LHC top partner searches beyond the 2 TeV mass region
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
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
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 :
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 . 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
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)  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 = √
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  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 −
yRf |M1|M4 + e−iφy2 f 2
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
∼ 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
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  and shower them with Pythia 6 , with a fixed renormalisation and
factorisation scale and assuming the CTEQ6L  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  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.
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  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
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. , 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 , “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 
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. , 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 .
In order to speed up the numerical calculations, we generate template states at fixed
pT scaling rule of ref. . 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 . 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 ,
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
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.  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
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.
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. , 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.
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.
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. , 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).
1 − cos
f = 0
where Π~ ≡ (Π1, Π2, Π3, Π4)T and Π ≡
gauge, where the Goldstone multiplet reduces to
∇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
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
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
, 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
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
2 R )
2 T M
Gyhuk = √yR2 cos
− √yR2 cos
The kinetic terms include an e-term contribution which yields
+ 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. ,
icα T¯α − X¯2/3 α γμ (∂μh) T˜α
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
where, using eq. (B.4)
M2ti − M3ti
Mit2 − Mit3
TR − X2/3 R
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
yR cos √(1−√2cL)
−yR sin (1 −
yL sin (1−√2cR) yL sin (1−√2cR)
yL cos (1−√2cR)
− 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
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
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
Decays of top partners
√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
≈ 32π g2v2/4 4M42 yR
2 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
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
, while for d- and e-term contributions of similar size, the terms can enhance each of the
For Tf2 we obtain analogously:
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
+ √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. The expressions
derived in appendix B.3 and B.4 for the couplings and decay widths are calculated at O( )
and are only given for illustration and in order to cross check our numerical implementation.
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