjects from soft showering, on top of reducing backgrounds. If subjets do not satisfy above criteria, the MDT procedure rede nes j1 as j and repeats the rewinding procedure in (2). Once the MDT tags a signal MJ and locates two prongs in the MJ, it decontaminates QCD corruptions in subjets by reclustering energy deposits in the MJ again with the C/A algorithm of a small radius jet size R lt, (4) Filtering: we reculster constituents of an MJ with the C/A algorithm of radius, nd n new subjets fs1; s2; ; sng ordered in descending PT . Here R is the maximum allowed size for subjets in order to minimize the QCD contamination. The MDT takes into account an O( s) correction from hard radiation, by allowing up to three subjets in rede ning an MJ as R lt = min pMJ = (5) Assigning subjets to prongs from a Z: if we have only two subjets fs1; s2g, we take these two subjets as two particles from a Z boson. In the case where we have three subjets fs1; s2; s3g, we merge s3 with other subjet si which has the smaller angular distance from s3. By this merging process, we identify subjets fj1; j2g in an MJ as fpj1 ; pj2 g = PT -ordered fpsi +ps3 ; psj g with for n = 2 ; for n = 3 : We summarize parameters of the MDT procedures for two benchmark points in table 2. As an MDT procedure has a cut y on the phase space, we expect certain e ects on the angular distributions in return as the cone size of a merged jet restricts the polar angles of decaying particles from Z bosons. Since a jet clustering procedure with the MDT is a key process to recover the parton-level information from the corresponding reconstruction-level information, we investigate e ects from the MDT to understand phase-space distortion in reconstruction-level analyses. and y as in the original BDRS Higgs boson tagger [13] for MZ MH Z-tagging e ciencies in the table are evaluated after selection cuts in table 3 for a given merged jet size. A jet size RMJ is chosen such that tagging e ciencies with di erent RMJ's remain unchanged. O(100) GeV. Phase-space distortion from a jet substructure As discussed earlier, constructing a merged jet to capture partons from the decay of a heavy (boosted) particle often accompanies cuts to suppress the rate to misidentify an ordinary QCD jet as an MJ. In the MDT procedure, symmetric cuts and y are utilized to reduce single-prong jets from QCD backgrounds. While the cut does not give any strong restriction on signal MJs, the y cut may result in a limit on the phase space of the subjets from a Z boson. Suppose that the softer subjet j2 carries away z fraction of the total momentum, i.e., zPT (MJ). We then nd that symmetric cut y in eq. (4.6) can be z) PT (MJ) where in the rst step we make use of eq. (2.1) in the limit of PT (MJ) mMJ. A similar expression is readily available for the harder subjet j1 which takes away the momentum of 1)PT (MJ). Solving the two inequalities for z (one from eq. (4.10) and the other from the corresponding one for j1), we nd that for a given y , the momentum sharing z should be con ned to a region de ned by which, in turn, restricts the angular distance between the two subjets in terms of y , To develop our intuition on the e ects from this restriction, we apply symmetric conditions of the MDT to parton-level simulation data for S ! ZZ ! qq`+` . In a parton-level simulation, only the y cut in eq. (4.6) remains e ective. Thus we impose a symmetric cut y∗ Re(yst∗=0.09) Re(yst∗=0.3) Re(yst∗=0.09) ∗cu=t= 00.0 y y ∗cut ∗cut between subjets evaluated from eq. (4.12) with a symmetric cut y in the BDRS tagger. y to the two quarks from a Z boson. We then plot distributions of Rqq with the events whose y values are greater than a certain y . Figure 5 shows those distributions for three (right panel). well-motivated in the sense of reducing backgrounds by focusing on the central region. We clearly observe that as we increase the y cut, more phase space with large is removed. This implies that even though we begin with a su ciently large cone size RMJ to retain most of phase space as in table 2, the y cut in the MDT procedure e ectively restricts the available region of than typical choices of RMJ, for example, Rqq below Re(yst ). Moreover, we nd that Rqq is smaller Re(yst =0:09) Re(yst =0:09) ' 1:1 < RMJ (= 1:2) for MS = 750 GeV; ' 0:55 < RMJ (= 0:6) for MS = 1:5 TeV; which are marked by blue arrows in gure 5. The resulting restriction on cos (i.e., the Z rest-frame polar angle of the harder quark relative to the Z boost direction) can be derived from eqs. (2.5) and (4.12): 3 PT (MJ) larger than Re(yst ), the cone size RMJ does not invoke any direct deformation on the phase space, compared to cuts in the MDT procedure, which are introduced to reduce background Our Monte Carlo study indeed con rms this observation. In gure 6, we contrast distributions at the parton level with those at the detector level. For parton-level parton level, no selection detector level, CA R = 1.0 detector level, CA R = 1.4 parton level, no selection detector level, CA R = 0.6 detector level, CA R = 1.0 parton level, no selection detector level, CA R = 1.0 detector level, CA R = 1.4 distributions under the hypotheses 0++ (left column) and 0 + (right column) at the parton level (solid lines) and the detector level (dotted lines). Black solid lines in the four panels are theoretical expectations without any restriction on the angular distance between two quarks as in eqs. (3.16) and (3.17). distributions, we restrict the angular distance between two quarks from a Z boson decay by two di erent upper bounds of 750 GeV (upper panels), the two upper bounds are chosen to be 1:0 (red lines) and 1:4 (lower panels), they are chosen to be 0:6 (red lines) and 1:0 (blue lines). We clearly see distributions depart further from the theory expectation (solid black curves) with the smaller cone size Rqq, whether the resonance is CP-even (left panels) or CP-odd (right panels). When it comes to detector-level analyses, however, once we introduce a fairly hard y cut resulting in Re(yst ) < RMJ, the above-discussed parton-level e ect simply disappears. Corresponding dotted lines in gure 6 clearly support our expectation that parton level, no selection detector level, CA R = 0.6 detector level, CA R = 1.0 s = 13 TeV, MS = 1500 GeV s = 13 TeV, MS = 1500 GeV distributions are not much di erent even with di erent RMJ values.8 understand this point from \constant" MJ-tagging e ciencies even with di erent C/A jet sizes in table 2. Although we vary the size of MJs with di erent RMJ values, the overall cut on the angular distance of a quark pair is determined by Re(yst ), allowing us to have a \stable" MJ-tagging rate. Another important message that one may realize from this series of exercises is that the impact of analysis cuts upon detector-level reconstructed objects is in more favor of our goal of discriminating CP states, unlike typical expectations in detector-level data analyses. More speci cally, the di erence of distributions between CP-even and CP-odd cases appears enhanced even after incomplete integrations over angular variables such as polar angles i in eqs. (3.14) and (3.15) (see also gure 3). This enhancement overcomes the adverse e ects of detector resolution which often degrade subsequent data analyses. Analysis with matrix element methods In this section, we discuss further analyses with matrix element methods using fourmomentum information of subjets obtained by the jet substructure technique delineated in the previous section. We begin with a general overview for CP state discrimination with various measures, followed by matrix element methods and our main results with them. Determining the CP property To deal with experimental systematics properly and maximize distinctive asymmetric features between the di erential distributions for CP-even and CP-odd resonances, a simple measure A has been introduced for the S ! ZZ ! 4` channel [62]: where N simply denotes the number of events. One may make use of the below-de ned cumulative probability over A as a measure to determine the unusualness for any observation Aobs under a given hypothesis, p0++ (Aobs; A ) = P (A p0 + (Aobs; A ) = P (A where P implies the associated probability. An alternative method to obtain a probability density function (pdf ) is the kernel density estimation (KDE). One may estimate a pdf from simulated data, and use the estimated function fKDE in performing a log-likelihood ratio test as q = 8Additional cuts including a detector geometry cut and object selection cuts (especially PT ) give further restrictions on the phase space. Thus angular distributions are distorted further, compared to parton-level to obtain the most powerful test between two simple hypotheses at a given signi cance according to the Neyman-Pearson lemma [63, 64]. The pdf P (q j0PC) for a test with a given hypothesis 0PC and the given number of events Nevt is calculated from a huge number of pseudo-experiments which are generated with hypothesis 0PC. The corresponding cumulative probabilities based on q are p0++ (qobs; q ) = P (q p0 + (qobs; q ) = P (q However, the above approaches, which are based on distributions, rely on the projection of our observed momenta of visible particles, fpreco g = fpj1 ; pj2 ; p` ; p`+ g, into a single angular variable . Although in our study, phase-space reduction by cuts in jet substructure methods can enhance the di erence between two CP hypotheses as we have observed in the previous section, it does not guarantee whether this projection attains the best sensitivity in cases where there exist at least three correlated angular variables as in eqs. (3.14) and (3.15). In the next section, we instead directly convert the observed momenta into a probability under a given model hypothesis. We then utilize this probability as a likelihood ratio test between di erent hypotheses on the CP state of a scalar resonance S in our study. Matrix Element Method hypothetical process is given by As brie y mentioned in eq. (1.2), the probability based on the matrix element in a given gj ) = fp1 (x1)fp2 (x2) Z where fpi (xi) is a parton distribution function of parton pi inside the beam with a fractional energy of xi. qi describes the phase space of parton-level particles qi which are related to observed momenta fprecog of corresponding particles. If detectors were perfect, such a relation would be trivial. However, as instrumental e ects including detector smearing and responses become important factors in precise measurements, transfer functions W(qi; fprecog) are introduced to map the information from reconstructed particles to the parton-level input for the MEM by modelling energy smearing, in particular, e ects in jet reconstruction stemming from showering, hadronization/fragmentation, and jet energy scales with gaussian functions that were obtained in the course of understanding top-quark properties in the Tevatron experiments [65{70]. To reduce the dependence on the transfer function in (5.7), one may use a deeper substructure of merged jets, e.g., ner subjet analyses as in the shower deconstruction method [37, 71, 72]. Fine structure analyses often bene t the studies based on parton-showering-sensitive features, e.g., distinguishing merged jets from ordinary QCD jets. We, however, emphasize that the deeper pattern of parton showering is less relevant to identifying the CP state of resonance S with merged jets. In our study, we instead take a simpli ed but conservative approach for which we set W(qi; fprecog) to be a delta function of momenta of quarks from the decay of Z boson at the point of momenta of the two prong subjets from the mass drop tagger as we are not aware of precise information on detector responses. Ignorance of details of parton showering and the detector response signi cantly simpli es the probability in (5.7) at the cost of maximal sensitivity suggested by the Neyman-Pearson lemma. Indeed, such details are less relevant as long as reconstructed subjets do depict quarks from the Z boson decay reasonably well. We can further minimize potential impact from ignorance of higher-order parton showering by selecting a merged jet with its mass around mZ . To regain sensitivity from above projections, we model a pdf based on the reconstruction-level distributions as we describe below, instead of modeling the transfer function. We remark that for the case at hand, all kinematic information can be restored with measured four-momenta of visible particles, meaning that the xi's in parton distribution functions become xed. Hence, the probability evaluated from a matrix element can be simpli ed as follows: 1 fp1 (x1)fp2 (x2) We then decompose the matrix element into the production part p1p2 ! S and the decay as long as the decay width through a narrow width approximation (NWA) which is valid S of resonance S is negligible compared to its mass MS. We also note that S is a scalar particle so that any helicity connections with partons in production part are disconnected unlike higher spin cases [44]. Therefore, we have the ratio of probabilities with di erent CP hypotheses 0PC as M(S!qq`+` )(fj2; j1; `+; ` g; 0PC) 2 ; where we dropped the common parts involving a production mode. Here we use the fact that cross sections 0PC are xed by the observed value. There is a subtlety in calculating a matrix element M as the current jet algorithms cannot specify the charge or avor for light quarks. In order to deal with this issue, we symmetrize a matching between subjet (j1; j2) and (q; q) as M(S!qq`+` )(fj1; j2; `+; ` g; 0PC) 2 which alters the above-given probability ratio to the symmetrized ratio called a kinematic discriminant (KD) number of reconstructed events for each hypothesis that are prepared with Monte Carlo simulation at the detector level, ensuring the consideration of various experimental e ects. Assuming that each pseudo-experiment is independent and identically distributed, we set two likelihoods L(0PC) with the xed number of events Nevt Corresponding test statistic q M is de ned as the log-likelihood ratio, P0++ (KDi) A pdf of P (qMj0PC) for a test statistic q with a given hypothesis 0PC and a given number of events Nevt is calculated from a huge number of pseudo-experiments. Cumulative probabilities based on q M are given by p0++ (qMobs; qM) = P (qM p0 + (qMobs; qM) = P (qM We nally present our main results on distinguishing CP-even and CP-odd states in this section, comparing three methods, two with angular variables A , and the other with an MEM-based variable. To maximize relevant performances, we rst construct pdf s for test statistics in both methods based on the log-likelihood ratio. In our analyses we do not consider backgrounds since (1) we compare the performance of each method in the best case, and (2) background subtraction can be performed with sPlot [73]. We rather focus on studying e ects from cuts to reduce backgrounds. Detailed information on potential backgrounds and recipes to take them into consideration in KD-based analyses shall be provided in appendix A, and we simply continue our discussion here, having the dominant reducible backgrounds in our mind. As discussed earlier, the main SM backgrounds to two leptons plus a single MJ are Z(! `+` ) + js where a QCD jet can mimic an MJ by dressing up a mass due to QCD contaminations [46, 51, 74{76]. Obviously, the resonance mass window cut is useful to suppress backgrounds, i.e., the invariant mass formed by an MJ and a lepton pair should fall into the range around the mass of S. We set a di erent mass range in each benchmark point to consider e ects of smearing. To reduce backgrounds further, it is noteworthy that for a signal event, a merged Z-jet and a di-leptonic Z are typically symmetric since they originate from a single resonance, whereas for a background event, the corresponding objects are asymmetric because a quark-initiated jet and Z are expected to have a sizable mass gap between them. This observation motivates us to introduce a PT -asymmetric variable yZZ [75] that is expected to be a reasonable choice to reduce Z + js backgrounds: yZZ = one merged jet, two ` PT > 25 GeV PT (MJ) > 0:4 m(MJ; `+; ` ) within MS within MS rapidities of nal particles do not depend on the CP states of a spin 0 particle, we expect that the e ciencies in di erent CP states of S are the same. Cut-e ciency ows for our benchmark points are summarized in table 3. Note that the e ciencies here are the same for both CP-even and CP-odd states. Basically, the reconstruction e ciency through detector geometry (i.e., rapidity coverage) and PT selection depends on the rapidity of visible objects. However, their rapidity depends on the former of which has nothing to do with the CP state (as discussed in section 3) and the latter of which is sensitive only to the Z decay structure. Imposing those cuts on Monte Carlo event samples, we conduct posterior analyses to determine the CP state of S using the pdf s from three methods listed below. 1. A variable in eq. (5.1) 2. Log-likelihood ratio q on distributions in eq. (5.4) 3. Log-likelihood ratio q M based on the MEM in eq. (5.13) the rst row, q in the second row, and q M in the third row. To ensure enough statistics, we prepare 5 million pseudo-experiments for both BPs at the center-of-mass energy of 13 TeV. The rst two columns show their distributions under the 0++ hypothesis (red histogram) column) and Nevent = 50 (second column). In discriminating di erent hypotheses 0++ and 0 + with a test static , we calculate p0 + ( obs; ) to reject the 0 + hypothesis in favor of 0++ (Type I error ) [30], exhibiting \Brazilian" plots in the third column, i.e., 1 (green) and 2 (yellow) bands around the peak in p0++ ( obs; ) according to the number of required events to separate the two hypotheses. We clearly observe that the most CP-sensitive method is to utilize a test static with the MEM-based log-likelihood ratio. In our study, we nd that the separating power of the MEM-based method remarkably does not change much with resonance mass representing the moderate boost region, the required number of events to have Type I error in the level of 3 is Ne(v3en)t = 18+1140 within 1 deviation for the 0++ hypothesis. For BP2 RMJ = 1:2: the method based on A variable of eq. (5.1) in the rst row, a log-likelihood ratio test based on the angular distributions from eq. (5.4) in the second row, and a log-likelihood ratio test based on the MEM of eq. (5.13) in the third row. di erential distribution in as it is the most crucial angular variable encapsulated in the MEM to determine the CP state. If we neglect restriction on the phase space of leptons as lepton isolation Riso is larger than the minimum angular distance Rff in eq. (4.2), the most relevant one is from the phase-space reduction in the jet clustering procedure as in eq. (4.15). The corresponding coe cient ratios R , which are de ned in eq. (3.21), for the two BPs are ' 0:299 for BP1 ; ' 0:309 for BP2 : As the shapes in distributions between the two benchmark points become similar after MDT procedures, we anticipate that Ne(v3en)t for both BPs are of same order, accordingly. As the second phase of the LHC accumulates more data, resonance searches in the TeV mass range are readily available in many channels. A wide range of new physics models predict such massive particles which often decay into heavy SM states such as top quark, the associated nal state, the hadronic ones, which typically come with larger branching fractions, are anticipated to play an important role in discovery potential as well as property measurement at earlier stages. Nevertheless, relevant analyses are often challenging because (hadronic) decay products are inclined to be highly collimated due to the substantial mass gap between the heavy resonance and the SM heavy states involved in the process of interest. In this paper, we tackled this challenge with the aid of jet substructure techniques, and showed that it is possible to measure physical properties of new particles using subjet information. More speci cally, we illustrated that the Matrix Element Method can be a powerful method for identifying properties of a new particle in the nal state with two jets and two leptons via a pair of SM gauge bosons. As a concrete example, we focused on discriminating the CP property of a spin-0 resonance which decays into a pair of SM gauge bosons. For a systematic approach, we adopted the prescription of the \merged" jet to capture two quarks from the decay of an SM gauge boson, which also helps to reduce combinatorial issues. We then studied e ects from jet clusterings and associated jet substructure methods on the phase space for visible particles. A certain extent of prejudice in performing data analyses with detector-level reconstructed particles is typically expected in comparison with relevant theoretical expectations. However, our study based on both analytical calculations and Monte Carlo simulation demonstrated that restrictions on the phase space invoked by jet clustering procedures could enhance the di erence in angular distributions for new particles with di erent CP states, unlike the naive expectation stated above. We also showed that the performance of our data analyses does not signi cantly depend on the size of MJs, as internal cuts in jet grooming procedures a ect the phase space for visible particles stronger. We believe that our nding here bene ts the determination of a reasonable size of MJs to make a balance between analysis performance and enhancement of the ratio of signal-over-background. In our analyses with the MEM, we refrained from integrating partonic phase space through transfer functions which map reconstructed objects to the partonic phase space. We rather modeled a probability density function (pdf ), generating many pseudoexperiments with Monte Carlo simulation for a given signal hypothesis. This procedure can take into account various e ects from jet clustering procedures together with detector e ects as well as o er computational advantages compared to the situation where 2Nvis dimensional integration is required in dealing with transfer functions. Two benchmark points were selected to cover various phase space regions from the moderately boosted one to the highly boosted one. According to our numerical studies, discriminating di erent CP states requires O(20) signal events at the level of 3 signi cance over the mass range of a new particle from over 700 GeV that the current LHC has the equal level of sensitivity in a merged jet with dileptons compared to a full leptonic channel [46]. Acknowledgments M.P. appreciates useful discussions with Veronica Sanz about the e ciency in tagging MJs in terms of the resonance mass. M.P. also appreciates the kind hospitality of Kavli-IPMU while part of this work had been performed. M.P., K.K., and D.K. thank the organizers of the CERN TH institute funded by CERN-KOREA program where a part of this work was completed. K.K. thanks the hospitality and support from PITT PACC. This work is supported by IBS under the project code, IBS-R018-D1. K.K. and D.K. are supCross section ( ) selection criterion PT of leading jet one merged jet, two ` PT > 25 GeV PT (MJ) > 0:4 m(MJ; `+; ` ) within MS ZZ Z + jets becomes the dominant background, compared to irreducible electroweak process pp ! ZZ. ported by DOE (DE-FG02-12ER41809, DE-SC0007863). D.K. is supported in part by the Korean Research Foundation (KRF) through the CERN-Korea fellowship program. C.H. is supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. Background consideration in MEM analyses The major irreducible background in which the nal state particles are the same as those in our case (i.e., jj`+` ) is ZV pair production. Here V includes not only Z but W bosons which decay into two jets because a W -induced MJ can easily fake a Z-induced MJ due to jet mass resolution. On the other hand, the major reducible background is Z + js where a QCD jet j can mimic an Z-induced MJ by acquiring a non-vanishing mass due to QCD corruptions. To estimate contributions from above backgrounds, we perform detector-level Monte Carlo simulation for ZV and Z + js, and summarize the associated ows in table 4. We also demonstrate, in gure 9, m(MJ;`+;` ) distributions for the backgrounds and signal after all the cuts except m(MJ;`+;` ) in table 4, suggesting that the Z + js dominates ZV backgrounds by far. In the presence of backgrounds (denoted as bkg), we express probability density function P with respect to a set of discriminator variables fxg for the signal-plus-background hypothesis as follows: where rS(B) is the \observed" fractional signal (background) cross section to the total observed one. Here P(fxgj ) is an individual pdf under hypothesis (either signal or background), which is built from the associated amplitude. It turns out that the best discriminator is the set of momenta fpg itself. The matrix elements for the signal and background processes are needed to convert observed momentum information into a form 1/(0−1 1E0−2 L = 20 fb-1, LO samples 0++, normalized arbitrarily 400 600 800 1000 1200 1400 1600 1800 2000 of probability under a given hypothesis. We then de ne the likelihood ratio q M = P(fpgij0++) + R P(fpgijbkg) P(fpgij0 +) + R P(fpgijbkg) where R is the ratio of the \observed" background to the \observed" signal cross sections. If the relevant backgrounds are well under control or su ciently suppressed, i.e., R the above expression is approximated to M = P(fpgijbkg) P(fpgijbkg) P(fpgijbkg) P(fpgijbkg) Note that it is not necessary to consider the second term in order to discriminate the CP property of resonance S, because the rst term already carries relevant information to be used for the hypothesis test as we have seen in section 5. Certainly, using the second term can improve the discriminating power according to the Neyman-Pearson lemma. However, the likelihood ratio between signal and background is not easily factorizable into matrix elements, and therefore, we conservatively utilize the rst term only for the hypothesis test. We conduct similar exercises as in gure 7 for BP1 including the contribution from all backgrounds shown in gure 9, and exhibit the resulting discrimination power in gure 10. We evaluate q M using only the dominant term in eq. (A.3), setting us free from the pdf under the background hypothesis. For each of the event samples for the CP-even and CP-odd, we take the same numbers of signal and background events. Comparing them with the corresponding plots in the second row of gure 7, we see that (not surprisingly) backgrounds shown in gure 9. more events are required to discriminate the CP property of the scalar. In this sense, more reduction of background events would help to probe the properties of the new particles. As the main background is from Z + js in which QCD jets fake MJs, an analytic matrix element of Z + js after the MDT should be provided in order to implement the background into the MEM more accurately. The leading order and next-to-leading order results are shown in refs. [77, 78]. However, it would be challenging to go beyond next-to-leading logarithmic accuracy since the original de nition of the MDT carries nonglobal logarithms [77, 78]. While a modi ed Mass Drop Tagger or a soft drop have been proposed [16, 77, 78] and next-to-next-to-leading logarithmic accuracy has been shown recently [79], dedicated examinations along the line are certainly beyond the scope of the paper in which a simple MDT is employed. We therefore do not provide any further discussion on the MEMs including backgrounds. Phase space restriction from other jet substructure methods Besides the MDT, there are other jet substructure methods which have been widely used in the literature. We give brief comments on how they a ect the phase space. Trimming. The trimming procedure [15] uses a kt algorithm to divide a merged jet where fcut is a parameter. The remaining subjets are then reclustered as a trimmed jet. Similar to the MDT, the fcut applies a cut on the PT fraction of a subjet z such that z > fcut. Like eq. (4.12), it e ectively reduces the cone size of MJs. Pruning. The pruning method [14] uses the C/A or kt algorithm to cluster the jets. limit on the cone size of MJs. N-subjettness. N-subjettiness [23, 24] is de ned as N = reconstructed jets. nding algorithm. Here ji denotes the usual ith subjet, while k runs over all constituent particles in a given MJ. 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Chengcheng Han, Doojin Kim, Minho Kim, Kyoungchul Kong, Sung Hak Lim, Myeonghun Park. Identifying a new particle with jet substructures, Journal of High Energy Physics, 2017, 27, DOI: 10.1007/JHEP01(2017)027