Boosted Event Topologies from TeV Scale Light Quark Composite Partners
We propose a new search strategy for quark partners which decay into a boosted Higgs and a light quark. As an example, we consider phenomenologically viable right handed up-type quark partners of mass in composite pseudo-Nambu-Goldstone-boson Higgs models within the context of flavorful naturalness. Our results show that and signal significance of is achievable at LHC with 35 of integrated luminosity, sufficient to claim discovery of a new particle. A combination of a multi-dimensional boosted Higgs tagging technique, kinematics of pair produced heavy objects and -tagging serves to efficiently diminish the large QCD backgrounds while maintaining adequate levels of signal efficiency. We present the analysis in the context of effective field theory, such that our results can be applied to any future search for pair produced vector-like quarks with decay modes to Higgs and a light jet.
The Large Hadron Collider (LHC) has begun to explore the electroweak symmetry breaking (EWSB) scale. With a successful completion of Run I, highlighted by the discovery of the Higgs boson Aad et al. (2012); Chatrchyan et al. (2012a), the Standard Model (SM) is now complete. The Higgs boson accounts for the EWSB, generates masses of fermions, provides an explanation for the short range of the weak force, as well as unitarizes the -boson scattering cross section. However, within the SM there is no explanation for why the Higgs boson mass itself is . The naive expectation from perturbation theory shows that the Higgs mass should be close to the ultra-violet (UV) scale of the theory, due to the large couplings of the Higgs to the top quark ( the hierarchy problem). There is a-priori no physical principle which prevents the Higgs mass from being finely tuned, although it is extremely uncommon to encounter such finely tuned quantities in nature. The latter prompted much of the theoretical work in the past decades to seek the explanation for the hierarchy problem within the scope of the “naturalness” paradigm.
There are two common “natural” solutions to the hierarchy problem. The first is to introduce additional symmetries to protect the Higgs mass from large corrections. The second is to model the Higgs boson as a composite object Kaplan and Georgi (1984); Kaplan et al. (1984); Georgi et al. (1984); Banks (1984); Georgi and Kaplan (1984); Dugan et al. (1985); Arkani-Hamed et al. (2002); Contino et al. (2003); Giudice et al. (2007); Barbieri et al. (2007); Panico and Wulzer (2011); De Curtis et al. (2012); Marzocca et al. (2012); Bellazzini et al. (2012); Panico et al. (2013); Bellazzini et al. (2014), such that the Higgs mass becomes irrelevant above some dynamically generated compositeness scale, analogous to the pion mass in Quantum Chromo Dynamics (QCD). From the low energy effective theory point of view, both mechanisms introduce additional degrees of freedom ( top partners) to the SM111For solutions within composite Higgs models which do not require top partners cf. Refs. Galloway et al. (2010); Cacciapaglia and Sannino (2014)., which cancel the top loop induced quadratic divergences in the Higgs mass. The top partners can be scalars, as in the case of supersymmetry, or fermions, as in the case of composite Higgs models. Together, the two mechanisms provide a “litmus test” for the naturalness paradigm.
The LHC is finally able to put naturalness to a meaningful test, where most of the experimental effort has been focused on searches for top partners Chatrchyan et al. (2014a); Aad et al. (2014a). The fact that no super-partners have been observed at the LHC is already pushing the supersymmetric models into a tuned regime. However, as the bounds on the scalar top partner mass increase, there have been several attempts to relax the bounds on the top partners via compressed/stealth spectrum, R-parity violation, Dirac gauginos, split families, etc. Fan et al. (2011); Hall et al. (2012); Papucci et al. (2012); LeCompte and Martin (2012, 2011); Csaki et al. (2012); Fan et al. (2012); Kribs and Martin (2012); Craig et al. (2012); Evans and Kats (2013); Dreiner et al. (2012, 2013); Mahbubani et al. (2013); Blanke et al. (2013); Han and Katz (2013); Kribs and Martin (2013). Composite Higgs models are in a similar situation, although the bounds on the spin partners in such models are somewhat milder compared to the already existing bounds from LEP and Tevatron constraints on the oblique parameters Grojean et al. (2013); Ciuchini et al. (2013). With the increased center of mass energy, Run II of the LHC will soon be able to cover the interesting region of parameter space of composite top partners Backović et al. (2014).
An interesting avenue to bypass existing bounds is to employ non-trivial flavor structure for top partners 222 Commonly referred to as “flavorful naturalness” Blanke et al. (2013)., where a large mixing is allowed between the right-handed (RH) top and RH charm partners. The basic idea comes from a simple observation that scalar top partners ( stops) need not be mass eigenstates in order to cancel the large SM loop corrections to the Higgs mass. Instead, a stop flavor eigenstate made up of a stop-like and scharm-like mass eigenstates can serve the same purpose Mahbubani et al. (2013); Blanke et al. (2013). An analogous approach has recently been applied to composite Higgs models for light non-degenerate composite quarks Delaunay et al. (2014). The analysis focused on the Minimal Composite Higgs model (MCHM) Agashe et al. (2005) based on the coset structure , in which the Higgs doublet was realized as a pseudo-Goldstone boson.
Implementing non-degenerate composite quarks into composite Higgs models without conflict with the existing bounds from flavor physics and electro-weak (EW) precision observables is a non-trivial task. However, Ref. Galon et al. (2013) showed that flavor alignment allows models with non-degenerate light generation partners to satisfy the constrains from flavor physics observables 333As shown in the case of original supersymmetric flavorful naturalness, mixing between left-handed partners of top and charm give rises to more severe constraints from FCNC processes, and it was preferred to choose the mixing through the RH partners for the simplicity. The situation is similar for composite Higgs models. Thus, we focus on the RH up-type partners in our analysis.. In addition, models with custodial parity Agashe et al. (2006); Contino et al. (2007) have been shown to be consistent with the constraints from EW precision tests Delaunay et al. (2011a); Redi and Weiler (2011). Collider implications for such scenario have also been studied in Refs. Delaunay et al. (2011b); Redi et al. (2013).
Ref. Delaunay et al. (2014) studied the implications of non-degenerate composite partners of the first two generation quarks for LHC phenomenology and derived the LHC bounds on fermionic resonances in the fourplet representations. In particular, Ref. Delaunay et al. (2014) showed that, without assuming degenerate compositeness parameters, the fourplet RH up-quark partners have to be heavier than TeV or the degree of compositeness of RH up quark has to be very small. In the latter case, a lower mass bound of GeV still applies. At the same time, the fourplet RH charm quark component can be mostly composite and its partners can be as light as GeV even with a large degree of right-handed compositeness.
Contrary to fourplet partners, singlet partners are barely constrained by the LHC Run I searches. Ref. Flacke et al. (2014) recently obtained the first non-trivial bound on singlet partners utilizing the results from ATLAS collaboration (2013). However, the bound ( the RH up-type partner mass GeV) is very mild as the experimental searches were not designed to search for Higgs bosons arising from composite light quark partner decays.
The main focus of this paper is to design a dedicated search for singlet partners of light quarks, and study the potential of such searches to discover the quark partners at the Run II of the LHC. For the purpose of illustration, we study right-handed up-type quark partners, which are QCD pair-produced and decay dominantly into a Higgs boson and an up-type quark. We design the analysis in an effective theory framework, such that – although being motivated by composite quark partner searches – our results can be applied to any heavy vector-like quark model in which the vector-like quark has a decay channel into a Higgs and a light quark.
We focus on the potential of LHC Run II to probe light quark partners of mass , where the decays of light quark partners typically result in boosted Higgs bosons. In order to increase the signal rate, we consider only the decays of the Higgs boson to a pair. Seemingly complicated, such final states are particularly interesting, as traditional event reconstruction techniques fail. Due to the large degree of collimation of Higgs decay products, methods of Higgs tagging via “jet substructure” need to be employed Butterworth et al. (2008). In addition, the boosted di-Higgs event topology accompanied by two light jets offers a myriad of handles on large SM backgrounds. As we will show in the following sections, a combination of kinematic constraints of pair produced heavy particles, boosted Higgs tagging and double -tagging is able to achieve a signal to background ratio for light quark partner masses of 1 TeV. The same analysis shows that signal significance of can be achieved with of integrated luminosity, sufficient to claim a discovery.
For the purpose of boosted Higgs tagging, we use the Template Overlap Method (TOM) Almeida et al. (2012, 2010); Backovic et al. (2013, 2014). We propose a new form of overlap analysis which utilizes both Higgs template tagging and top template tagging in order to optimize the rejection of SM backgrounds while maintaining sufficient signal efficiency. The “multi-dimensional” TOM tagger compares the likelihood that a boosted jet is a Higgs to the likelihood that a boosted jet is a top quark, whereby a Higgs tag assumes that a jet is sufficiently Higgs like and not top like. Furthermore, we find that requiring at least one -tag in each of the Higgs tagged jets significantly improves signal purity, especially with respect to large multi-jet backgrounds.
We organized the paper in three sections. Sec. II summarizes the theoretical framework of MCHM with partially composite RH up-type quark partners and introduces the effective model of the light up-type quark partners. In Sec. II we also discuss the diagonalization of mass matrices, calculation of the couplings in the mass eigenbasis and other relevant parameters which enter the effective parametrization used throughout the paper. Sec. III deals with a phenomenological study of LHC Run II searches for up-type quark partners. We propose and discuss in detail a set of observables which can be used to efficiently detect and measure the partners at mass scales, as well as present results on and signal significance using our cutflow proposal. We conclude in Sec. IV. A brief discussion of models in which the quark partner is not dominantly RH can be found in the Appendix.
Ii Partially composite light quark partners
In this article we focus on the MCHM based on the coset structure . We follow the conventions and notation of Ref. Delaunay et al. (2014) based on the Callan-Coleman-Wess-Zumino (CCWZ) formalism Callan et al. (1969); Coleman et al. (1969). The Higgs multiplet is non-linearly realized as the Goldstone Boson multiplet of the breaking. Gauging the and assigns the correct quantum numbers to the Higgs multiplet, which is parameterized by the Goldstone boson matrix. In unitary gauge, it reads Delaunay et al. (2014); De Simone et al. (2013)
where is vacuum expectation value of the non-linearly realized Higgs field which is related to the Standard Model vacuum expectation value by .
In composite Higgs models, the Higgs transforms non-linearly under the global spontaneously broken symmetry group, while elementary fermions transform linearly. Yukawa-type interactions of purely elementary quarks (and leptons) with the Higgs are hence forbidden. However, the strongly coupled sector is expected to contain QCD charged fermionic resonances ( “quark partners”) at or below a scale which can have Yukawa-type couplings with elementary quarks and the Goldstone boson matrix (which contains the Higgs). Electroweak symmetry breaking then yields mass mixing terms between the composite quark partners and the elementary quarks such that the lightest quark mass eigenstates (which are identified with the SM-like quarks) are partially composite. The mass spectrum and couplings of the SM-like quarks and their heavy partners to electroweak gauge bosons and the Higgs depend on the representations in which the elementary quarks and the heavy partner quarks are embedded. For concreteness, here we focus on one minimal embedding.
The elementary left-handed and right-handed quarks are embedded into incomplete representations of
with a charge of for and for . The lightest composite quark partner resonances are assumed to be in the of as well
with charge of for and for .
Using the CCWZ prescription we can construct the fermion Lagrangian of the model which reads
where and are the CCWZ connections (cf. Appendix A of Ref. Delaunay et al. (2014) for the explicit expressions), and are matrices in flavor space, and
where the pre-Yukawa couplings are matrices in flavor space.
Typically, the composite sector is assumed to be flavor-blind in order to avoid constraints from flavor changing neutral currents (cf. e.g. Ref. Redi and Weiler (2011)). In such a setup, the flavor structure only enters via the pre-Yukawa couplings, and the partners of the different SM quark flavors are mass degenerate, up to Yukawa-suppressed corrections. However, as has been pointed out in Ref. Gedalia et al. (2012), partners are allowed to be non-degenerate within models of flavor alignment Fitzpatrick et al. (2008); Csaki et al. (2010). In this article we allow for non-degenerate quark partner masses and treat them as free parameters.
LHC run I established various constraints on the different quark partners already:444All bounds quoted refer to QCD pair production and subsequent decay of the quark partners. This production channel only depends on the mass of the quark partner and is therefore rather model-independent. The various partners can also be single-produced via electro-weak interactions. The mass bounds from such channels can be more stringent in some part of the parameter space (cf. e.g. Delaunay et al. (2014); De Simone et al. (2013)) but the production cross section for these processes depends on the model parameters such that these constraints can be alleviated.
The top partner multiplet contains a charge particle as the lightest member with a mass . Its decay channel yields a same-sign dilepton signal which has not been observed, yet. This results in a lower mass bound of established by CMS Chatrchyan et al. (2014b).
The singlet top partner (as well as the the charge 2/3 partners in multiplet) has decay channels into , , and . CMS established a lower bound on the mass of a charge 2/3 partner of 687 - 782 GeV Chatrchyan et al. (2014a), with the strongest bound applying if is the dominating decay. The analogous ATLAS bounds are 350 - 810 GeV Aad et al. (2014b).
3rd family charge -1/3 partners can decay into , , and . CMS constrained their mass to lie above 582 - 785 GeV, again depending on the branching ratios Chatrchyan et al. (2013a, 2012b).555Again, the bounds are strongest when the branching ratio into is large. However, a recent CMS study Chatrchyan et al. (2014c) focussed on the the all-hadronic channel and showed that limits are improved when making use of jet-substructure techniques. Assuming 100 % branching ratio of , Chatrchyan et al. (2014c) obtained a lower bound on the mass of 846 GeV. The current ATLAS lower mass bound on the charge partners is 350 - 800 GeV Aad et al. (2014b).
Bounds on partners in the multiplets have been studied in detail in Ref. Delaunay et al. (2014), where a bound of for QCD pair produced partners was established, which also applies to partners in the multiplets. These bounds on light quark partners are weaker than the bounds on 3rd generation quark partners. Third generation partners decay into electroweak gauge bosons (or a Higgs) and a third generation quark, leading to final states which can be efficiently “tagged” at the LHC and hence allow to reduce or eliminate the numerous SM backgrounds. On the other hand, partners of light quarks decay into light quark flavors which are significantly more difficult to distinguish from the SM background channels.
So far, the most unconstrained partners are the light quark singlet partners and . The dominant decay mode into , leads to a (potentially large) di-Higgs signature which has not been searched for at LHC run I.666ATLAS Aad et al. (2015, 2014c) and CMS Chatrchyan et al. (2014d, 2013b) published results on di-Higgs signals which result from the decay of a heavy resonance (KK-graviton or, respectively, a heavy Higgs), but these searches do not apply to the di-Higgs signal considered here, as the sum of the invariant mass of the decay products does not form a resonance in our case. The only constraint we are aware of has been obtained in Ref. Flacke et al. (2014), where the absence of decays with high has been used to establish a bound of GeV.
In this article, we study the discovery reach for the weakest constrained and therefore potentially lightest quark partner at LHC run II: a light-quark singlet partner. Focussing on the singlet partner, the model defined in Eq. (5) can be simplified. For simplicity, we take the limit , and discuss the model for the up-partner only. Note that the phenomenology of partners is analogous.777In this article we focus on parameter independent bounds which arise from QCD pair production of quark partners. For (parameter dependent) single production, the quark flavor affects the production cross section (cf. Flacke et al. (2014)).
Expanding around the vacuum expectation value yields the effective quark mass terms
Note that the effective mass terms and arise from the left- and right-handed pre-Yukawa mass terms which have inherently different symmetry properties. The coupling links a fundamental fourplet to a composite singlet while the coupling links a fundamental singlet to a composite fourplet. Therefore, and are independent parameters which are not required to be of the same order of magnitude by naturalness. For simplicity, we choose here, and discuss consequences of the opposite limit in Appendix A.
For , the mixing mass terms have a hierarchy . The eigenvalues of the squared mass matrix are
where the lighter eigenvalue is to be identified with , implying . The bi-unitary transformation which diagonalizes the mass matrix is a rotation by on the left- and right-handed up-quarks where
The couplings of the mass eigenstates to the bosons follow from rewriting
in the mass eigenbasis . Note that the couplings arising from the gauge couplings are universal. A rotation into the mass eigenbasis of these terms does not induce any “mixed” interactions of the to and and leaves the couplings to right-handed light quarks unaltered. Mixing in the left-handed sector induces non-universality of the light quark couplings to the , but the correction to the left-handed coupling is of order , such that corrections to the hadronic width of the are negligible 888For partners, the analogous corrections are such that no bounds apply as long as .. The “mixed” coupling of the to and in the left-handed sector is
Analogous to the neutral current, the mass mixing in the left-handed sector also induces negligible corrections to the vertex and a “mixed” coupling between the , , and :
The Higgs couplings to the quark mass eigenstates follow from expanding Eq. (8) to first order in and subsequent rotation into the mass eigenbasis. In the gauge eigenbasis the Yukawa terms read
Rotating into the mass eigenbasis, the mixing Yukawa interactions
In the regime considered here, the mixing couplings to which are proportional to can be neglected, and the model is described by the simple effective action
The Lagrangian in Eq. (20) and the definition of the effective coupling of Eq. (19) is valid for up-type quark partners. The analogous calculation for down-type partners yields the same Lagrangian with the charge factors being replaced by as directly follows from the charge assignments.
The phenomenology of this model is particularly simple:
The partner state carries color charge and can therefore be produced via QCD pair production.999For a large value of and depending on the partner quark flavor, additional production channels exist which have been discussed in Ref.Flacke et al. (2014), however here, we focus on the parameter independent QCD pair production.
This model hence predicts as a distinct signature at the LHC. In the following sections, we will explore the prospects for discovery of such signals at the LHC Run II, with the focus on partner masses of .
In our model, the dominant branching ratio to is a consequence of the fact that the quark partner is an singlet, where we assumed . A dominant branching ratio can also be achieved in model implementations where is a part of an doublet, in the limit of . Conversely, the regions of parameter space where (in the case of SU(2) singlet) and (in the case of SU(2) doublet) would result in significant branching ratios to other final state such as and .
Note that most of our proposal for searches (with the exception of our -tagging strategy which would have to be modified) in the following sections can be applied to and final states as well, as the final state kinematics are most affected by the mass of , and to a lesser degree by the structure of the vertex, where .
Iii Searching for light quark partners at the LHC Run II
In the benchmark model we consider, the singlet partner decays exclusively into a Higgs and an up-type quark. The topology of signal events is characterized by a pair of boosted Higgs bosons (if the mass of the singlet partner is sufficiently heavy) accompanied by two light jets. We further require that the Higgs decays into in order to avoid a reduction of signal cross section due to small branching ratios of the Higgs to other SM final states. Due to the boosted Higgs topology, the final state pairs are expected to be collimated into a cone of roughly where is the transverse momentum of the decaying Higgs.
Here we consider only pair production of partners at a TeV collider (see Fig.1), where the pairs are produced via QCD interactions. Hence, the production cross section is rather model independent, depending solely on . The dominant background channels to the all hadron final states in our signal events are + jets, + jets, and light multi-jet channels.111111Another potentially interesting and very clean search channel for di-Higgs production is the di-photon channel. However, for strongly boosted di-Higgses, the backgrounds can be efficiently removed as we will show, such that at high boost, the all hadronic channel can dominate. A qualitatively similar behavior can already been seen at both ATLAS Aad et al. (2015, 2014c) and CMS Chatrchyan et al. (2014d, 2013b) when comparing the respective di-photon and searches at 8 TeV. The scope of our current effort is to study the ability of various jet observables to suppress the before-mentioned background channels and enhance the signal for partners of mass . To our knowledge, such searches for light quark fermionic light quark partners in the fully hadronic channels have not been studied in the past. As here we are interested in a “proof of concept” type of study, we will only consider signal and background events in a pileup-free environment.
iii.1 Data Generation and Pre-Selection Cuts
We generate all events using leading order
MadGraph 5 Maltoni and Stelzer (2003) at a TeV collider, assuming a CTEQ6L Nadolsky et al. (2008) set of parton distribution functions. At the hard process level, we require that all final state partons pass cuts of GeV, . Next, we shower the events with
PYTHIA 6 Sjostrand et al. (2006) using the MLM-matching scheme Artoisenet et al. (2010) with
xqcut GeV and
qcut GeV. We match the multi-jet events up to four jets, while the and samples are matched up to two extra jets. We cluster all showered events with the
fastjet Cacciari et al. (2012) implementation of the anti- algorithm Cacciari et al. (2008).
In order to perform the analysis with a manageable number of events in the background channels (), we impose a generator level cut on , a scalar sum of all final state parton transverse momenta. The motivation for the generator level cut comes from the fact that pair produced light quark partner events contain two objects of mass TeV, implying that the signal will be characterized by of roughly 2 TeV. In order to avoid possible biases on the background data by increasing the cut too much, we hence require TeV on all generated backgrounds.
We summarize the cross sections for the signal parameter point of and the most dominant backgrounds in Table 1. For completeness, we show the pair production cross section as function of in Fig.2, where we assume and the branching ratio of Higgs to a pair of quarks is included. Notice that the total production cross section for partner masses above 1.3 TeV goes into the sub-femtobarn region which will be challenging to probe at the Run II of the LHC with of integrated luminosity. A closer look at the numerical values of the signal and background cross sections suggests that a total improvement in of is desired to reach . For that purpose, we will introduce a new cut scheme in Section III.4, which exploits the characteristic topology and kinematic features of the signal events.
Right: Signal and background cross sections as a function of cut. The plot is normalized to NLO as in Table 1.
iii.2 Tagging of Boosted Higgs Jets
The decay products of a boosted Higgs are collimated into a cone of , where is the transverse momentum of the Higgs boson. Since we consider light quark partners of mass , the resulting Higgs bosons will have GeV, and hence will decay into a cone of roughly . Clustering the decay products of a boosted Higgs into a large cone (), will typically result in a single “fat jet” of mass . However, traditional jet observables such as jet and are inadequate to efficiently distinguish between Higgs, top and QCD “fat jets”, and a further consideration of Higgs “jet substructure,” is needed to reduce the enormous QCD backgrounds.
Many methods designed to tag the characteristic “two prong” substructure of the hadronically decaying Higgs exist in the literature Butterworth et al. (2008); Almeida et al. (2012); Backovic et al. (2013); Schlaffer et al. (2014); Soper and Spannowsky (2011). Here we will use the
TemplateTagger v.1.0Backović and Juknevich (2014) implementation of the Template Overlap Method Almeida et al. (2010, 2012); Backovic et al. (2013, 2014).
The Template Overlap algorithm for boosted jet tagging attempts to match a parton level model (template) for a boosted jet decay ( the system with the constraint of ) to the energy distribution of a boosted jet. The procedure is performed by minimizing the difference between the calorimeter energy depositions within small angular regions around the template patrons and the parton energies, over the allowed phase space of the template four-momenta. Refs. Almeida et al. (2010, 2012); Backovic et al. (2013) studied the use of TOM to tag boosted Higgs decays in the context of the Standard Model. To our knowledge, our current effort is the first attempt to utilize TOM for boosted Higgs studies in a BSM scenario.
An attractive feature of TOM is a relatively weak susceptibility to pileup contamination Backovic et al. (2014). The overlap analysis is affected only by the calorimeter depositions which land in angular regions of typically from the template patrons. The rest of the jet energy distribution does not contribute to the estimates of the likelihood that a particular template matches the jet energy distribution. As pileup contamination scales as , where is the jet cone, the effects of pileup on the TOM analysis will be of order few percent, compared to (say) the of a typical fat jet of
Ideally, in order to maximize the information extracted from jet substructure, one would perform TOM analysis for all heavy standard model decays on each candidate fat jet. Such analysis would result in a vector of overlap scores
where . Various correlations within the multi-dimensional overlap space could then be exploited to fully maximize the ability of TOM to tag the desired heavy particles. The full multi-dimensional TOM analysis is beyond the scope of our current effort and we find it sufficient to use only a combination of two body Higgs as well as three body top template analysis (in order to further suppress the large background) 121212Note that the addition of a three body (NLO) Higgs template analysis could further suppress the multi-jet and backgrounds, but would not significantly help in suppression of the background Backovic et al. (2013).. As the three prong decay of a boosted top is more complex of an object than the typical two prong decay of a boosted Higgs, it is possible for a top fat jet to pass the two-body Higgs template tagging procedure. On the other hand, it is difficult for a Higgs to appear as a fake top Backovic et al. (2013). We hence require all Higgs candidate jets to pass the requirement
As we will show in the following sections, the combined requirement on and is very efficient at removing the fake rate.
For the purpose of this analysis, we generate 17 sets of both two body Higgs and three body top templates at fixed , starting from in steps of , while we use a template resolution parameter and scale the template subcones according to the rule of Ref. Backovic et al. (2013).
The signal final states we consider contain four -jets from two Higgses, which can be extremely useful in disentangling the signal events from the background channels. However, requiring four -tags in a boosted configuration comes at a severe cost of the signal efficiency as even in the optimistic scenario of a single -tag efficiency of 75%, -tagging four jets alone would cut out about 70% of the signal events. Instead, here we will consider two -tags, and require that they are contained within the two Higgs candidate jets.
A full analysis of -tagging requires a detailed detector study which is beyond the scope of our work. Here we adopt a simplified, semi-realistic -tagging procedure, whereby we assign to each jet a -tag if there is a parton level or quark within from the jet axis. We then weight each event by the benchmark -tagging efficiencies:
where are the efficiencies that a , or a light jet will be tagged as a -jet. For a Higgs fat jet to be -tagged, we then require that a -tagged jet lands within from the fat jet axis. Furthermore, we take special care of the fact that more than one -jet might land inside the fat jet and reweigh the -tagging efficiencies according to the rule of Table 2.
|-tag scores of a fat jet||Efficiency||values|
|0 (jet: u,d,s,g)||0.01|
iii.4 Event Selection and Reconstruction of the Pair
We proceed to discuss in detail the cut scheme we propose for the all-hadronic searches for pair produced partners. For the convenience of the reader, we outline the event selection in Table 3, while a detailed description and definition of the observables can be found in the following text.
|Cut Scheme||Basic Cuts||Demand at least four fat jets () with|
|Declare the two highest fat jets|
|to be Higgs candidate jets.|
|At least 1-tag on both Higgs candidate jets.|
|Select the two highest light jets ()|
|with to be the quark candidates.|
We begin by requiring at least four anti-, jets with
The requirement on the presence of four fat jets pre-selects signal event candidates, as we expect two pairs of boosted Higgs-light jets to appear in the final state 131313Selecting 4 fat jets also simplifies the TOM jet substructure analysis. . In order to determine which of the four jets are the Higgs candidates, we select the two highest fat jets which satisfy the TOM requirement of
of Section III.2. The requirement on peak template overlap is designed to select the two Higgs candidate jets in the event, while ensuring that the jets are not fake tops. If less than two fat jets pass the overlap requirement, the event is rejected.
The overlap selections in Eq. (25) deserve more attention. Figure 3 illustrates how utilizing multi-dimensional TOM analysis ( and ) can help in reducing the background contamination of signal events. If we consider only (dashed line), a significant fraction of would pass any reasonable overlap cut. However, in a two dimensional distribution, it is clear that many of the events which obtain a high also obtain a high score. Contrary to events, the signal events almost never get tagged with a high score, as it is difficult for a proper Higgs fat jet to fake a top. Hence, an upper cut on (solid line) efficiently eliminates a significant fraction of events, at a minor cost of signal efficiency. Note that the peak at in the signal distributions corresponds to events where the hardest/second hardest fat jet is likely a light jet.
Figure 4 illustrates the effects of cuts on the mass distribution of the two highest jets. Note that the intrinsic mass filtering property of TOM can be clearly seen in the results. The mass resolution of the Higgs fat jets improves upon the cut on the overlap, while the contributions from both high mass and low mass background regions are significantly diminished.
In addition to jet substructure requirements for Higgs tagging, we require both Higgs candidate jets to contain at least one -tagged jet within the fat jet, as prescribed in Section III.3.
In order to pick out the light jets, we re-cluster each event with (also necessary for -tagging) and select the two highest jets which pass the requirement of
where stands for the plain distance in between the jet ( the up type quark) and each of the Higgs candidate fat jets. We declare these jets to be the quark candidates.
Since we expect two Higgs fat jets in the final state, a comparison between the masses of the two hardest fat jets which pass the overlap criteria provides a useful handle on the background channels. In order to exploit this feature, we construct a mass asymmetry
where are the masses of the two Higgs candidate jets. Figure 5 (left panel) shows the distribution of for signal events and relevant backgrounds. Even after the overlap selections, the background distributions are significantly wider than the signal. Hence, in order to further suppress the background channels, we impose a cut of
Upon identifying the and Higgs jets, we proceed with the reconstruction of the partner. The signal events are characterized by a distinct “2 fat jet 2 light jet” topology, a final state which represents somewhat of a combinatorial challenge (for each fat jet, two combinations with a light jet are possible). In order to find the correct Higgs-light jet pairs, we construct four different combinations of invariant masses
where are the four momenta of the two jets which pass the Higgs tagging requirements and are the four momenta of the two hardest isolated from the Higgs jets by A correct Higgs-light jet pair then minimizes the value of
Consequently, we take the configuration of Higgs - light jet pair which minimizes to construct , the masses of the two partners in the event. Figure 6 shows the reconstructed invariant mass distribution of the pair (assuming ) and the background distributions. The signal events show a prominent peak at the correct partner mass for both partners in the event, while the background distributions are smeared over a wide range of mass values. The results of Figure 6 illustrate well the degree to which our proposal is able to resolve the mass of the partners.
The value of represents the minimum of a mass asymmetry between the two reconstructed objets and hence utilizes the fact that the partners are pair produced. In addition to allowing us to overcome the combinatorial issues when reconstructing the partners, provides another handle on the background channels. Because the partners are pair produced, we expect the value of to peak at 0 for signal events, while we expect the background channels to be characterized by wider distributions of as there is no kinematic feature in the background channels which would lead to a reconstruction of two same mass resonances. Figure 5 (right panel) shows distributions for signal and relevant backgrounds. As in the case of , the background distributions of are significantly broader compared to the signal, hence providing another unique handle on the background channels. In order to exploit this feature, we impose a cut on
as a part of our event selection.
Finally, since we are interested in partners with mass , we require that both Higgs-light jet pairs pass the requirement
for the benchmark values of respectively, where we construct the mass of and from Higgs-light jet pairs which minimize .
iii.5 LHC Run II Sensitivity to Partners of Mass
In this section we investigate the ability of our cutflow proposal to detect light quark partners which decay to a Higgs-light jet pairs at the Run II of the LHC. Table 4 and 5 show the main results, with respect to the initial cross section values in Table 1. For all results on significance we assume a nominal integrated luminosity of .
Our results show that boosted jet techniques combined with fat jet -tagging and kinematic constraints of pair produced heavy particles can achieve with signal significance of at , assuming light quark partners of The significance we obtain is sufficient to claim a discovery of light quark partners. In addition, we find that probing masses higher than will require more luminosity and will be challenging at Run II of the LHC. However, even with signal significance of more than is achievable for , enough to rule out the model point.
Requiring that there exist four fat jets with in an event, together with our boosted Higgs tagging procedure result in an improvement of by roughly a factor of 70-100 at signal efficiency relative to the pre-selection cuts. Additional cuts on mass asymmetries improve by roughly of factor a 3 in total.
The greatest improvement in both and comes from fat jet -tagging, where we find an enhancement by a factor of in and in signal significance. The improvement is largely due to the enormous suppression double fat-jet -tagging exerts on the multi-jet and backgrounds, with the signal efficiency of . The high rejection power of -tagging can be understood well from results presented in Figure 7. The signal events almost always contain at least one quark in each of the fat jets which pass the boosted Higgs tagging criteria. Conversely, almost no multi-jet and events contain two “Higgs like” fat jets with each of the tagged heavy boosted objects containing a -jet. The only background channel which seems to contain a significant fraction of events with both fat jets containing a proper -tag is Standard Model . Still, we find that only about of the events survive the double -tagging criteria.
We studied the LHC Run II discovery potential for the light quark partners in composite Higgs models. As an example, we considered a simplified model based on the coset structure containing one up-type quark in the decoupling limit. Of particular interest were pair produced up-type quark partners of mass which then decay into two boosted Higgses (which we take to decay further hadronically) and two hard jets – a final state which can not be efficiently tagged and reconstructed by “traditional” jet techniques. We proposed a new event cut scheme, designed to exploit the characteristic features of the pair produced event topology. We found that a combination of -tagging, jet substructure, and kinematic cuts resulting from the fact that quark partners are pair produced allows to suppress the large QCD backgrounds to a degree where and is possible for quark partners of mass with of integrated luminosity. Our results show that the LHC Run II could achieve sufficient sensitivity to light quark partners of mass to claim discovery. Probing masses higher than using our proposed cut-scheme will be difficult at Run II of the LHC, yet with we find that a signal significance of more than is achievable for , sufficient to rule out the model point.
The event selection procedure we propose begins by requiring the presence of four fat jets (), two of which are tagged as Higgs candidates. We perform Higgs tagging by considering a combination of the Higgs two body peak overlap, , and the top three body overlap , where we require a lower cut on and an upper cut on . The two-dimensional overlap analysis allows us to suppress the QCD backgrounds, including , to a much better degree compared to the analysis utilizing only . In addition to jet substructure tagging, we also require the two Higgs candidate jets to be -tagged, as well as that the mass difference between the Higgs jets is small. Kinematics of heavy pair produced quark partners offer an additional handle on the background channels, and we require that the mass difference between the reconstructed partners also be small. The greatest improvement in the signal significance comes from -tagging, as requiring two Higgs fat jets to be -tagged diminishes the enormous multi-jet background.
Our study represents a “proof of principle” that successful searches for TeV scale light quark partners decaying to