Top Partner Probes of Extended Higgs Sectors
MMCTP-13-11MIT-CTP 4453
Prepared for submission to JHEP
Top Partner Probes of Extended Higgs Sectors
John Kearney, a, Aaron Pierce, a and Jesse Thaler b a Michigan Center for Theoretical Physics, Department of Physics, Ann Arbor, MI 48109, USA b Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
E-mail: [email protected] , [email protected] , [email protected] Abstract:
Natural theories of the weak scale often include fermionic partners of the topquark. If the electroweak symmetry breaking sector contains scalars beyond a single Higgsdoublet, then top partners can have sizable branching ratios to these extended Higgs sectorstates. In fact, top partner decays may provide the most promising discovery mode for suchscalars, especially given the large backgrounds to direct and associated production. In thispaper, we present a search strategy for top partner decays to a charged Higgs boson anda bottom quark, focusing on the case where the charged Higgs dominantly decays to third-generation quarks to yield a multi- b final state. We also discuss ways to extend this searchto exotic neutral scalars decaying to bottom quark pairs. Corresponding author. a r X i v : . [ h e p - ph ] J u l ontents With the discovery of a 125 GeV Higgs boson at the LHC, we are getting our first glimpseat the origin of electroweak symmetry breaking (EWSB). If naturalness is a reliable guide,then we expect additional dynamics at the TeV scale to regulate quadratic divergences in theHiggs potential. In the Standard Model (SM), the large top quark Yukawa coupling induceslarge radiative corrections to m h . Consequently, models of new physics generally involve newcolored particles, top partners, to cancel these quadratic divergences. In the case where theHiggs is a pseudo-Nambu-Goldstone boson (PNGB), such top partners are fermionic.Another common feature of new physics models is an extended Higgs sector, which ofteninvolves a second Higgs doublet or additional singlet scalars. This feature is particularlyprevalent when the Higgs arises as a PNGB, since the breaking of a global symmetry G → H often gives rise to more than just a single complex Higgs doublet. Because these extendedscalars states typically carry only electroweak quantum numbers, they have small directproduction cross sections at hadron colliders like the LHC. Therefore, it is important toexplore new search strategies in order to fully investigate the possible dynamics of EWSB.In this paper, we show how top partners can open additional discovery channels forextended Higgs sectors. In particular, top partners can be copiously pair-produced at theLHC through QCD processes, and the decay of top partners may provide the best avenue forobserving additional scalars. For concreteness, we will focus on the decay of a top partner T to a charged Higgs H ± and a bottom quark b , T → bH ± , H ± → tb, (1.1)– 1 –here we utilize the charged Higgs decay mode that typically dominates for m H ± > m t + m b .We will also show how the same search strategy is sensitive to neutral singlets ϕ via T → tϕ , ϕ → bb. (1.2)However, we wish to emphasize a more general point: if new top partners are found, searchesfor exotic decays to scalars should be a priority . Our approach shares some intellectual an-cestry with strategies to find Higgs bosons through supersymmetric particle decays [1, 2], aswell as studies designed to pick out the SM Higgs boson from top partner decays using jetsubstructure techniques [3].Previous studies of the detectability of charged Higgs states with m H ± > m t + m b havefocused on top quark associated production gb → tH ± [4, 5]. The cross section for thisprocess can in principle be large because extended Higgs sector states often have significantcouplings to top quarks. However, as we will review, there are a number of obstacles thatmake this search challenging. Assuming top partners exist, we will show how pair productionof top partners followed by the decay T → bH ± can be a complementary search strategy.Should these exotic top partner decays be observed, they will become an important windowto the structure of new physics at the TeV scale.The proposed search is particularly well-motivated by little Higgs (LH) scenarios [6–10],which prominently feature both top partners and extended Higgs sectors [11]. In fact, LHmodels often contain more top partners than strictly necessary to regulate the Higgs potential,perhaps because of an underlying custodial symmetry [12–14] or an enhanced global symmetryof the strong dynamics [15, 16]. The search described here is relevant for standard top partnersas well as their exotic cousins. Similarly, as emphasized in Ref. [17], the scalar sector of LHmodels must contain more than just a single Higgs doublet. At minimum, additional scalarsare necessary to achieve the desired the quartic potential for the Higgs boson. Moreover,unless the theory has a symmetry like T -parity [18, 19], precision electroweak constraintsplus the model building constraint of “dangerous singlets” imply the presence of at least twoHiggs doublets [17]. While we are motivated by LH models, the phenomenology we discuss inthis paper is relevant for any theory with exotic top-like states and extended Higgs sectors.For example, similar phenomenology can be present in heavy fourth generation models withmultiple Higgs doublets as long as the dominant mixing is with the third generation [20, 21].The remainder of this paper is organized as follows. In Sec. 2, we compare the discoveryprospects for a charged Higgs boson via top quark associated production pp → tH ± versustop partner decay T → bH ± . In Sec. 3, we demonstrate a viable search strategy designedto uncover T → bH ± , using realistic detector modeling and matched Monte Carlo samplesto estimate the backgrounds. We show in Sec. 4 how the same search is applicable for otherscalar states that may be produced in top partners decays, such as T → tϕ with ϕ → bb .We conclude in Sec. 5 with possible extensions of our analysis.– 2 – tH − b tbg Figure 1 : Feynman diagram contributing to gb → tH ± with H ± → tb decay. Many models with extended Higgs sectors contain a charged Higgs state H ± with a potentiallylarge H ± → tb branching ratio. For example, in a Type II two Higgs doublet model (2HDM),the absence of a measured deviation from the SM prediction for b → sγ indicates that thecharged Higgs bosons must be somewhat heavy, m H ± ∼ >
300 GeV [22, 23], ensuring the H ± → tb decay mode is open. Indeed, for such heavy charged Higgs bosons, H ± → tb dominates over much of the parameter space. In this paper, we assume for simplicity thatthe branching ratio Br( H ± → tb ) = 1. We briefly comment on the possibility of other usefuldecay modes in the conclusion. We highlight the main obstacles to observing pp → tH ± inSec. 2.1, and then discuss the potential advantages of the decay T → bH ± in Sec. 2.2. There can be appreciable production of H ± in association with a top quark via gb → tH ± (see Fig. 1), enabling a search for H ± → tb in the ttb final state. In particular, the finalstates in which a single top decays leptonically allow for the reconstruction of both tops (withreduced combinatoric background relative to the dileptonic or dihadronic final states) andthus the potential observation of a H ± resonance peak in the m tb distribution.Unfortunately, this channel is subject to large SM backgrounds from tt +jets (with a lightjet faking a b ) and ttbb . One might hope that the tt +jets background could be avoided byrequiring 3 b -tagged jets in the final state, as advocated in Refs. [4, 5, 24] and studied at thedetector level in Ref. [25]. However, tt +jets is still a formidable background even after 3 b -tagged jets are required, in part because there is a relatively high charm mistag rate ( (cid:15) c ≈ . (cid:15) c ≈ .
01 as assumed in Refs. [4, 5, 24, 25]), and in part because there isa non-negligible probability for QCD jet combinations to exhibit significant invariant masses(i.e. m jj ∼ m W or m jjj ∼ m t ). Alternatively, one could attempt to search for a chargedHiggs in a ttbb final state from pp → tH ± b , with the requirement of 4 b -tagged jets in the– 3 – g T bT W − bH + tgg bg T bT W − th, Z bgg Figure 2 : Feynman diagrams contributing to top partner pair production, with top partnersdecaying to yield a 4 b , 2 W ± final state. Our signal, containing decays of the type T → bH ± → btb (left), potentially has a background from the decays T → tZ, th → tbb (right).final state as suggested in Ref. [28]. Requiring an additional b -jet does suppress the tt +jetsbackground. However, the additional b -jet produced in pp → tH ± b is frequently relativelysoft, suppressing the signal process if typical b -jet p T criteria are imposed. Furthermore, evenif the tt +jets background can be reduced to acceptable levels via this strategy, there is anirreducible background due to SM ttbb production. Consequently, even using sophisticatedtechniques to distinguish signal from background, the reach of this search strategy remainslimited. The discovery reach found in Ref. [29] is tan β ∼ >
50 for m H ± = 500 GeV in a TypeII 2HDM. Comparing with Ref. [30], this corresponds roughly to σ ( pp → tH ± ) ∼ >
700 fb.Thus, the discovery of a charged Higgs boson via top quark associated production seemsextremely challenging, particularly for intermediate tan β and larger m H ± . This motivatesan investigation of alternative methods for searching for charged Higgses.
In this paper, we advocate an alternative method for observing H ± at the LHC, namely in thedecays of fermionic top partners. Colored top partners can be copiously produced at hadroncolliders via QCD processes pp → T T as shown in Fig. 2. If the branching ratio for T → bH ± is non-negligible, top partner decays can yield a significant number of events containing atleast one H ± , potentially permitting discovery. Since the T → bH ± branching ratio is notnecessarily suppressed at intermediate values of tan β (but rather depends on specific model-building details), searches in this channel can complement top quark associated productionsearches outlined above. Ref. [29] assumed a conservative b -tagging efficiency of (cid:15) b = 0 .
5, so the reach might improve somewhatwith better b -tagging. For much larger values of m H ± ∼ > For very large m T ∼ > – 4 –ike the SM top fields, top partners are generally electroweak singlets or doublets, per-mitting renormalizable Yukawa couplings between a top partner, the Higgs field, and a SMtop quark. Consequently, top partners will typically exhibit decays to SM particles throughthese couplings: T → bW ± , tZ, th. (2.1)Decays involving non-SM particles, such as T → bH ± , are generally expected to be subdomi-nant due to phase space suppression. The exclusively SM decay modes in Eq. (2.1) have beenextensively studied as possible discovery channels for top partners [32–35], and recent limitsfrom the LHC have been set in Refs. [36, 37].We envision a scenario where the top partner T is discovered—hopefully soon—via oneof the decay modes in Eq. (2.1). We then have the opportunity to search for subdominantdecays like T → bH ± . In fact, when top partners are pair produced in pp → T T , one can usea decay mode like T → bW ± to “tag” events as potential top partner pair events and therebyreduce SM backgrounds (notably, events with lighter SM tops). For concreteness, considerthe event topology in Fig. 2, pp → ( T → bW ± had )( T → bH ± → bt lep b ) → b + 2 j + (cid:96) ± ν, (2.2)where the subscript “had” (“lep”) refers to decays of the corresponding W ± to jj ( (cid:96) ± ν ). Asthe W ± from the T → bW ± had decay will be relatively boosted, its hadronic decay will yielda distinctive signature of two fairly collimated jets with m jj ∼ m W that reconstruct a toppartner with a b -jet. Meanwhile, the leptonic decay on the other side of the event reducescombinatoric background, allowing a reconstruction of a second top partner in the event.The dominant SM backgrounds are ttbb and tt +jets with two light jets faking b ’s. How-ever, the presence of four relatively hard b -jets in the signal means that a requirement offour b -tagged jets can be used (in addition to top partner reconstruction) to greatly suppressthese backgrounds. The low fake rate suppresses tt +jets, whereas ttbb can be effectively sup-pressed since the additional b ’s often come from gluon splitting, such that frequently eitherone b -jet is soft and does not pass a minimum p T,j requirement, or the b ’s are collimated andconsequently coalesce into a single jet. High b -multiplicity requirements have similarly beenapplied to reduce tt +jets and ttbb backgrounds in the context of SUSY stop searches [38] andsearches for top partners decaying to exclusively SM states [39].With the SM background under control, a remaining challenge is that other top partnerdecays can yield the same final state as Eq. (2.2), notably T → t lep h bb and T → t lep Z bb (seeFig. 2). These “background” events exhibit a key kinematic difference, however, since the bb -pair from the h or Z is constrained to have an invariant mass of m bb = m h or m Z . Forsignal events the bb invariant mass can be much larger. Consequently, we will see that a cuton the minimum m bb in the event can be used to efficiently isolate rare T → bH ± decays. Aslong as the branching ratio T → bH ± is of order 10%, then the search presented below willbe sensitive to the bH ± states. For simplicity, we do not distinguish between particles and anti-particles when writing decay chains. – 5 –
Search Strategy
In this section, we describe a search strategy that can be used to discover the presence ofa charged Higgs produced in T → bH ± based on the topology described in Sec. 2.2. As abenchmark, we choose m T = 700 GeV, a representative value that satisfies current bounds[36, 37, 40] but is not so high as to create tensions with naturalness. Since a H ± discoverywill require high luminosity ( (cid:39)
300 fb − ), we consider events for the LHC with √ s = 14 TeV.We first describe some of the details of our simulation framework, and then presentpossible event selection criteria that can identify a reasonable fraction of T → bH ± eventswhile rejecting much of the SM and T → th, tZ backgrounds. For our study, we use
MadGraph 5 [41] to generate parton-level events, interfaced with
Pythia 6.4 [42] for decay and hadronization. For top partner pair production, we generateMLM-matched [43, 44] samples of pp → T T + nj (3.1)with n = 0 , , T → bW ± , th, tZ, bH ± (3.2)in MadGraph – subsequent decays are carried out in
Pythia . Using unmatched samples,we have confirmed that we obtain similar results by (1) simulating the full
T T → bW ± X → bbbbjj(cid:96)ν ( X = bH ± , th, tZ ) decay chain in MadGraph and (2) simulating
T T → bW ± X in MadGraph with subsequent decays in
Pythia , indicating that the latter method shouldindeed be sufficient for the matched samples. For the benchmark value of m T = 700 GeV,the MadGraph matched cross section is σ MLM ( pp → T T + nj, m T = 700 GeV) = 470 fb . (3.3)For the dominant SM backgrounds, we generate MLM-matched samples of pp → tt + nj for n = 0 , , pp → ttbb . The productioncross sections from MadGraph for the SM processes are σ MLM ( pp → tt + nj ) = 700 pb , (3.4) σ ( pp → ttbb ) = 10 . . (3.5)All of the processes considered above are subject to sizable higher-order QCD corrections.At NLO for the 14 TeV LHC, Hathor [45] gives inclusive cross sections (see Fig. 3) σ incl ( pp → tt ) = 900 pb , (3.6) σ incl ( pp → T T, m T = 700 GeV) = 600 fb , (3.7)– 6 – HC, s (cid:61)
14 TeV
500 600 700 800 900 100010010 m T (cid:64) GeV (cid:68) Σ N L O (cid:72) pp (cid:174) TT (cid:76) (cid:64) f b (cid:68) Figure 3 : Cross section for inclusive top partner pair production pp → T T at the LHC with √ s = 14 TeV as a function of top partner mass m T (from Ref. [45]). For our studies, we usethe benchmark value m T = 700 GeV.so we apply a K -factor of K ≈ . tt +jets and T T +jets samples. The appropriate K -factor for ttbb is less readily determined, but since the ttbb and tt +jets backgrounds areultimately comparable, we also apply K = 1 . ttbb to avoid significantly underestimatingthe ttbb background. As the realistic K -factor for ttbb is likely less than that for tt +jets, thisis a somewhat conservative choice.Both the signal and background processes will contain two W bosons from top or toppartner decay. As we will require events to contain one hard, isolated lepton which can beused to trigger the event, we allow the W pair to decay via all channels capable of yielding jj(cid:96) /E T , namely W W → ( jj or τ ν τ )( (cid:96)ν or τ ν τ ) (3.8)where the lepton or jets may arise from τ decay. In particular, we do not account for fakeleptons in this analysis, which are expected to be a small effect.Detector simulation was carried out using Delphes 2.0.3 [46] (with [47, 48]) includingjet clustering with
FastJet [49], using resolution parameters appropriate for the ATLASdetector. Data analysis was performed using
ROOT [50]. Electrons are required to have p T,e >
20 GeV and | η | < .
47 (excluding the barrel to endcap transition region 1 . < | η | < . p T,µ >
20 GeV and | η | < .
5. Furthermore, isolationcriteria are imposed. Electrons are isolated if the transverse momentum deposited in anisolation cone of radius ∆ R = (cid:112) (∆ φ ) + (∆ η ) = 0 . p ∆ R< . T < p ∆ R< . T < R > . p T,j >
20 GeV (to suppress leptons from heavy-flavor decaysinside jets). Jets are clustered using the anti- k T algorithm [51] with R = 0 . p T,j >
20 GeV , | η | < .
5. These criteria are similar to those used in ATLAS searchesfor comparable final states [36, 52].For b -tag, light ( u, d, s ) jet mistag, and c -mistag efficiencies, we use the functions givenin Ref. [39] as suitable fits to the measured efficiencies [26, 27], namely (cid:15) b = 0 . (cid:16) p T
36 GeV (cid:17) × (1 . − . | η | ) , (3.9) (cid:15) j = 0 .
001 + 0 . p T GeV , (3.10) (cid:15) c = 0 . , (3.11)respectively. In order to reduce the required number of generated events to achieve rea-sonable statistics (particularly for the tt +jets background), we consider all possible taggingconfigurations for any given event and weight each configuration appropriately, as opposedto implementing b -tagging (and mis-tagging) at the level of the detector simulation. The signal in Eq. (2.2) is characterized by a high multiplicity of relatively hard jets (includingfour b -jets), a lepton, and missing energy. The hardest b will be quite hard as it likely arisesfrom the T → bW ± had decay. Since the neutrino arises at the end of a longer decay chain, thesignal is not characterized by particularly large missing energy, though a mild /E T cut canstill help reduce backgrounds. We perform the following basic cuts to select events of thistype:1. Exactly 1 isolated lepton ( p T,(cid:96) >
20 GeV);2. Missing energy /E T >
20 GeV;3. Event contains ≥ b -tagged jets and ≥ p T,j >
20 GeV);4. Transverse momentum of the hardest b -jet satisfies p T,b >
160 GeV;5. m eff > . m eff = (cid:80) j p T,j + p T,(cid:96) + /E T , and the sum runs over all of the jetsin the event.As shown later in Table 1, these cuts reduce the SM backgrounds by orders of magnituderelative to the events containing top partners. The exact values chosen give good top partner-to-SM background discrimination for m T = 700 GeV, but should be adjusted depending onthe measured value of m T (which, as mentioned in Sec. 2.2, we assume has been measuredvia a dominant decay mode).To further suppress the tt +jets and ttbb backgrounds and to isolate top partner pairproduction events containing T → bH ± decays, we apply the following invariant mass cuts: We do not include the effects of event pileup in this study. Our expectation is that pileup would be mostimportant in the reconstruction of the hadronic W (see cut 7 below). However, since the W is at reasonablyhigh p T , some additional handles, including possibly jet substructure techniques, may be able to reject fake W ’s from pileup jets. – 8 –. Smallest invariant mass for two b -tagged jets in the event satisfies min( m bb ) >
150 GeV.As already mentioned at the end of Sec. 2.2, this helps suppress the background of T → th and T → tZ , but as discussed more below it also helps control the SM backgrounds.7. Hardest b -tagged jet (denoted b ) and two untagged jets have invariant mass m b jj ≈ m T , with the two untagged jets required to have m jj ≈ m W and somewhat small∆ R jj . For the case of m T = 700 GeV, we require m b jj ∈ [600 , m jj = m W ±
20 GeV and ∆ R jj < . b -tagged jets (denoted b , , ) that, together withthe lepton and missing energy (from the neutrino), reconstruct a second top part-ner, i.e. satisfying m b b b (cid:96) /E T ≈ m T . For m T = 700 GeV, we require m b b b (cid:96) /E T ∈ [500 , h/Z → bb , it is effective at rejecting ttjj and ttbb events as well. For the ttbb background, this is because the relatively collimated b ’s from gluon splitting can exhibit low invariant mass. For the tt +jets background, this cutrejects events where one of the quarks from the hadronic top decay is mistagged as a b -jet;due to the relatively large (cid:15) c , this can be particularly valuable in suppressing the backgroundevents with a mis-tagged charm from W ± → cs . In the decay of a top quark t → bqq (cid:48) where q is mistagged as a b -jet m bq = ( p b + p q ) = ( p t − p q (cid:48) ) = m t − p t · p q (cid:48) = m t − m t E q (cid:48) ≤ m t , (3.12)where E q (cid:48) is the energy of q (cid:48) in the rest frame of the top quark. So, a sufficiently hard cut onmin( m bb ) can help mitigate SM backgrounds that yield the same bbbbjj(cid:96)ν final state. Sincethe majority of events are not expected to saturate the bound, we choose the cut min( m bb ) >
150 GeV > m h , m Z as a compromise between rejecting backgrounds and accepting signalevents, some of which have coincidentally small min( m bb ).To demonstrate how these invariant mass cuts are effective, Fig. 4 shows distributionsof min( m bb ) (cut 6) versus m b jj (cut 7) for a variety of top partner processes and SMbackgrounds after applying only basic cuts. We take m T = 700 GeV and m H ± = 500 GeV,and the benchmark cuts maintain a good fraction of the signal topology in Eq. (2.2). Thecut on m b jj ≈ m T serves to isolate top partner events with a T → bW ± had decay. Thetop partner clearly shows up as a band in the m b jj distribution in panels Fig. 4a–Fig. 4c.Furthermore, whereas Fig. 4b and Fig. 4c are peaked at ( m b jj , min( m bb )) ≈ ( m T , m h,Z ),Fig. 4a exhibits a band at m b jj ≈ m T with min( m bb ) extending over a range of valuesincluding min( m bb ) > m h,Z . As a result, the cut on min( m bb ) isolates the T → bH ± decay As described in cut 7, m b jj is only shown if there is an untagged jet pair satisfying m jj = m W ±
20 GeVand ∆ R jj < . – 9 – a) T T → bW ± had bH ± lep ) [GeV] bb min(m [ G e V ] jj b m (b) T T → bW ± had t lep h bb ) [GeV] bb min(m [ G e V ] jj b m (c) T T → bW ± had t lep Z bb ) [GeV] bb min(m [ G e V ] jj b m (d) T T → bW ± lep t had h bb ) [GeV] bb min(m [ G e V ] jj b m (e) tt +jets ) [GeV] bb min(m [ G e V ] jj b m (f) ttbb ) [GeV] bb min(m [ G e V ] jj b m Figure 4 : Distributions of min( m bb ) against m b jj after applying basic cuts (1–5), for m T =700 GeV , m H ± = 500 GeV. Here, m b jj corresponds to all untagged jet pairs satisfying m jj = m W ±
20 GeV and ∆ R jj < .
5. Dashed lines denote the signal region (cuts 6 and7). For Fig. 4a through Fig. 4d, grayscale represent Events/Br bW X [300 fb − ], where Br bW X denotes the branching ratio for the process T T → bW ± X . For Fig. 4e and Fig. 4f, grayscalerepresents Events [300 fb − ]. – 10 – [GeV] T El b b b m
400 500 600 700 800 900 1000 1100 1200 / G e V - E v en t s / f b – bH – bW fi TT th – bW fi TT tt+jetsttbb
Figure 5 : Distribution of m b b b (cid:96) /E T after cuts 1 through 7 have been applied. As in Fig. 4, m T = 700 GeV and m H ± = 500 GeV, and in addition we take Br bW bH ± = 0 . bW th =0 .
2. The shape of the distribution for
T T → bW ± tZ is similar to that for T T → bW ± th .Dashed lines denote the region selected by cut 8, m b b b (cid:96) /E T ∈ [500 , m bb cut against the SM backgrounds for the reasons described above. The process pp → ( T → bW ± lep )( T → bH ± had ) (3.13)is largely rejected by our cuts, but is counted as signal as it involves a charged Higgs. Distributions of m b b b (cid:96) /E T are shown in Fig. 5 for the signal T T → bW ± bH ± anddominant SM background processes after cuts 1 through 7 have been applied. The presenceof a resonance structure at m b b b (cid:96) /E T ≈ m T in the signal distribution means that cut 8 on m b b b (cid:96) /E T can be used to isolate events with a second top partner and further reduce the SMbackgrounds. Note that the sharpness of the signal peak is enhanced by cut 7 which helps toresolve combinatoric ambiguity. Efficiencies for the various cuts from Sec. 3.2 are shown in Table 1 for a representative heavycharged Higgs mass, m H ± = 500 GeV. For these efficiencies, the SM background contri-butions from tt +jets and ttbb are comparable. Also shown are the dominant backgroundcontributions arising from decays of top partners to electroweak bosons. In principle, topquark associated production of H ± is also a “background” (as it does not serve our goal of In principle, one could enhance the signal sensitivity by crafting a selection criteria designed for Eq. (3.13).We found only a marginal improvement, however, since it is harder to develop a good T → bW ± lep tag to rejectthe tt +jets background. – 11 –rocess T T → T T → SM bW ± bH ± bW ± th bW ± tZ tt + nj ttbbσ × Br [fb] 300 Br bW bH ±
170 Br bW th
44 Br bW tZ . × . × Basic Cuts 3 . × − . × − . × − . × − . × − Cut 6: min( m bb ) 1 . × − . × − . × − . × − . × − Cut 7: m b jj . × − . × − . × − . × − . × − Cut 8: m b b b (cid:96) /E T . × − . × − . × − . × − . × − Events [300 fb − ] 130 Br bW bH ± bW th bW tZ Table 1 : Cumulative efficiencies for signal and background events to pass the selection cri-teria. Signals are generated for a representative heavy charged Higgs mass, m H ± = 500 GeV.In all events, W ± bosons decay as specified in Eq. (3.8), and the Higgs and Z bosons inthese events decay to bb . We take Br( h → bb ) = 0 .
58, Br( Z → bb ) = 0 .
15, and as-sume Br( H ± → tb ) = 1. Br bW X denotes the branching ratio for T T → bW ± X . Thecut ranges are defined as min( m bb ) >
150 GeV (cut 6), m b jj ∈ [600 , m b b b (cid:96) /E T ∈ [500 , H ± coupling to top partners), but it tends to be negligibleunless σ ( pp → tH ± ) ∼ > O (600) fb. In terms of the complementarity of these two channels asmethods for searching for H ± , it is worth noting that this is exactly the region in which atop quark associated production search becomes potentially viable, see Sec. 2.1.The discovery potential of this search depends on the branching ratios of the top partners.As an illustrative example, consider the parametrization T → bH ± Br = (cid:15)bW ± Br = (1 − (cid:15) ) tZ Br = (1 − (cid:15) ) th Br = (1 − (cid:15) ) . (3.14)The 2 : 1 : 1 ratio for the bW ± : tZ : th modes is what one might approximately expect dueto the Goldstone Boson Equivalence Theorem [53–55]. Using the efficiencies in Table 1 for m T = 700 GeV , m H ± = 500 GeV, we find using Poisson statistics that with L = 300 fb − ofintegrated data, one can probe (cid:15) = (cid:40) .
04 at 2 σ ( S = 5 . , B = 6 . SM + 1 . . .
12 at 5 σ ( S = 13 . , B = 6 . SM + 1 . . , (3.15)indicating that this channel is viable even for relatively modest T → bH ± branching ratios.The change in B results from the change in Br bW th,bW tZ as a function of (cid:15) , i.e. these decayprocesses contribute an expected 1.2 background events at (cid:15) = 0 .
04 but 1.0 events at an (cid:15) = 0 .
12. In realistic 2HDMs with fermionic top partners, such as the “Bestest Little Higgs”[56], a wide variety of decay branching ratios are possible for the various top partners in– 12 – T m H ± Efficiency Events [ L = 300 fb − ] (cid:15) (2 σ ) (cid:15) (5 σ )700 400 1 . × −
130 Br bW bH ± . × −
130 Br bW bH ± . × −
73 Br bW bH ± Table 2 : Efficiencies for passing the given selection criteria for m T = 700 GeV and severalrepresentative values of m H ± . Also shown are corresponding values of (cid:15) (defined in Eq. (3.14))yielding 2 σ and 5 σ significance assuming Br( H ± → tb ) = 1 and L = 300 fb − . The 2 σ (5 σ )significances correspond to S ≈ . .
7) and B ≈ . . T → bW ± → bjj , there is also in principlean upper limit on the (cid:15) that can be probed using this approach, above which the channelwould be suppressed by small Br( T → bW ± ). We view this possibility as unlikely because, asmentioned, the T → bH ± decay is likely to be subdominant due to phase space suppression.If the T → bH ± decay does dominate, alternative search strategies would likely be preferredto tease out the existence of the H ± . However, such top partners would at least be discoveredvia the kinds of multi- b searches used to hunt for T → th final states, as long as no m bb = m h requirement is applied.Efficiencies for passing the given selection criteria, and corresponding values of (cid:15) yielding2 σ and 5 σ significances with the branching ratios described above, are given in Table 2 forseveral representative values of m H ± . For m H ± ≈ m T , the efficiency for the signal process topass the selection criteria falls because the b quark from T → bH ± becomes softer, increasingthe likelihood of an event failing cut 6 by having min( m bb ) <
150 GeV. Thus, in these regionsof parameter space, a larger T → bH ± branching ratio is required for this to be a viable searchstrategy – unfortunately, also in these regions, the phase space suppression of T → bH ± willbe greater, likely reducing this branching ratio. For optimal coverage of this squeezed region,it might be worth pursuing a set of dedicated cuts. For larger values of m T , we anticipatethat comparable separation from SM backgrounds could be achieved with slightly looser cutsdue to the increased hardness of the event. The corresponding increase in efficiency couldpartially mitigate the rapid decrease in σ NLO ( pp → T T ) with m T (Fig. 3).To demonstrate the potential reach of this search at the LHC with very high luminosity,we present the analog of Table 2 for m T = 1 TeV and L = 3000 fb − in Table 3. The increasein luminosity is necessary to compensate for the decrease in production cross section, σ incl ( pp → T T, m T = 1 TeV) = 60 fb . (3.16)In this case, we modify cuts 7 and 8 to require m b jj ∈ [900 , m b b b (cid:96) /E T ∈ [800 , m T = 1 TeV.For instance, heavier top partners produce events with larger p T,b and m eff , such that harsher– 13 – T m H ± Efficiency Events [ L = 3000 fb − ] (cid:15) (2 σ ) (cid:15) (5 σ )1000 400 1 . × −
110 Br bW bH ± . × −
150 Br bW bH ± . × −
120 Br bW bH ± Table 3 : Efficiencies for passing the given selection criteria for m T = 1 TeV and severalrepresentative values of m H ± . Also shown are corresponding values of (cid:15) (defined in Eq. (3.14))yielding 2 σ and 5 σ significance assuming Br( H ± → tb ) = 1 and L = 3000 fb − . In this case,we require m b jj ∈ [900 , m b b b (cid:96) /E T ∈ [800 , tt +jets and ttbb SM processes contribute 6.9 and 3.9 background events, respectively. The2 σ (5 σ ) significances correspond to S ≈ . .
2) and B ≈ . . [GeV] edgebb m
150 200 250 300 350 400 450 500 550 / G e V - E v en t s / f b – bH – bW fi TT th – bW fi TT tt+jetsttbb
Figure 6 : Distribution of m edge bb taking m T = 700 GeV , m H ± = 500 GeV , (cid:15) = 0 .
12. The
T T → bW ± tZ distribution is not shown as it is similar in shape to the T T → bW ± th distribution, but is suppressed as Br( Z → bb ) < Br( h → bb ). For these values, the b ’s from T → H ± b → tbb are constrained to have m edge bb ≤
460 GeV (dashed line, see Eq. (3.17)).basic cuts may be preferred to further suppress SM backgrounds. As the W ± from the T → bW ± had decay would be more boosted, cut 7 could also be modified to require morecollimated jets—jet substructure techniques may even prove useful in this regime. Finally,as heavier top partners permit more phase space for decays, the min( m bb ) required couldconceivably be increased. Appropriately optimizing cuts for different candidate values of m T would extend the reach of this search.The above analysis strategy was aimed at getting a signal to background ratio of O (1),so relatively harsh cuts were needed to control the SM background from top quarks. Onedrawback of this analysis strategy is that the number of signal events passing these criteriais likely to be small, precluding the observation of, e.g., a resonance peak at m tb = m H ± .– 14 – T m ϕ Efficiency Events [300 fb − ] (cid:15) (2 σ ) (cid:15) (5 σ )700 350 1 . × −
120 Br bW tϕ . × −
88 Br bW tϕ Table 4 : Efficiencies for passing the given selection criteria for several representative valuesof m ϕ . Also shown are corresponding values of (cid:15) yielding 2 σ and 5 σ significance assumingBr( ϕ → bb ) = 1. As in Table 2, 2 σ (5 σ ) significances correspond to S ≈ . .
7) and B ≈ . . m H ± unless looser eventselection criteria (and alternative ways of controlling the SM top backgrounds) are used.However, with sufficient data, there are numerous methods through which the charged Higgsmass could be extracted from this channel, even if H ± has leptonic decays. For example, oneway to access the H ± mass is via the edge in the m bb distribution for the b ’s produced in thedecay T → H ± b → tbb , m bb ≤ m T (cid:115) − m H ± m T (cid:115) − m t m H ± . (3.17)This, too is likely to be challenging due to small statistics, but given lighter top partners, asufficiently large data set, or generous branching ratios, it could be worth pursuing further.To give an idea of how this might work, we first attempt to identify the b quark coming fromthe top decay by minimizing | m b k (cid:96) /E T − m t | ( k = 2 , ,
4, i.e. excluding the harder b used inthe other side T reconstruction). We denote this b as b t . We can then examine the invariantmass distribution of the remaining two b quarks: m edge bb . A sample distribution is shown for m T = 700 GeV, m H ± = 500 GeV, and (cid:15) = 0 .
12 in Fig. 6. For these values, m edge bb ≤
460 GeV.Unlike attempting to observe a resonance in an m tb distribution, the m edge bb distribution hasthe advantage of not being subject to combinatoric ambiguity once m b t (cid:96) /E T ≈ m t has beenused to identify the bottom arising from the leptonic top quark decay. The strategy outlined above is clearly suitable for searching for any charged scalars ϕ ± pro-duced in top partner decays T → bϕ ± with ϕ ± → tb . However, it is also applicable to heavierneutral scalar states ϕ produced via T → tϕ and decaying as ϕ → bb , pp → ( T → bW ± had )( T → tϕ → t lep bb ) → b + 2 j + (cid:96)ν. (4.1)While one could imagine other dedicated searches for such a ϕ , the search strategy providedalready for H ± would at least uncover an excess as long as m ϕ >
150 GeV to satisfy theconditions of cut 6.Efficiencies for two sample values of m ϕ are given in Table 4, along with correspondingvalues of (cid:15) yielding 2 σ and 5 σ significances (as above, taking Br( T → tϕ ) = (cid:15) and Br( T → – 15 – [GeV] peakbb m
150 200 250 300 350 400 450 500 550 / G e V - E v en t s / f b j t – bW fi TT th – bW fi TT tt+jetsttbb
Figure 7 : Distribution of m peak bb taking m T = 700 GeV , m ϕ = 350 GeV, (cid:15) = 0 .
13. Weassume Br( ϕ → bb ) = 1. In contrast to Fig. 6, this b pair should reconstruct the ϕ ,producing a resonance peak at m ϕ (dashed line). bW ± : th : tZ ) = (1 − (cid:15) ) × ( : : )). As expected, the efficiencies and branching ratiosreach are comparable to the T → bH ± search.Of course, the bb pair produced in T → tϕ → tbb should exhibit a resonance structureat m bb = m ϕ , so by employing a similar tactic to that used above to identify the edge(i.e. by forming m peak bb using the pair of b ’s in { b , b , b } that do not give the minimum | m b k (cid:96) /E T − m t | ) one could attempt to search for a resonance peak. A sample distribution for m T = 700 GeV , m ϕ = 350 GeV, and (cid:15) = 0 .
13 is shown in Fig. 7. The resonance peak is notparticularly sharp in part because we are not using the full neutrino four-momentum to rejectthe b jet from the top decay and mitigate combinatoric confusion. The peak could potentiallybe improved by solving for the full four-momentum with p νT = /p T and requiring m (cid:96)ν = m W and m bbb(cid:96)ν = m T . Again, the feasibility of discovering a resonance structure in this fashionis limited due to the small statistics, but such a structure could in principle help not only todetermine m ϕ but also to distinguish between T → bH ± and T → tϕ . If the weak scale is in fact natural, new states should soon be discovered at the LHC. Thesenew states would of course provide insights into why the Higgs boson has a weak scale mass,but they might also provide an unexpected window into a rich scalar sector that wouldbe otherwise difficult to access experimentally. In this paper, we have argued that heavycharged Higgs bosons can be challenging to observe in standard channels, but they mightwell be discoverable in the decays of top partners. Top partner decays can also be sensitiveto exotic neutral scalars. – 16 –e have focused on methods for observing extended Higgs sector scalars that decaypredominantly via H ± → tb or ϕ → bb . These decay channels are likely to dominate if theextended Higgs sector scalars have large couplings to third-generation quarks. That said,other decay modes may also be present depending on the exact structure of the theory. Forinstance, decays like H ± → τ ± ν τ or H ± → W ± h may provide alternative signatures of scalarsproduced either directly or in fermionic top partner decays.The strategy presented here makes use of the (likely significant) T → bW ± decay to tagtop partner pair production events. However, if other top partner decay modes dominate,alternative search strategies would be preferred. In particular, if the top partner decayspredominantly as T → th , a cut on min( m bb ) can no longer be employed to separate signalfrom background. The decay T T → thbH ± would yield a striking 6 b , 2 W ± final state, butcombinatoric backgrounds associated with the large number of b -jets would make it difficultto disentangle this decay pattern from, e.g., T T → thth . Similarly, bottom partners B arealso expected to be light if they are in an electroweak doublet with the top partner T , andthe decay mode BB → tW ± tH ± ( BB → bhtH ± ) yields a striking 4 b , 4 W ± (6 b , 2 W ± ) finalstate, albeit with significant combinatoric confusion.Finally, while this search strategy could reveal the presence of extended Higgs sectorscalars, distinguishing between T → tϕ → tbb and T → H ± b → tbb would likely provechallenging given the small statistics. Of course, the first priority is to determine the presenceof additional scalar states, but how to determine their properties is a question of great interest,especially given the difficulty in uncovering them in the first place. We leave these questionsfor future investigation, as we await hints of naturalness from the LHC. Acknowledgments
We thank Timothy Cohen, Bogdan Dobrescu, and Martin Schmaltz for useful conversations.J.K. thanks Josh Gevirtz for assistance with
Root . The work of J.K. and A.P. is supportedin part by NSF Career Grant NSF-PHY-0743315, with A.P. receiving additional support fromthe U.S. Department of Energy (DoE) Grant
References [1] A. Datta, A. Djouadi, M. Guchait, and Y. Mambrini,
Charged Higgs production from SUSYparticle cascade decays at the CERN LHC , Phys.Rev.
D65 (2002) 015007, [ hep-ph/0107271 ].[2] A. Datta, A. Djouadi, M. Guchait, and F. Moortgat,
Detection of mssm higgs bosons fromsupersymmetric particle cascade decays at the LHC , Nucl.Phys.
B681 (2004) 31–64,[ hep-ph/0303095 ].[3] G. D. Kribs, A. Martin, and T. S. Roy,
Higgs boson discovery through top-partners decays usingjet substructure , Phys.Rev.
D84 (2011) 095024, [ arXiv:1012.2866 ]. – 17 –
4] V. D. Barger, R. Phillips, and D. Roy,
Heavy charged Higgs signals at the LHC , Phys.Lett.
B324 (1994) 236–240, [ hep-ph/9311372 ].[5] J. Gunion,
Detecting the t b decays of a charged Higgs boson at a hadron supercollider , Phys.Lett.
B322 (1994) 125–130, [ hep-ph/9312201 ].[6] N. Arkani-Hamed, A. G. Cohen, and H. Georgi,
Electroweak symmetry breaking fromdimensional deconstruction , Phys.Lett.
B513 (2001) 232–240, [ hep-ph/0105239 ].[7] N. Arkani-Hamed, A. Cohen, E. Katz, A. Nelson, T. Gregoire, et al.,
The Minimal moose for alittle Higgs , JHEP (2002) 021, [ hep-ph/0206020 ].[8] N. Arkani-Hamed, A. Cohen, E. Katz, and A. Nelson,
The Littlest Higgs , JHEP (2002)034, [ hep-ph/0206021 ].[9] M. Schmaltz and D. Tucker-Smith,
Little Higgs review , Ann.Rev.Nucl.Part.Sci. (2005)229–270, [ hep-ph/0502182 ].[10] M. Perelstein, Little Higgs models and their phenomenology , Prog.Part.Nucl.Phys. (2007)247–291, [ hep-ph/0512128 ].[11] J. Kearney, A. Pierce, and J. Thaler, Exotic Top Partners and Little Higgs , arXiv:1306.4314 .[12] S. Chang and J. G. Wacker, Little Higgs and custodial SU(2) , Phys.Rev.
D69 (2004) 035002,[ hep-ph/0303001 ].[13] S. Chang,
A ’Littlest Higgs’ model with custodial SU(2) symmetry , JHEP (2003) 057,[ hep-ph/0306034 ].[14] K. Agashe, R. Contino, L. Da Rold, and A. Pomarol,
A Custodial symmetry for Zb anti-b , Phys.Lett.
B641 (2006) 62–66, [ hep-ph/0605341 ].[15] E. Katz, J.-y. Lee, A. E. Nelson, and D. G. Walker,
A Composite little Higgs model , JHEP (2005) 088, [ hep-ph/0312287 ].[16] J. Thaler and I. Yavin,
The Littlest Higgs in Anti-de Sitter space , JHEP (2005) 022,[ hep-ph/0501036 ].[17] M. Schmaltz and J. Thaler,
Collective Quartics and Dangerous Singlets in Little Higgs , JHEP (2009) 137, [ arXiv:0812.2477 ].[18] H.-C. Cheng and I. Low,
TeV symmetry and the little hierarchy problem , JHEP (2003)051, [ hep-ph/0308199 ].[19] H.-C. Cheng and I. Low,
Little hierarchy, little Higgses, and a little symmetry , JHEP (2004) 061, [ hep-ph/0405243 ].[20] S. Bar-Shalom, M. Geller, S. Nandi, and A. Soni,
Two Higgs doublets, a 4th generation and a125 GeV Higgs , arXiv:1208.3195 .[21] M. Geller, S. Bar-Shalom, G. Eilam, and A. Soni, The 125 GeV Higgs in the context of fourgenerations with 2 Higgs doublets , Phys.Rev.
D86 (2012) 115008, [ arXiv:1209.4081 ].[22] O. Deschamps, S. Descotes-Genon, S. Monteil, V. Niess, S. T’Jampens, et al.,
The Two HiggsDoublet of Type II facing flavour physics data , Phys.Rev.
D82 (2010) 073012,[ arXiv:0907.5135 ]. – 18 –
23] C.-Y. Chen and S. Dawson,
Exploring Two Higgs Doublet Models Through Higgs Production , arXiv:1301.0309 .[24] S. Moretti and D. Roy, Detecting heavy charged Higgs bosons at the LHC with triple b tagging , Phys.Lett.
B470 (1999) 209–214, [ hep-ph/9909435 ].[25] K. Assamagan,
The charged Higgs in hadronic decays with the ATLAS detector , ActaPhys.Polon.
B31 (2000) 863–879.[26]
ATLAS Collaboration
Collaboration,
Calibrating the b-Tag Efficiency and Mistag Rate in pb − of Data with the ATLAS Detector , .[27] ATLAS Collaboration
Collaboration,
ATLAS: Detector and physics performance technicaldesign report. Volume 1 , .[28] D. Miller, S. Moretti, D. Roy, and W. J. Stirling,
Detecting heavy charged Higgs bosons at theCERN LHC with four b quark tags , Phys.Rev.
D61 (2000) 055011, [ hep-ph/9906230 ].[29] K. A. Assamagan and N. Gollub,
The ATLAS discovery potential for a heavy charged Higgsboson in gg → tbH ± with H ± → tb , Eur.Phys.J.
C39S2 (2005) 25–40, [ hep-ph/0406013 ].[30]
LHC Higgs Cross Section Working Group
Collaboration, S. Dittmaier et al.,
Handbook ofLHC Higgs Cross Sections: 1. Inclusive Observables , arXiv:1101.0593 .[31] S. Yang and Q.-S. Yan, Searching for Heavy Charged Higgs Boson with Jet Substructure at theLHC , JHEP (2012) 074, [ arXiv:1111.4530 ].[32] T. Han, H. E. Logan, B. McElrath, and L.-T. Wang,
Phenomenology of the little Higgs model , Phys.Rev.
D67 (2003) 095004, [ hep-ph/0301040 ].[33] M. Perelstein, M. E. Peskin, and A. Pierce,
Top quarks and electroweak symmetry breaking inlittle Higgs models , Phys.Rev.
D69 (2004) 075002, [ hep-ph/0310039 ].[34] Y. Okada and L. Panizzi,
LHC signatures of vector-like quarks , arXiv:1207.5607 .[35] A. De Simone, O. Matsedonskyi, R. Rattazzi, and A. Wulzer, A First Top Partner’s HunterGuide , JHEP (2013) 004, [ arXiv:1211.5663 ].[36]
ATLAS Collaboration
Collaboration, G. Aad et al.,
Search for pair production of heavytop-like quarks decaying to a high-pT W boson and a b quark in the lepton plus jets final state at √ s = 7 TeV with the ATLAS detector , Phys.Lett.
B718 (2013) 1284–1302, [ arXiv:1210.5468 ].[37]
CMS Collaboration
Collaboration, S. Chatrchyan et al.,
Search for pair producedfourth-generation up-type quarks in pp collisions at √ s = 7 TeV with a lepton in the final state , Phys.Lett.
B718 (2012) 307–328, [ arXiv:1209.0471 ].[38] D. Berenstein, T. Liu, and E. Perkins,
Multiple b-jets reveal natural SUSY and the 125 GeVHiggs , arXiv:1211.4288 .[39] K. Harigaya, S. Matsumoto, M. M. Nojiri, and K. Tobioka, Search for the Top Partner at theLHC using Multi-b-Jet Channels , Phys.Rev.
D86 (2012) 015005, [ arXiv:1204.2317 ].[40] K. Rao and D. Whiteson,
Triangulating an exotic T quark , Phys.Rev.
D86 (2012) 015008,[ arXiv:1204.4504 ].[41] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, and T. Stelzer,
MadGraph 5 : Going Beyond , JHEP (2011) 128, [ arXiv:1106.0522 ]. – 19 –
42] T. Sjostrand, S. Mrenna, and P. Z. Skands,
PYTHIA 6.4 Physics and Manual , JHEP (2006) 026, [ hep-ph/0603175 ].[43] M. L. Mangano, M. Moretti, F. Piccinini, and M. Treccani,
Matching matrix elements andshower evolution for top-quark production in hadronic collisions , JHEP (2007) 013,[ hep-ph/0611129 ].[44] S. Mrenna and P. Richardson,
Matching matrix elements and parton showers with HERWIGand PYTHIA , JHEP (2004) 040, [ hep-ph/0312274 ].[45] M. Aliev, H. Lacker, U. Langenfeld, S. Moch, P. Uwer, et al.,
HATHOR: HAdronic Top andHeavy quarks crOss section calculatoR , Comput.Phys.Commun. (2011) 1034–1046,[ arXiv:1007.1327 ].[46] S. Ovyn, X. Rouby, and V. Lemaitre,
DELPHES, a framework for fast simulation of a genericcollider experiment , arXiv:0903.2225 .[47] J. de Favereau, X. Rouby, and K. Piotrzkowski, Hector: A Fast simulator for the transport ofparticles in beamlines , JINST (2007) P09005, [ arXiv:0707.1198 ].[48] L. Quertenmont and V. Roberfroid, FROG: The Fast & Realistic OPENGL Displayer , arXiv:0901.2718 .[49] M. Cacciari, G. P. Salam, and G. Soyez, FastJet User Manual , Eur.Phys.J.
C72 (2012) 1896,[ arXiv:1111.6097 ].[50] R. Brun and F. Rademakers,
ROOT: An object oriented data analysis framework , Nucl.Instrum.Meth.
A389 (1997) 81–86.[51] M. Cacciari, G. P. Salam, and G. Soyez,
The Anti-k(t) jet clustering algorithm , JHEP (2008) 063, [ arXiv:0802.1189 ].[52]
ATLAS Collaboration
Collaboration, G. Aad et al.,
Measurement of the top quark pairproduction cross-section with ATLAS in the single lepton channel , Phys.Lett.
B711 (2012)244–263, [ arXiv:1201.1889 ].[53] J. M. Cornwall, D. N. Levin, and G. Tiktopoulos,
Derivation of Gauge Invariance fromHigh-Energy Unitarity Bounds on the s Matrix , Phys.Rev.
D10 (1974) 1145.[54] C. Vayonakis,
Born Helicity Amplitudes and Cross-Sections in Nonabelian Gauge Theories , Lett.Nuovo Cim. (1976) 383.[55] B. W. Lee, C. Quigg, and H. Thacker, Weak Interactions at Very High-Energies: The Role ofthe Higgs Boson Mass , Phys.Rev.
D16 (1977) 1519.[56] M. Schmaltz, D. Stolarski, and J. Thaler,
The Bestest Little Higgs , JHEP (2010) 018,[ arXiv:1006.1356 ].[57] S. Godfrey, T. Gregoire, P. Kalyniak, T. A. Martin, and K. Moats,
Exploring the heavy quarksector of the Bestest Little Higgs model at the LHC , JHEP (2012) 032,[ arXiv:1201.1951 ].].