LHC top partner searches beyond the 2 TeV mass region

Journal of High Energy Physics, Sep 2015

Abstract We propose a new search strategy for heavy top partners at the early stages of the LHC run-II, based on lepton-jet final states. Our results show that final states containing a boosted massive jet and a hard lepton, in addition to a top quark and possibly a forward jet, offer a new window to both detecting and measuring top partners of mass ∼ 2TeV. Our resulting signal significance is comparable or superior to the same sign dilepton channels for top partner masses heavier than roughly 1 TeV. Unlike the di-lepton channel, the selection criteria we propose are sensitive both to 5/3 and 1/3 charge top partners and allow for full reconstruction of the resonance mass peak. Our search strategy utilizes a simplified b-tagging procedure and the Template Overlap Method to tag the massive boosted objects and reject the corresponding backgrounds. In addition, we propose a new, pileup insensitive method, to tag forward jets which characterize our signal events. We consider full effects of pileup contamination at 50 interactions per bunch crossing. We demonstrate that even in the most pessimistic pileup scenarios, the significance we obtain is sufficient to claim a discovery over a wide range of top partner parameters. While we focus on the minimal natural composite Higgs model, the results of this paper can be easily translated into bounds on any heavy partner with a \( t\overline{t}Wj \) final state topology.

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LHC top partner searches beyond the 2 TeV mass region

Received: November LHC top partner searches beyond the 2 TeV mass region Mihailo Backovi´c 0 1 3 6 7 8 Thomas Flacke 0 1 2 3 4 7 8 Seung J. Lee 0 1 2 3 4 5 7 8 Gilad Perez 0 1 3 6 7 8 0 Seoul 130-722 , Korea 1 335 Gwahak-ro , Yuseong-gu, Daejeon 305-701 , Korea 2 Department of Physics , Korea University 3 Weizmann Institute of Science , Rehovot 76100 , Israel 4 Department of Physics, Korea Advanced Institute of Science and Technology 5 School of Physics, Korea Institute for Advanced Study 6 Department of Particle Physics and Astrophysics 7 Open Access , c The Authors 8 Seoul 136-713 , Korea We propose a new search strategy for heavy top partners at the early stages of the LHC run-II, based on lepton-jet final states. Our results show that final states containing a boosted massive jet and a hard lepton, in addition to a top quark and possibly a forward jet, offer a new window to both detecting and measuring top partners of mass ∼ 2 TeV. Our resulting signal significance is comparable or superior to the same sign dilepton channels for top partner masses heavier than roughly 1 TeV. Unlike the di-lepton channel, the selection criteria we propose are sensitive both to 5/3 and 1/3 charge top partners and allow for full reconstruction of the resonance mass peak. Our search strategy utilizes a simplified b-tagging procedure and the Template Overlap Method to tag the massive boosted objects and reject the corresponding backgrounds. In addition, we propose a new, pileup insensitive method, to tag forward jets which characterize our signal events. We consider full effects of pileup contamination at 50 interactions per bunch crossing. We demonstrate that even in the most pessimistic pileup scenarios, the significance we obtain is sufficient to claim a discovery over a wide range of top partner parameters. While we focus on the minimal natural composite Higgs model, the results of this paper can be easily translated into bounds on any heavy partner with a tt¯W j final state topology. mass; region; Beyond Standard Model; Heavy Quark Physics; Technicolor and Composite 1 Introduction Partially composite top partners Brief description of the benchmark model Production of top partners Top partner decays Single production cross section — Same sign di-leptons vs. lepton-jet final Data simulation and event pre-selection Tagging of boosted objects Forward jet tagging Resonance mass reconstruction Projected MX5/3/B sensitivity Effect of pileup on MX5/3/B sensitivity A few remarks on the complementarity of top partner searches A SO(5)/SO(4) essentials Details of Composite Higgs Models with Partially Composite Top B.1 Partial compositeness: masses and mixing B.2 Interactions of quarks with quark partners in the gauge eigenbasis B.3 Derivation and discussion of the interactions of quarks with quark partners in the mass eigenbasis B.4 Decays of top partners B.5 Concluding remarks Introduction The discovery of the Higgs boson at the Large Hadron Collider (LHC) is a great victory for the Standard Model (SM) of particle physics. With its minimal scalar sector of electroweak symmetry breaking, the SM at short distances is a complete weakly coupled theory up to very large energy scales. Furthermore, the SM admits a set of accidental symmetries that eliminate proton decay and suppress custodial, flavor and CP violating processes. Even though the SM cannot explain several experimental observations such as the neutrino masses, the baryon asymmetry of the universe and the origin of dark matter one cannot deduce with any certainty the energy scale at which the extensions of the SM would be relevant, with the exceptions of the Planck scale and the scale of the Landau pole of the hyper charge interactions. The only fuzzy scale, potentially accessible to the LHC, is related to the recently discovered Higgs boson. As a fundamental scalar the Higgs mass is ultra-violet (UV) sensitive. Hence, we expect that on the quantum level the Higgs mass will pick up large contributions from high energy scales, resulting in a very large mass of the Higgs boson. This, of course, is in direct contradiction with our direct and indirect knowledge of the Higgs boson dynamics. A simple possibility to stabilize the Higgs mass and the electroweak scale in a controlled manner is to add new fields to SM, with the same gauge quantum numbers as the SM fields, such that the contributions of the new fields to the Higgs mass eliminate the UV sensitivity. In the absence of interactions the Higgs will loose its quantum sensitivity (setting quantum gravity aside), and hence the most severe known sensitivity of the Higgs to quantum corrections arise as a result its large coupling to the top quark. To ensure the stabilization of the electroweak scale, the virtual contributions of some of the new particles to the Higgs mass should cancel the contributions coming from the SM top quarks. These new states are collectively denoted as top partners. In known examples the partners might be scalars as in the case of supersymmetry or fermions as in the case of composite Higgs models (CHMs). Current bounds on the top partner masses are roughly & 700 GeV for supersymmetric scalar states and & 800 GeV for composite-Higgs fermionic states (see e.g. refs. [1, 2] for recent results). While the bounds on the top partner masses are fairly strong they are not bullet proof, and they also only result in moderate pressure on naturalness (here we are not concerned with various definitions of fine tuning). Probably the most relevant question amidst the “LHC battle for naturalness” is how are we going to discover top partners (if any exists) or improve the bounds on the top partners both in terms of mass reach and in terms of robustness. The two criteria can be used to guide the focus of theoretical, phenomenological and experimental effort. One can define two “mini-frontiers” for the battle for naturalness at the LHC [3]: 1. The mini energy frontier, where the effort is directed towards searching for ultra massive top partners. The experimental focus of the energy frontier searches is defined by the highest center-of-mass energies that can be reached by the LHC. 2. The mini intensity frontier, where the effort is focused on searching for partners with mass below or near the current bounds. The mini intensity frontier focuses the searches for top partners to possibilities that partners are elusive (i.e. when for some reason the current searches are not sensitive enough to their presence). The physics describing the above frontiers is qualitatively different both in terms of the phenomenology describing them and in terms of the necessary experimental effort. It is important to notice that prior to the start of the LHC the starting points of the framework of supersymmetry and pseudo-Nambu-Goldstone boson (pNGB) composite Higgs models were different in the context of naturalness. If we were to remove our LHC-based knowledge (the results of the ATLAS and CMS direct searches) then supersymmetric models are not subject to any substantial pressure from naturalness. For instance, stop (as well as most of the other superpartners) masses close to that of the top quark are not in conflict with existing data. This is not the case when pNGB composite Higgs models are considered as the combination of LEP and Tevatron data is already constraining the model’s decay constant f to lie above the f > O(800 GeV) scale [4, 5]. Beyond the mere fact that this rather strong constraint on the value of f forces some amount of fine tuning, it also suggests that we should have expected that the composite fermion resonances would be somewhat heavy with masses probably larger than f . Even at the centre of mass energy of 8 TeV, the typical fermonic top partner production cross sections and the collected luminosity were simply not enough to produce the heavy partners. Thus, there is very little surprise that the first run of the LHC, which was limited in centre of mass energy, did not observe them. In order to make experimental progress on fermionic top partner searches at the LHC, it is hence necessary to focus on the region of parameter space where the top partner masses are larger than f . So far, the parameter space region of heavy fermionic top partners has not been explored, providing the main motivation for our current study of heavy top partners at the mini energy frontier. The main focus of this work is to study the reach of the LHC in the next run to discover and measure (or exclude) the presence of top partners in regions of model parameter space which results in large top partner masses. When searching for top partners one needs to distinguish between event topologies of pair produced and singly produced top partners [6, 7]. While the former is more robust as the partners are produced via SM QCD processes it suffers from a severe “large x suppression” from the parton distribution function (PDF) for large top partner masses. As two heavy particles are produced, the quarks and gluons in the proton have to carry a high x in order to achieve a heavy final state. The expected reach of searches for doubly produced top partners is rather limited even when considering high luminosities [8]. Single production processes, on the other hand, are model dependent but are subject to much lower level of PDF suppression and thus can potentially lead to a much better experimental reach. Following the original papers that have emphasized the importance of the same sign lepton signal [9–11], most experimental studies to date have focused on the final states characterised by two leptons of the same charge. Standard Model processes are highly unlikely to produce final states with two same sign leptons, deeming such signals a “clean” signature of BSM physics.1 However, not all top partners produce distinct signatures in the same sign di-lepton channel, implying that the same sign di-lepton searches are sensitive only to exotic top partners (i.e. charge 5/3). Furthermore, the di-lepton final states suffer from low branching ratios and from the fact that the resonance masses are smeared due to the missing energy having at least two hard neutrino components. 1It is important to note that since the dominant backgrounds to the same sign di-lepton processes come from detector effects such as photon conversions, accurate estimates of background channels are challenging. In this paper we consider the case where the heavy partners decay to hadronic-leptonic final states. For other studies involving hadronic final state see refs. [6, 7, 12–14]. We provide a strategy and a detailed phenomenological study which shows that in preferred regions of pNGB composite Higgs models one can discover top partners (at 5 sigma CL) with mass as high as 2 TeV at the 14 TeV LHC run, and with integrated luminosity of 2 TeV partners (at 2 sigma CL) with as little as 10 fb−1. Our study adopts the Template Overlap Method (TOM) [15–18] to tag the highly boosted decay product of the partners and in part reject the corresponding SM backgrounds. The final state of our signal events is characterized by multiple b-jets, which we employ through a semi-realistic b-tagging procedure. We take into account the contamination from pileup, assuming average of 50 interactions per bunch crossing and show where the effects of pileup on our selection criteria can be mitigated and where additional improvement might be necessary. Finally, our study of singly produced top partners employs the presence of a high energy forward jet in the signal events, which is in principle susceptible to contamination from pileup. We propose a modification of forward-jet tagging, show that the signal distributions are hardly affected by reduction in forward jet cone size, while the background is significantly suppressed upon requiring a forward jet tag. As this is the first time that such a technique is proposed we present the results with and without the use of the new forward-jet tagger. At large top partner masses the mass splitting between the partners due to electroweak symmetry breaking is subdominant. Hence, as we are not confined to the same sign dilepton final states, our event selection strategy is adequate for searches for all partners that decay to tops and W s and not only the 5/3 charged ones. For the sake of concreteness and simplicity our current study focuses only on the relatively simple final state of tt¯W j. Note, however, that it is straight forward to generalize our study to include other final states as well. In section 2 we provide a brief introduction to our benchmark composite Higgs model. We include only the bare minimum of information directly relevant for the phenomenology of top partners and postpone a detailed discussion of the composite Higgs models and derivations of the equations until the appendix. Section 2 also contains a discussion of dominant production and decay modes of fermionic top partners. The main results of the paper are discussed in detail in section 3. We include a detailed overview of our forward jet tagging proposal in section 3.3, as well as discuss our simplified b-tagging algorithm and the boosted jet tagger in sections 3.2 and 3.4. We present the results on the sensitivity of run-II LHC searches for 14 TeV to heavy top partner masses in section 3.6. Finally, in section 3.8 we comment on the use of various final states to extract additional information about top partners, if a signal is ever observed. A highly detailed description of our benchmark composite Higgs model, top partner production mechanisms and decays can be found in the appendix. 2Note that unlike the model independent top partner pair production cross section, the single production (on which our analysis is relying) has a model dependent production cross section. The model dependence is encompassed in the effective coupling constants of top partners, which depend on several model parameters. Brief description of the benchmark model In this article, we use the Minimal Composite Higgs Model (MCHM) [19] as a benchmark for illustrating the performance of our event selection searches for top partners. Here we give a brief overview of the model features important for our phenomenological study. For a detailed description of the model see appendix B. The Higgs doublet in MCHM is a Goldstone boson multiplet which arises from the gauged in order to provide the electroweak gauge bosons.3 breaking of a global SO(5) × U(1)X down to SO(4) × U(1)X ' SU(2)R × SU(2)L × U(1)X of a strongly coupled theory. The SU(2)L and a U(1) subgroup of SU(2)R × U(1)X are The low energy description of the strongly coupled sector with “weakly coupled” deformations is expected to contain additional scalar, fermionic and vector resonances, typO(1) ≤ g resonances are required in order to accommodate an effective potential for the Higgs which induces Electroweak Symmetry Breaking (EWSB) and the Higgs mass. We use a bottom-up approach and only include a minimal set of light fermionic resonances: a top partner multiplet in the 5 of SO(5). The partner multiplet contains a partner charge 2/3 (Tf1,2 and Ts), where Ts is a singlet while the other four states form a 4 under the SO(4). A generic feature of composite Higgs models is that the 5/3 charge partner (X5/3) is the lightest state amongst the partners in the 4. Furthermore, if one neglects the electrical charge sign of the decay products, the phenomenological signatures of X5/3 and the B are identical. We will hence focus our effort on searches for X5/3/B states and postpone the searches for other top partners until future studies. Upon the diagonalization of the mass matrix (see the appendix for more detail) the masses of the top, and the partners, are given by: mt = √ MB = MX5/3 = M4 , MT f1 = M4 + O( 2) , MT f2 = MT s = the up-type and down-type quarks. left to right) at a proton-proton collider. them (see [20] for a detail discussion on the model’s flavor parameters), f is the compositeness scale, yL,R are the left handed/right handed pre-Yukawa couplings, and Eq. (2.1) reveals an important point which we will employ in the following sections. The mass splitting between the M5/3 and B goes as f /M4, implying that the heavier the X5/3 partner is, the more mass degenerate it becomes with the B state, provided yL is not ≡ v/f . Our current study will focus only on the tW decays of the top partners, since this is the only mode X5/3 can decay to due to charge conservation. The dominant couplings of X5/3 and B states are of strength M4MT s − √2cR yRf |M1|M4 + e−iφy2 f 2 L √2cR where cR is a right-handed strong sector coupling between the partners in the 1 and 4.4 Production of top partners The top partners are colored and can therefore be pair-produced via QCD interactions, where the production cross section only depends on the mass of the respective top partner. The top partners can also be single-produced via the interactions of eq.(2.2). For low top partner masses, pair production dominates, but for higher top partner masses, singleproduction becomes kinematically favorable, as can be seen in figure 2.5 Since here we are interested in heavy top partners, we will focus our attention on single production only. Figure 1 shows the dominant production channels for the respective top partners. The X5/3 partner is produced together with a jet and an anti-top, where the dominant effective 4Notice that these couplings are chiral, where the partner couplings to left-handed tops are suppressed by O( 2). The dominance of right hand couplings to tops result in characteristic features in the angular and pT distributions of the top decay products [21, 22] and could help reveal the structure of top partner couplings (in case a signal is observed at the future LHC runs). 5The single production cross section depends on the model parameters beyond the mass of the top partners as can be seen already from the couplings in eq.(2.2). Hence, the top partner mass scale at which single production becomes dominant depends on the model parameters. We will return to this point coupling is right-handed. Due to the larger up quark PDF in the proton, X5/3 production is preferred as compared to X¯5/3 production, which requires a d or a u¯ in the initial state. The B¯ is produced together with a jet and a top via a right-handed coupling with preference of B¯ over B production, again due to the larger up quark PDF. The fourplet top partners Tf1 and Tf2 are produced together with a jet and a top via a right-handed coupling. Analogously, their anti-particles are produced together with a jet and an anti-top. As their production arises from a Z which is radiated off an initial state u, the production rates for them and their antiparticles are comparable. Finally, the singlet top partner Ts dominantly couples to W b via a left-handed coupling. It can thus be produced together with only a jet, but requires a (PDF suppressed) b quark in the initial state. Due to the larger up-quark PDF, Ts production is preferred over T¯s production at a proton-proton collider. The effective couplings eq. (2.2) relevant for single production6 depend not only on the mass of the top partners but also directly on the other model parameters — in particular on cR (for X5/3, Tf1, Tf2 and B single production) and cL (for Ts single production) — the production cross sections of the fourplet (singlet) states scale with |cR|2 (|cL|2). For effective couplings in eq. (2.2) become comparable in magnitude, and can cancel or enhance shows the single production cross section of X5/3 and X¯5/3 for different values of cR as a comparison we also show the pair production cross section for X5/3 + X¯5/3 . In the limit of large cR, the production cross section of the B¯ is marginally lower than the one for X5/3 because the B is slightly heavier. The Tf1,2 production cross sections are lower because the dominant production channel involves two couplings to the Z rather than to the W which yields a suppression of ( gg//2√cw )4 2 ∼ 0.4.7 As an illustration, figure 2, right panel, shows the single production cross section of X5/3, B, Tf1, Tf2, Ts and their reproduce the top mass. Top partner decays For all top partners, the dominant couplings to W, Z, h and an SM quark are chiral (either left- or right-handed coupling dominates). In this case, the partial widths for a decay of a fermion F into a fermion f and a gauge boson or Higgs are Γ(F → W f ) = MF m2W 32π Γ(F → Zf ) = MF m2W 32π 6The analogous couplings for the charge 2/3 partners are given in eq. (B.39). cross section (at leading order) for X5/3 and single production cross section for X5/3 or X¯5/3 as a production cross section of other top partners and their antiparticles as a function of M4 . Other Γ(F → hf ) = MF |3λ2|e2πff Γh , Using these relations weMF2can estimate the partial widths and BRs of the different top m2W/Z/h are kinematic functions, and MF is the mass of the fermion. partners, using the effective couplings eqs. (B.39)–(B.48). For the X5/3 partner one obtains Γ(X5/3 → W t) ≈ M4 m2W 32π There are several interesting features of the X5/3 decay width to tW . First, note that although the effective coupling is O( ), the partial width is not suppressed. For large cR (and M1 and M4 of similar size), it is proportional to |yR2c2R|. For |yR2c2R| . 5, this still yields broad. Resonances of ultra-large widths are difficult to measure since they tend to “blend” into the continuum spectra of differential cross sections. Hence, sections of parameter space which can be probed by the future LHC runs are limited by the width/mass resolution. The X5/3 is the lightest partner state in the 4 (fourplet) such that decays into B, Tf1, Tf2 and SM particles are kinematically forbidden. Hence X5/3 always decays into For the B decay width and its branching ratios, the analogous discussion applies. The total B width is of similar size as the X5/3 width (cf. appendix B for the explicit expression). 8The singlet partner Ts can be lighter than the X5/3 if M1 < M4, but even then, the “cascade” decay when we have substantial mass splitting. We do not consider this extreme case further as this scenario, in which the fourplet partners are at mass scale substantially above the singlet partner is much better tested by searching for Ts, directly. The decay B → W t dominates over B → Zb and B → hb because effective couplings for the latter decays are of higher order in . “Cascade” decays B → W Tf1,2 are kinematically suppressed (if not forbidden) due to the small mass splitting between B and Tf1,2. For more details on top partner decays see appendix B. Single production cross section — Same sign di-leptons vs. lepton-jet final In addition to very interesting event topology, the single X5/3/B production is also interesting because at high enough MX5/3/B it becomes the dominant production mode. The kinematics of singly produced X5/3/B events are mostly determined by two parameters: tion is subject to many other model parameters. Here we are not interested in details of models but in general features of tt¯W j event topologies and will hence leave the production cross section as a free parameter. We consider a range of MX5/3/B, while keeping the width additional benefit of presenting the analysis in a model independent fashion and being able to apply our results to other new physics searches in the tt¯W j channel. In order to determine the “reasonable range” of cross sections, we consider several combinations of model parameters in a general partially composite model. We do not make any assumptions about the mass hierarchy in the model (e.g. we do not only consider M4), while we make sure that each model parameter point the decoupling limit of M1 reproduces the correct mt. is to be found during the future runs of the LHC, it will be found almost exclusively in the events containing at least one boosted top quark and one boosted W . Previous searches for X5/3/B partners focused mostly on the same sign di-lepton searches, due to the extremely clean signal, but at a cost of the signal rate. Compared to the inclusive single X5/3/B production, the signal rate is diminished by the branching ratio of W decays to leptons, σ2Xl5/3 = σtot × Br(W → lν)2 = σtot × (2/9)2 ∼ 0.05 σtot , state is 50%, implying that the total same sign di-lepton cross section is at least a factor of 2 smaller after the event selections. Instead, here we propose to search for top partners in channels which contain at least one lepton and a fat jet. Figure 3 shows an example diagram of singly produced X5/3/B, including the decay modes, where we take the initial state radiated top to decay inclusively. Compared to the same sign di-lepton searches, the starting signal cross section in our search strategy is if we consider both the top and the W decaying hadronically (but not simultaneously). Note that the signal cross section is increased roughly by an additional factor of two for by a boosted tW system in the case of X5/3/B, as denoted by the ovals, in addition to a high energy forward jet and a top. Notice that the only difference in the X5/3 production and B production is the sign of the decay products’ charges. We consider inclusive decays of the initial state radiated top. high MX5/3/B, where we expect X5/3 and B to be nearly mass degenerate. The same sign di-lepton cross section, however, remains the same at high MX5/3/B, as the top and the W from the B decay are of the opposite charge s = 14 TeV pp collider are characterised by four distinctive features: 1. A single, high energy forward jet. 3. One hard (pT > 100 GeV) lepton, resulting from a top or W decay. 4. Two b jets, one of which can be a part of a top fat jet. Figure 4 shows the features of the signal and background fat jet pT spectrum. The pT distribution of background events is characterised by a steep decline as a function of transverse momentum. Conversely, the signal distributions tend to peak at roughly the partner becomes more likely to be produced off-shell. As we will demonstrate in the following sections, our event selection based on the unique single X5/3/B event topology, combined with boosted jet techniques, b-tagging and forward jet tagging can achieve sensitivity to X5/3/B top partners over a wide range of model parameters at the 14 TeV run of the LHC. We further argue that our results for various masses of MX5/3/B, while we show the backgrounds on the right panel. All plots are normalised to unit area. are comparable and in some cases superior to the same sign di-lepton searches, with an additional advantage that our method allows for the reconstruction of the resonance in a simple manner. In section 2.1 we pointed out that at large MX5/3/B we expect the X5/3 top partner and the B to be nearly mass degenerate if the left-handed pre-Yukawa coupling is not too large, a fact which has significant implications on the phenomenology of the heavy top partners and highlights a key advantage of our method over the same sign di-lepton searches. Since we do not consider the charge of the leptons as a part of the selection, the fact that the mass splitting between X5/3 and B is small means that our search is sensitive to both channels, effectively doubling the signal cross section. Conversely, requiring a presence of two same sign leptons, provided that the mass of the partner is reconstructed out of two leptons and missing energy, would essentially veto the B production, as the B partner decays to a top and W of the opposite charge. On the other hand, without mass reconstruction, B cannot be distinguished from X5/3 by the simple requirement of same sign di-leptons, as there is an associated top produced along with single B, which could provide the same sign lepton as the one from boosted W . In the following sections we will consider the production of top partners both individually and under the assumption they are mass degenerate where relevant. Data simulation and event pre-selection We generate all our simulated events at √ MadGraph 5 [23] and shower them with Pythia 6 [24], with a fixed renormalisation and factorisation scale and assuming the CTEQ6L [25] parton distribution functions. In order to improve the statistics in the background channels, we impose a generation level cut of HT > 600 GeV on the background events, where HT is the sum of all hard parton pT values in the event. We require that all final state hard level patrons are generated W +jets are matched up to four extra jets, using the MLM matching scheme [26] with the consider tt¯ and W + jets in our analysis. Branching ratio of 2/9 for leptonic decays of the W in W +jets is included in the cross section, as well as the branching ratio of (2/9) × (2/3), for the semi-leptonic tt¯ decays. For improved statistics at high MX5/3/B, we consider tt¯ samples with two HT cuts, while we only take W +jets sample with HT > 600 GeV since at the end of the analysis it is a sub-leading background. flavor scheme. For the purpose of pileup studies, we generate a large sample of minimum bias events using Pythia 6 with default tunes. We simulate the effects of pileup contamination on signal/background events by adding to each event a random number of pileup events drawn Next, we cluster the showered events using the FastJet [27] implementation of the and b-jets. For the purpose of pileup mitigation, it is useful to consider a smaller R for the fat jet cone involves an elaborate procedure of calibrating jet energy scales and other systematics which is beyond the scope of our current work. For simplicity, here we will by reducing the fat jet cone. We consider signal events in which both the top and the W daughters of X5/3/B decay leptonically (but not simultaneously), while we take the other, non-boosted top to decay inclusively. Table 1 shows a list of possible backgrounds and the corresponding cross sections. The main background channel in our search strategy is SM tt¯ production and W +jets, while even at generation level the other SM backgrounds are subleading. Since we require at least one hard lepton in our analysis, we will only consider the background channels in which one of the tops or W bosons decays leptonically. We normalize the tt¯ cross section to the NNLO result from ref. [29], while the NLO corrections in W + jets are not expected factor, wile in the following sections we will show that our results are not strongly affected by the W + jets K-factor. All events are subject to Basic Cuts: > 40 GeV, where l represent the hardest lepton with mini-ISO > 0.8 [30], “fj” stands for the fat jet, In addition to Basic Cuts, we consider a series of additional selections designed to further suppress the background channels while maintaining as much of the signal as possible. In order to suppress the tt¯ background further we require mj0l > 200 GeV, hardest mini-isolated lepton in the event. The rest of the cuts we employ in this analysis deserve more attention and are described in detail in the following sections. Tagging of boosted objects Events which pass the Basic Cuts are subject to jet-substructure analysis. Many available methods for boosted top tagging exist in the literature (see for instance refs. [15, 16, 18, 31–48] and references therein). In addition, several interesting proposals for boosted W tagging appeared recetly in refs. [49–51]). Here, we use the TemplateTagger v.1.0 [43] implementation of the Template Overlap Method [15–18] as our boosted jet tagger, by virtue of the weak susceptibility of the method to pileup contamination. TOM approach to jet substructure aims to match the energy distribution of a jet to a parton-like configuration of heavy particle decays. The output of the method is the overlap score Ov, a measure of likelihood that a jet is, say, a top quark, a Higgs or a W boson, as well as the partonic configuration (i.e. peak template) which maximized the Ov score. The latter is of much importance, as one can in principle approximate the fat jet with the peak template. We will utilize this possibility in the following sections when considering effects of pileup on the measurements of the top partner mass. Our analysis of jet substructure follows the prescription of ref. [18], with the main difference that we divide events into hadronic top and hadronic W candidates before analyzing the fat jets. Note that our work in this paper represents the first use of TOM as a boosted W tagger. We begin by selecting the hardest mini-isolated lepton in the event and determining whether it originated from a top quark or a W . If there is a pT > 25 GeV, declare that the lepton is a part of a leptonically decaying top, and hence the hardest fat jet in the event is a W candidate. Otherwise, we declare that the W decayed leptonically, and that the hardest fat jet is a top candidate. An alternative method of determining the “candidacy” of a fat jet would be to simply use the fat jet invariant mass cut, but such a choice requires techniques to subtract or correct for pileup contamination of the jet mass. Here, instead, we aim for pileup insensitive criteria for both jet substructure and event selection, whenever possible. The leptonically decaying t/W also serves as a pileup insensitive estimator of the fat jet pT in the Template Overlap analysis, as the fat jet and the leptonic object recoil agains this is a good approximation in the boosted regime. shows the peak template distributions for hadronic t/W (top panel / bottom panel) candidate events with no pileup (solid lines), while the right panels are the peak overlap for hadronic t/W (top panel /bottom panel) candidate events in the presence of 50 average pileup events (dashed lines). The plots assume Basic Cuts and pT > 500 GeV for the fat jet. Notice that the signal distribution is weakly affected by pileup contamination. each other. We find that the scalar sum of the leptonic object constituent’s pT (i.e. the lepton, missing energy and ,if the leptonic object is a top, a light jet) is a good estimator of the fat jet transverse momentum [18]. In order to speed up the numerical calculations, we generate template states at fixed pT scaling rule of ref. [17]. We produce two separate sets of templates, the three body template sets for top states and two body template sets for the W states, where we use the appropriate set based on whether the fat jet is a top candidate of a W candidate. Note that the use of the leptonic top TemplateTagger does not add much to the analysis, as the background objects already contain a leptonically decaying top (in case W is the fat jet), and the leptonic W is too simple of an object to require a substructure analysis (in case that t is the fat jet). Finally, for an event to pass our boosted object selection, we require that the fat jet has an overlap score: Ov > 0.5, for both the hadronic top and hadronic W candidates. Figure 5 shows an example distribution of Template Overlap for signal and background events, after the Basic Cuts. The left panel shows only the events which were categorized as hadronic top candidates, while the right panel shows the corresponding plot for hadronic W candidates. In both cases the W +jets events are rejected very well by TOM, as our lepton requirement deems that the W decays leptonically and the fat jet is hence either a light jet or a combination of light jets which get clustered together. Semi leptonic tt¯ events are more challenging to reject via Template Overlap, since the final state content in terms of jet substructure is more similar to signal events. If a tt¯ is categorised as a hadronic top candidate, TOM will likely tag the event with a high overlap score, since the fat jet is indeed a hadronically decaying top. If the events is categorized as a hadronic W candidate, the expected peak overlap score will likely be lower since TOM will try to match the substructure of a top to a decay of a W boson. It is important to note that when it comes both to tt¯ and W +jets background, higher order effects on the shape of the kinematic distributions become significant at high energies. Extra hard gluons are likely to appear in a highly energetic tt¯ final state, causing the topantitop system not to appear back to back in the transverse plane. Such “asymmetric” events offer an additional handle to reject Standard Model di-top events. Proper treatment of the effect requires a full NLO event simulation, which is beyond the scope of our current study. It is impotent to note that since here we only consider a leading order tt¯ sample matched to one extra jet, our estimates for the Template Overlap’s ability to reject Standard Model tt¯ events is likely underestimated. One of the most attractive features of TOM is its weak susceptibility to pileup contamination. Refs. [17, 18] showed that the effects of pileup are not significant on TOM (up to 50 pileup events). The low susceptibility to pileup is a manifest of the fact that, by construction, TOM is sensitive mostly to the hard energy depositions within the fat jet and less so to the incoherent soft radiation. Here we find similar results both in the case of the top as well as the W, as shown in figure 5. The signal distributions maintain a very similar shape upon the addition of pileup contamination, with the signal efficiency of the The shape of the background distributions is affected more drastically in the presence of pileup. However, notice that the region of Ov > 0.5 remains weakly affected, resulting in a small effect on the background fake rate upon the overlap selection cut. Forward jet tagging The event topology in figure 3 offers another interesting handle on background mitigation — a high energy forward jet [6]. The question of how well forward jet tagging (FJT) will perform in the high pileup environment of the future LHC runs remains open [52, 53]. Yet, there is much interesting physics one can do with forward jets. Single top production [54], W hadronic-no pileup t hadronic, Nvtx = 50 W hadronic, Nvtx = 50 r fwd = 0.1 events, while the dashed lines are for hadronic W candidates, as defined in section 3.2. We find that improved. Notice the enormous effect pileup has on the forward jet multiplicity if standard ATLAS tagging Higgs events which originate from vector boson fusion and understanding of the proton structure at high x are just some of the examples. Here we are interested in forward jets only as event tags. The problem of forward jet tagging hence becomes simpler, as we are not concerned with precise measurements of forward jet energy and transverse momentum. We propose a novel approach to forward jet tagging, which addresses the effects of pileup contamination (at 50 interactions per bunch crossing). Pileup contribution to jet observables to higher values and a broadening of the kinematic distributions. In addition, larger jet cones are more likely to produce fake pileup jets, thus increasing the overall forward jet multiplicity. In order to limit the pileup contamination in the forward region, here we propose to cluster the jets in the forward region with a cone smaller than the re-calibration of jet observables as we do not propose to measure the forward jet, just tag it. We define forward jets by clustering the entire event using a cone of radius rfwd and then selecting the jets in the event which satisfy the following criteria: define forward jet tagging by requiring the number of forward jets in the event N fwd How is the forward jet multiplicity affected by pileup? Figure 6 provides the answer. the forward jet multiplicity distribution, with as many as 10 forward jets easily appearing in ≥ 1. extinguishes the effects of pileup, but at a cost to signal efficiency as only about 50% of a good compromise between effects of pileup and signal efficiency, and throughout the rest passes the forward jet criteria of eq. (3.4). For completeness, figure 7 shows distributions background channels. The effects of pileup at 50 interactions per bunch crossing is at a Even though the study of detector effects on our proposal to tag forward jets using small jet cones is essential before the method can be applied in experimental searches, we find that such a study is currently beyond the scope of our work. Yet, we remain optimistic that detector effects will be mild, even for cone size of r < 0.2, as we are only interested in tagging the forward jet and not measuring it. We would also like to emphasize that our proposal for forward jet tagging should be applicable in other analyses which feature forward jets, such as single top production and Higgs production via vector boson fusion. As the forward jet should properly factorize from the rest of the event in all the beforecharacteristic HT of the event. Hence, the forward jet multiplicity distributions of figure 6 should remain applicable beyond the scope of searches for TeV scale top partners, and we encourage experimental collaborations to further examine the performance of small radius jets in forward jet tagging. Our analysis utilizes the presence of multiple b-jets in the signal, whereby we use informaWe consider the benchmark efficiency of 75% for every b jet to be tagged as a b, with the fake rate of 18% and 1% for c and light jets respectively. We further consider a fat jet to distributions ignoring pileup while dashed lines indicate the distributions including pileup from an average of 50 interactions per bunch crossing. We apply different b-tagging criteria based on whether the fat jet is a hadronic top or hadronic W candidate. Namely, we require: is a hadronic W candidate. How large of a b-tagging efficiency should we expect for the signal events? Naively, folded into the above mentioned b-tagging efficiencies, we would hence expect the overall signal b-tagging efficiency to be ∼ 0.5. Figure 8 shows more precise and complete information on the b-tagging of signal events (for the purpose of illustration, here we show only hadronic top candidate events). From the left panel, we can see that the geometrical acceptance for events which contain two large fat jet clustering cone R = 1.0. In addition, we find that the isolation criteria on the b-jet outside the fat jet reduce effect can be understood almost entirely from a simple geometrical argument. Consider for of the hardest fat jet in the event, as prescribed in the bulleted list of this section. The dotted blue line refers to the event b-tag score considering isolated b-jets only. The dashed red curve is the show all events which pass the Basic Cuts and have an overlap score of Ov > 0.5 on the left panel, while the right panel assumes only the events which pass the Basic Cuts, overlap cuts and contain two proper b-jets. No b-tagging efficiencies have been applied. instance the b-tagging criteria for hadronic top candidate events. Because anti-kT jets are isolated both from the fat jet and the hardest lepton is given by: (b−tag isolated) ∼ 1 − the radius of the b-tagged jets, and R is the radius of the fat jet. The (R + r)2 term serves to isolate the b-jet from the fat jet while the term proportional to R2 isolates the jet from since tracks with |y| < 5 are all taken into account during jet reconstruction. Next, for roughly the fraction of isolated b-tag events with a b-tag score greater than b in the left panel of figure 8. We conclude that the expected b-tagging efficiency for the hadronic top candidate events (including the 75% efficiency of b-tagging) will be of order (b−tag) ∼ 0.8 × 0.7 × (0.75)2 ∼ 0.3 . A full study of pileup effects on b-tagging requires detailed detector information, an endeavor which is beyond the scope of our current analysis. However, we would like to point out that the experimental studies of ref. [55] suggest that b-tagging performance at the LHC will perform well at 50 interactions per bunch crossing. in presence of 50 average interactions per bunch crossing. The inclusive signal cross section and integrated luminosity are on the x and y axes respectively. We only show the hadronic top candidate events. The blue solid lines represent contours of constant S/ B. The dashed lines are S/B. The selection cuts for each MX5/3/B reflect the ones in table 6, where we mark the point presented in the table by a star, corresponding to the bench mark model defined with a set of fixed parameters V V G G .5 .8 In case a top partner is discovered at the LHC, combining results from different channels could greatly improve the significance of the signal. Yet, there is additional information one can obtain from measurements of both same sign di-lepton and other decay channels. For instance, a possible mass degeneracy between the X5/3 and B states could be difficult to untangle with the current mass resolution of the LHC experiments. In case a signal is observed, considering only the invariant mass distribution of a tW system or the HT distribution would likely not be sufficient to determine whether there are one or more resonances observed in the signal events. Complementary information from same sign di-lepton channel could aid in resolving the mass degeneracy. As noted before, same sign di-lepton searches are sensitive only to the production o the X5/3 partner and not the B state. A simple cross section measurement (upon unfolding) of both the same sign di-lepton and lepton-jet channels should thus show a difference Δσ = σXl+5f/j3+B − σX2l5/3 ∼ σB, where l + fj refers to lepton-jet channel and 2l represents the same sign di-lepton channels. sections can further reduce the systematic uncertainties. Furthermore, indirectly deducing the presence of a B in the signal is also possible by considering charge asymmetries. As outlined in section 2.2, X5/3 production dominates over X5/3 because the former is produced from g and an up-type quark in the initial state while the latter is produced from g and a down-type quark. In the same sign di-lepton search one lepton charge would be measured in the lepton-jet events we are investigating here (e.g. B or B¯, there is no charge asymmetry. B¯ production dominates over B production, again decay with equal probabilities. In conclusion, if the X their antiparticles), the charge asymmetry is partially washed out and does not match the charge asymmetry of the di-lepton signal. It hence indirectly points towards the presence of the B state. A possible advantage of the lepton asymmetry measurement would also be a reduced sensitivity to experimental systematics, although it will be susceptible to the effects of charge symmetric backgrounds. However, given our results from previous sections and a an S/B > 1, it is likely that the background effects on the charge asymmetry will be manageably low. Conclusions In this paper we study the potential of the early run-II of the LHC to discover and measure heavy fermionic top partners. So far, most experimental studies have focused on pair production relying on same-sign di-lepton signals as a main feature for distinguishing the top partner signals from the SM background. However, as pointed out in ref. [7], single production has an advantage of utilizing an efficient boosted tagging strategy without loosing signal efficiency from requiring two leptonic decays. In addition, the single production cross section becomes larger than that of pair production in the higher mass region (e.g. somewhere between 1 TeV and 1.5 TeV depending on models), which makes the single production process more relevant for the upcoming run of the LHC. In conjunction with the usage of jet substructure physics and b-tagging, we also propose a new method to tag forward jets that characterise our signal events. We demonstrate that both our substructure and forward jet handles are robust against contamination from pileup. For the purpose of illustration, we focused on partial composite scenarios for the top sector, where both top quark chiralities consist of an elementary fermion field which has a sizable mixing with the strong dynamics sector. We use the Minimally Composite Higgs Model, based on the coset space SO(5)/SO(4) as the benchmark model for signal events, where we kept the signal cross section a free parameter in order to reduce the model dependence of our results. Our analysis considered the most significant signal which comes X5/3 is typically the lightest top partner, with the mass splitting of B and X5/3 becoming small at high M4. In addition, the decay topology of X5/3 and B is effectively identical when the semi-leptonic final states are considered, such that the combined signal typically has the largest cross section. The singly produced X5/3 and B partners appear in a final state with an additional top and a light jet, so that the signal has a tt¯W j event topology. For our search strategy, we require that only one of the daughter products of the top partners (top or W ) decays leptonically, but not simultaneously. For jet substructure analysis we employ the TemplateTagger v.1.0 implementation of the Template Overlap Method, which is relatively robust against a large pile-up contamination. The presence of two highly boosted objects allows for a straight-forward reconstruction of the top partner mass, despite the missing energy component and high pileup. Since our signal has an additional high energy forward jet, we propose a new approach to forward jet tagging in order to limit the pileup contamination in the forward region. We since all we require is to tag the forward jet as opposed to measure it. In addition, we include a semi-realistic b-tagging algorithm into our analysis, as multiple b-jets appear in our signal events. As our forward jet tagging proposal is new, we presented the result of our analysis both with and without forward jet tagging, while we found that we can achieve the best result when both b-tagging and our forward jet tagging are employed. The main results of our analysis can be summarized as follows: • We showed that run-II of the LHC at 14 TeV can detect and measure 2 TeV top teractions per bunch crossing and no pileup subtraction. In a no-pileup environment, the significance is approximately twice as high. • A sizeable part of the model parameter space which results in a 2 TeV top partner • High levels of pileup (i.e. 50 interactions per bunch crossing) present a challenge for the lepton-jet final states. However, even with no pileup correction/subtraction lepton-jet channels provide sufficient sensitivity to major parts of the fermonic top partner parameter space, whereby the use of several pileup-insensitive observables greatly reduces the effects of pileup contamination. • The searches for singly produced fermionic top partners will greatly benefit from the mitigate effect of high pileup levels on forward jet multiplicity. • We find that the sensitivity the experiments can achieve in the hadronic W -leptonic 1 TeV, while the sensitivity of hadronic top channel is superior for higher masses. Note that it will be straightforward to combine our current analysis with the conventional same-sign lepton searches in the single production of charge 5/3, as well as pair production channels. Furthermore, our method can be easily adapted in other top partners searches, including charge 2/3 partners, and other models of top partners beyond the minimal composite Higgs models. We also want to emphasize that our analysis is done independent of the underlying physics model, by keeping the signal cross section a free parameter, such that any new physics searches with a tt¯W j event topologies can use our of the partner mass. Finally, in case a signal is observed at the future LHC runs, a combination of lepton-jet channels and same sign di-lepton channels offers valuable information beyond the simple improvement in signal significance. A possible mass degeneracy between the heavy partner states can be disentangled by comparing results of same sign di-lepton measurements and signals from lepton-jet events, as the former is sensitive only to 5/3 charge states, while additional states might appear in the latter. Acknowledgments The authors would like to thank the CERN theory group for the hospitality during the initial stages of this project. The heavy numerical calculations required for this project could not be possible without the support and understanding of Lorne Levinson and Pierre Choukroun of the Weizmann Institute. This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST) (No. 2012R1A2A2A01045722), and also supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the ministry of Education, Science and Technology (No. 2013R1A1A1062597). GP is supported by the IRG, by the Gruber award, and ERC-2013-CoG grant (TOPCHARM # 614794). Furthermore, a significant part of this work was done when GP held a Staff position at CERN. SL and TF are also supported by Korea-ERC researcher visiting program through the National Research Foundation of Korea (NRF) (No. 2014K2a7B044399, No. 2014K2a7A1044408, and No. 2015K2a7A1035922). SO(5)/SO(4) essentials We define here notation used in the main text and collect some useful expressions for the SO(5)/SO(4) coset. These relations are included for completeness and the convenience of the reader. They have been given before in ref. [57], mostly following the notation of The 10 generators of SO(5) generators in the fundamental representation are written as i 1 εαβγ δI δJ − δJ δI β γ β γ i 1 εαβγ δI δJ − δJ δI β γ β γ the basis of eq. (A.1), T a are bock-diagonal T a = where ta are the 6 SO(4) generators in the fundamental representation of SO(4). =  14×4 − " √ 1 − cos f  =  0 where Π~ ≡ (Π1, Π2, Π3, Π4)T and Π ≡ gauge, where the Goldstone multiplet reduces to f − ∇μΠi = ∂μΠi − iAaμ (ta)ij Πj , AaμT a = √ Wμ+ TL1 + iTL2 + √ Wμ− TL1 − iTL2 +g (cwZμ + swAμ) TL3 + g0 (cwAμ − swZμ) TR3 , where sw and cw are respectively the sine and cosine of the weak mixing angle. Note that gWμ1,2 , d3μ = sin(h¯/f ) Details of Composite Higgs Models with Partially Composite Top The model used in this article in order to illustrate the potential of boosted top searches in discovering composite quarks in composite Higgs models is the MCHM5, which is based on the breaking of SO(5) × U(1)X → SO(4) × U(1)X ' SU(2)R × SU(2)L × U(1)X of a strongly coupled theory. The SU(2)L and a U(1) subgroup of SU(2)R × U(1)X are gauged in order −1/3 incomplete representations. to provide the electroweak gauge bosons. The non-linearly realized Higgs is parameterized by the Goldstone boson matrix which in unitary given in eq.(A.4). Beyond the (pseudo-) Goldstone boson Higgs, the low energy description the strongly coupled sector is expected to contain scalar, fermionic and vector resonances, typically at of light fermionic resonances. The symmetry structure of the strong dynamics does not fix the embedding of the fermionic resonances. For simplicity we assume that the top partners live in a single 5 multiplet (transforming non-linearly under SO(5)) with a U(1)X charge of 2/3, while the elementary third generation quarks are embedded as incomplete 5 multiplets (transforming linearly under SO(5)) iB0 − iX5/3  −T + X2/3  √2T˜ −t0L qLt5 = √ t5R =  0  . The 3rd family (partner) particle content along with its quantum numbers is summarized in table 7. The states given above are the gauge eigenstates of the model, which mix due to EWSB as discussed below. The resulting mass eigenstates are two states b, B with X5/3 with charge 5/3. In what follows, we adopt the Callan-Coleman-Wess-Zumino prescription in order to write down the effective Lagrangian in a non-linearly invariant way under SO(5). The Lagrangian of the model is L = + iq¯L0D/ qL0 + it¯0RD/ t0R + i¯b0RD/ b0R + iψ˜4D/ ψ˜4 + iψ˜1D/ ψ˜1 − M4ψ˜¯4ψ˜4 − M1eiφψ˜¯1ψ˜1 ¯ ¯ − (yLf q¯Lt5U ψ˜R + yRf t¯5RU ψ˜L + h.c.) . and the Standard model covariant derivatives. The second line contains the composite quark mass terms with a fourplet mass M4 and a singlet mass M1 as well as the kinetic (∂μ − ig0XBμ − igsGμ)ψ˜1 and Dμψ4 = (∂μ + ieμ − ig0XBμ − igsGμ)ψ˜4 respectively. The ˜ appendix A. The third line of the Lagrangian describes electroweak gauge boson and Higgs interactions with composite quarks which arise purely in the strong sector. The structure combinations of electroweak gauge and higgs bosons. The size of the interactions depends on the parameters cL,R. Finally, last line of eq. (B.2) shows the coupling terms between the elementary and the composite quark sector whose structure is dictated by the Goldstone such that the lightest mass eigenstates (which are identified with the Standard Model b and t quark) are “partially composite”, i.e. they are linear combinations of the elementary and the composite quarks. Partial compositeness: masses and mixing Entering the Goldstone matrix into the effective Lagrangian and expanding around the vacuum expectation value, we obtain the quark mass terms M t =  − √ − y√L2f sin M b = The mass matrices depend on the fourplet and singlet mass scales M4 and M1 and the leftand right-handed pre-Yukawa couplings yL,R. A priory all these parameters are complex. However, all but one phase can be absorbed by field redefinitions of the quarks and quark indicated in the Lagrangian eq.(B.2)) and yL,R and M1,4 to be real in what follows, while cL,R are complex parameters. X5/3 is the only state with electric charge 5/3 and as such must be a mass eigenstate ULb/R = , tan θRb = 0 , tan θLb = − M4 with masses mb = 0 and MB = quark, while B is a heavy partner state.14 M42 + yL2f 2, where b is identified with the SM-like bottom In the charge 2/3 quark sector, the elementary top mixes with the two fourplet states T, X2/3 as well as with the singlet state T˜. For our phenomenological studies, we perform the diagonalization numerically. To provide a qualitative discussion, here, we provide some approximate results by expanding the mass matrix in ≡ v/f . The charge 2/3 mass eigenstates are TTff12,,LL//RR ≡ ψmt L/R = U Lt,/φ˜RU Lt/Rψt, are given in eqs. (B.12) and (B.13) and the masses are mt = √ MT f1 = M4 + O( 2) , MT f2 = MT s = The structure of the mixing matrices and masses can easily be understood from a mass insertion picture: at leading order (ignoring electroweak symmetry breaking), tL can only mix with states in an SU(2) doublet ( i.e. the charge 2/3 members of the fourplet: T and X2/3) while tR can only mix with the SU(2) (and thereby SO(4)) singlet state T˜. This mixing induces mass corrections for the singlet state and (one linear combination of) the fourplet states, while the lightest eigenstate does not obtain a mass at this order. Generating a mass for this state requires mixing of SU(2) doublet and singlet states and therefore at least one insertion of v/f . Therefore, mt as well as all matrix elements of UL/R between SU(2) doublet and singlet components are (at most) of O( ). For our later phenomenological studies, let us discuss typical parameter ranges and mass scales. In order to avoid too large fine-tuning, the compositeness scale f should be close to the electroweak scale. On the other hand, electroweak precision constraints imply f & 800 TeV [4, 5] so that we assume f to lie at the TeV scale. The composite mass scales M1 and M4 arise from the condensation of the strongly coupled theory and therefore run impose a bound of M4,1 & 800 GeV already, and in this article, we aim to explore prospects for LHC at 13 TeV to explore top partner masses around 2 TeV, i.e. above the 14In this article, we treat the bottom quark as massless. In order to induce a non-zero bottom mass, additional bottom partner quarks need to be introduced which however typically mix weakly with the partners of the top partner multiplet such that we ignore them, here. scale f . Finally, requiring the top mass eq. (2.1) to take its measured value requires yL and yR to be O(1). Therefore, the typical partner we consider contains the SO(4) singlet partner Ts whose mass scale is set by M1, a almost degenerate SU(2) doublet (X5/3, Tf1 with mass M4 and a second almost degenerate SU(2) doublet (Tf2, B) which for f < M4 2 L f2 4 M 2 R ) 2 T M iφe M Gyhuk =  √yR2 cos − √yR2 cos −yR sin The kinetic terms include an e-term contribution which yields Lq,gauge = + h.c. + canonical EM and QCD interactions − y2L sin y2L sin − √yL2 cos  (¯b0, B¯0)L,R, X¯5/3 L,R. The interaction terms of the model are derived by writing out the Goldstone matrix, the ≡ v/f . The pre-Yukawa terms yield a contribution to Higgs-quark couplings Lh,yuk = −hψ¯LtGyhukψRt + O( 2) + h. c. , Lc = − f icα T¯α − X¯2/3 α γμ (∂μh) T˜α √2cw T¯α +X¯2/3 α Z/ T˜α +B¯α0 W/ −T˜α − X¯5/3 α W/ +T˜α The contribution of the d-terms to quark - gauge boson interactions can easily be read off from the last line, leading to contributions analogous to eq. (B.16) with where δαL is 1 for α = L and 0 for α = R. tions with gauge bosons and the Higgs which read = 0, where, using eq. (B.4) =   cL(M2t1−M3t1)  −cLyR cos  cLyR cos √ 2cLyR sin Lq,int = Lc ⊂ −TL M2ti − M3ti Mit2 − Mit3 TR − X2/3 R − √ cLM4−cRM1 cLM4−cRM1 cRyL cos cLM1−cRM4  cLM1−cRM4  cR(M1t2−M1t3) equations of motion To rewrite the first term of eq. (B.21) we partially integrate it and make use of the quark Collecting all interaction terms then yields the interaction Lagrangian in the gauge hψ¯αb W/ −GαBψαt + X¯5/3 α W / + higher order in Gh =  yR cos √(1−√2cL) −yR sin (1 − √2cL) yL sin (1−√2cR) yL sin (1−√2cR) yL cos (1−√2cR)  cLM4−cRM1 cLM1−cRM4 − cos cα sin  − 3 cw Again, the coupling structure is easily understood in terms of SU(2) multiplets in expansion. Concerning the gauge couplings, at leading order, the elementary states couple SM-like, and the fourplet and singlet composite quarks have canonical couplings determined by their charge. At O( ), the d-terms lead to interactions between EW gauge bosons, fourplet and singlet states. Furthermore, there are no gauge interactions with one elementary and one composite quark; these are solely induced due to the mixing or the mass eigenstates. The higgs - quark interactions obtain contributions from the pre-Yukawa terms which where also responsible for the mass mixing. In addition, the d-terms contain derivative interactions of the Higgs to singlet and fourplet quarks which can be rewritten as Yukawa couplings via the quark equations of motion. Derivation and discussion of the interactions of quarks with quark partners in the mass eigenbasis From eq. (B.32), the interactions of the physical states are obtained by rotating into the mass eigenbasis via the transformations U Lt//bR given in eqs. (B.6), (B.12), (B.13). For our simulations we implemented the full set of interactions and diagonalized the mass matrix numerically, but the main phenomenological features can be readily understood from the dominant couplings of the lightest quark partner states to SM gauge bosons and SM-like quarks which are relevant for the single-production of the quark partner as well as its decay channels. eigenstate X5/3 R only couples to W + and X3/2 R via the e-term. The X5/3 R then mixes via mass and VEV insertions with t0R and T˜R, which make up the O(1) components of the mass eigenstate tR. From the mass matrix in eq. (B.4) it can be seen that the only mass insertion combination at O( ) goes from X2/3 R through X2/3 L to t0R. Combining the couplings and mass insertions and taking into account that the t0R component of tR has a coefficient M1/MT s yields the first contribution to the coupling gR the d-term. TR mixes via T˜L to t0R at O(1). Projecting t0R on tR and assembling the couplings and XW t in eq. (B.39). At O( ), the gauge eigenstate X5/3 R couples to W + and T˜R via insertions yields the second term of gR XW t in eq. (B.39). The analogous analysis for gL in couplings of O( 2) because the mixing of X(2/3 L) to t0L is of O( ) while the mixing of T˜L to t0L is of O( 2). Couplings of other heavy quark partners to SM quarks and EW gauge bosons or the Higgs can be understood analogously. X5/3: the exotically charged X5/3 has mass M4 and is thus the lightest fourplet quark partner. Its couplings to only SM particles are gXW t = GLXi UL i1 = O( 2) , L t † UR∗t13 + cR UR∗t14 + O( 2) , = − √ Other couplings to two SM particles are forbidden due to (electric) charge conservation. The structure of the dominant right-handed coupling can be understood from the mass insertion picture as shown in figure 15. does not have any pre-Yukawa couplings within this model so that a B¯hb coupling term is absent. A B¯Zb coupling is absent as well. In the gauge eigenbasis, no B¯0Zb0 couplings are present. In the right-handed sector, b0R and BR0 are already mass eigenstates. The left-handed coupling in eq. (B.36) is universal for b0L and BL0, and rotation into the mass eigenbasis does not induce a “mixed” B¯Zb interaction. B¯W t are present and given by gBW t = ULb 2iGLBij UL j1 = O( 2) . L t † gBW t = U Rb 2iGRB ij UR j1 = √ R t † UR∗t12 − cR UR∗t14 + O( 2) Tf1 and Tf2: the states Tf1 and Tf2 have charge 2/3 and can a priori couple to W b, Zb, or hb. However, both left- and right-handed couplings to W b are of order 2, and so are the left-handed couplings to Zt. The leading order right-handed couplings to Zt are yRf M1 + √2cR + √2cR while the leading couplings to the Higgs are √2 cL 1 − e−iφ M1 + cRe−iφM4 ! MT f2MT s MT f2MT s Note from the coupling expressions: for all top partners, the dominant couplings to W, Z, h and an SM quark are chiral (either left- or right-handed coupling dominates). In this case, the partial widths for a decay of a fermion F into a fermion f and a gauge boson or Ts: the state Ts also has charge 2/3. Its dominant couplings to W b, Zb, and hb are 2cw √2 Decays of top partners √2cLyLf √2cLyLf √2cL e−iφM12 + yR2f 2 MT f2MT s Γ(F → W f ) = MF m2W 32π Γ(F → Zf ) = MF m2W 32π Γ(F → hf ) = MF |3λ2|e2πff Γh , mate the partial widths aMndF2 BRs of the different top partners, using the effective couplings eqs. (B.39)–(B.48). ≈ 32π g2v2/4 4M42 yR 2 M1 − M1 − • Although the effective coupling is O( ), the partial width is not suppressed. • The partial width is proportional to |yR2c2R| (for large cR). X5/3 is the lightest fourplet state, so the BR of this channel is 100% unless MT s < (MT s/M4)2)2, so that this decay only plays a role when the is a substantial mass splitting. In this case, the partner states in the 4 are merely decoupled, and direct searches for the Ts partner are more promising. B: the discussion of B decays is analogous to the above discussion of X5/3 decays. The given in eq.(B.41): Γ(B → W t) ≈ M4 m2W 32π MT f2 MT f2MT s MT f2 MT f2MT s The decays B → Zb and B → hb which are a priory allowed by the quantum numbers only occur at higher order in and are therefore suppressed. Cascade decays to Tf1,2 are either degenerate with the Tf2 and only marginally mass split from the MT f1, these decays are mass splitting. Tf1 and Tf2: the total widths of Tf1,2 are of the same order as for X5/3, but they have two dominating decay channels into ht or Zt, while W b is suppressed. Concerning the BR √2 cL(1−e−iφ)M1+cRe−iφM4 MMT1s − √2 cL(1−e−iφ)M1+cRe−iφM4 , while for d- and e-term contributions of similar size, the terms can enhance each of the For Tf2 we obtain analogously: √2 cL(1−e−iφ)M42+cRe−iφMT2f2 Ts: for Ts we get decays into W b, Zt and ht. In addition, for MT s M4, decays into at least suppressed. The ratios of decay rates are + √2cL MMTTfs2 (e−iφM1M4+yR2f2)−√2cL(e−iφM12+yR2f2) 2 √2cL MMTTfs2 + √2cL MMTTfs2 In the limit cL → 0, this yields BRs of 2 : 1 : 1 to W b, Zt, and ht, up to kinematic corrections, while for cL ∼ 1 again, BRs vary. sen parameters, while for the charge 2/3 partners, BRs are strongly parameter dependent. In this appendix we derived the Feynman rules for the interactions of SM-like quarks to its composite partners. One main result — the interactions in the gauge eigenbasis — is given in eq.(B.32). This Lagrangian describes all interactions of two quarks one gauge boson or a Higgs, only omitting higher dimensional operators in which two quarks couple to a larger number of Higges or gauge fields. For our phenomenological studies in this article, we used this Lagrangian and diagonalized the quark mass matrix eq.(B.4) numerically, without using an expansion in to obtain the interactions in the mass eigenbasis. 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Mihailo Backović, Thomas Flacke, Seung J. Lee, Gilad Perez. LHC top partner searches beyond the 2 TeV mass region, Journal of High Energy Physics, 2015, 22, DOI: 10.1007/JHEP09(2015)022