LHC Signatures of Vector-Like Quarks

Abstract

This work provides an overview on the current status of phenomenology and searches for heavy vector-like quarks, which are predicted in many models of new physics beyond the Standard Model. Searches at Tevatron and at the LHC, here listed and shortly described, have not found any evidence for new heavy fermionic states (either chiral or vector-like) and have therefore posed strong bounds on their masses: depending on specific assumptions on the interactions and on the observed final state, vector-like quarks with masses up to roughly 400–600 GeV have been excluded by all experiments. In order to be as simple and model independent as possible, the chosen framework for the phenomenological analysis is an effective model with the addition of a vector-like quark representation (singlet, doublet, or triplet under 𝑆𝑈(2)_𝐿) which couples through Yukawa interactions with all SM families. The relevance of different observables for the determination of bounds on mixing parameters is then discussed and a complete overview of possible two body final states for every vector-like quark is provided, including their subsequent decay into SM particles. A list and short description of phenomenological analyses present in the literature are also provided for reference purposes.

1. Introduction

A fermion is defined to be vector-like if its left- and right-handed chiralities belong to the same representation of the symmetry group 𝐺 of the underlying theory, where 𝐺≡𝑆𝑈(3)_𝑐⊗𝑆𝑈(2)_𝐿⊗𝑈(1)_𝑌 in the Standard Model (SM). At present there is no evidence of the existence of vector-like quarks (VLQs), nevertheless they are key ingredients for many models of physics beyond the Standard Model (BSM) and there is a vast literature about their properties and phenomenology. Recent observations at the LHC strongly point towards the existence of a resonance which is compatible with an SM Higgs [1, 2], thus seeming to complete the SM picture. The putative Higgs discovery would leave unsolved many long-standing issues related to the nature of fermion mass hierarchies (Yukawa are completely free parameters) and to the Higgs mass stability itself (divergence of radiative corrections), which can probably be explained, extending the SM to encompass new, yet undiscovered, states. Dedicated experimental searches for VLQs have already been undertaken and will be improved in the next future; therefore a detailed understanding of the properties of VLQs is essential to drive and tune forthcoming analyses.

From a theoretical point of view, VLQs have been introduced in many different models. A description of the various models as well as their consistency against the observations of the 125 GeV Higgs-like resonance is beyond the scopes of the present analysis; details can be found in the original work and references therein. Here, it is sufficient to note how the emergence of VLQs is a recurrent consequence in many models of BSM physics. The most studied scenarios which predict the presence of VLQs can be divided into broad categories:(i)composite Higgs models: the EW symmetry breaking is driven by a condensate of the top quark and a VL singlet involving a seesaw mechanism between the two states [3–12]; (ii)extra dimensions: excited partners of SM quarks belonging to heavier tiers of universal extra-dimensional scenarios are vector-like; (iii)gauging of the flavour group: VL fermions are required for anomaly cancellation and can play a role in the mechanisms of quark mass generation [13–16]; (iv)little Higgs models: VL states appear as partners of SM fermions in larger representations of the symmetry group [17–22]; (v)supersymmetric nonminimal extensions of the SM: VL matter can be introduced in nonminimal supersymmetric models to increase corrections to the Higgs mass without affecting too much EW precision observables [23–28], and it appears also in nonminimal, GUT-inspired, and supersymmetric scenarios [29].

VLQs can also appear in models which try to explain measured asymmetries in different processes:(i)in [30, 31] VLQs are introduced to explain the observed 𝐴^𝑏_𝐹𝐵 asymmetry: bottom partners can mix with the bottom quark and induce modifications of its coupling with the 𝑍 boson;(ii)the forward-backward asymmetry 𝐴_𝐹𝐵 in top pair production, measured at Tevatron, can be explained with the existence of a color octet with a large decay width; this condition can be obtained if the color octet is allowed to decay to a heavy VL state and an SM fermion [32, 33].

From the phenomenological point of view, signatures of VLQs have been largely analysed in the literature, both from a model-independent perspective and within specific scenarios. The presence of flavour changing neutral currents, a distinctive feature of VLQs, leads to a wide range of possible final states, which have been (and will certainly be) analysed in detail in order to drive the experimental search of these new states.

The present study is organized as follows: in Section 2 the minimal extension of the SM with the presence of VLQs is described, together with an overview of observables which can provide bounds to the mixing parameters of the theory; Section 3 contains a summary of all searches for heavy fermions at Tevatron and LHC, focusing on the assumptions that lie beneath the obtained bounds; in Section 4 a list of all allowed final states coming from VLQ resonant production in two-body intermediate states at the LHC is presented, considering all the possible decay channels for the different VLQ representations; moreover, specific signatures, analysed in the literature, are shortly described; in Section 5 some examples of the possible contribution of VLQs to other observables are discussed.

Some of the results reported here were published in [34, 35].

2. Model Framework

2.1. Representations and Couplings

The minimal scenarios with the presence of VLQs besides SM particles are those in which the new states interact with SM quarks and the Higgs boson through Yukawa couplings. Classifying VLQs in multiplets of 𝑆𝑈(2)_𝐿, it is possible to write gauge invariant interaction terms only for singlet, doublet, and triplet representations. All the possibilities are shown in Table 1. Pure mixing terms between VLQs and SM states, allowed by gauge invariance for singlets and SM-like doublet representations, have been omitted because they can be eliminated through rotations of the states.

Table 1 

Allowed representations for VLQs, with quantum numbers under 𝑆𝑈(2)_𝐿 and 𝑈(1)_𝑌 and Yukawa mixing terms in the Lagrangian. Depending on the chosen representation, the Higgs boson may be 𝐻 or 𝐻^𝑐; therefore it has been noted as 𝐻^(𝑐) when necessary. The gauge invariant mass term common to all representations is a peculiar feature of VLQs.

After the Higgs develops its VEV, VL states are allowed to mix with SM quarks: the mixing occurs in the left-handed sector for the singlet and triplet representations and in the right-handed sector for the doublet representation. The mass eigenstates will be labelled as 𝑋_5/3,𝑡^′,𝑏^′,𝑌_−4/3. (1) The mass matrices for the SM-partners 𝑡^′ and 𝑏^′ can be diagonalized by unitary 4×4 matrices 𝑉_𝐿^𝑡,𝑏 and 𝑉_𝑅^𝑡,𝑏: 𝑚_𝑢𝑚_𝑐𝑚_𝑡𝑚_𝑡′=𝑉^𝑡_𝐿^†⋅ℳ_𝑡⋅𝑉^𝑡_𝑅,𝑚_𝑑𝑚_𝑠𝑚_𝑏𝑚_𝑏′=𝑉^𝑏_𝐿^†⋅ℳ_𝑏⋅𝑉^𝑏_𝑅, (2) where the actual expressions of ℳ_𝑡 and ℳ_𝑏 depend on the chosen representations and on the assumptions on the mixing parameters. The couplings with gauge bosons also depend on the chosen representations, but a common feature of every VLQ scenario is that tree-level FCNCs are developed through the mixing with SM quarks. The general form of 𝑍𝑞𝑞 couplings with the presence of VLQs is 𝑔^𝐼𝐽_𝑍𝐿=𝑔𝑐_𝑊𝑇₃−𝑄𝑠²_𝑊𝛿^𝐼𝐽+𝑓_𝐿𝑔𝑐_𝑊𝑉_𝐿^{𝑡,𝑏∗,𝑞′𝐼}𝑉_𝐿^{𝑡,𝑏𝑞′𝐽},𝑔^𝐼𝐽_𝑍𝑅=𝑔𝑐_𝑊−𝑄𝑠²_𝑊𝛿^𝐼𝐽+𝑓_𝑅𝑔𝑐_𝑊𝑉_𝑅^{𝑡,𝑏∗,𝑞′𝐼}𝑉_𝑅^{𝑡,𝑏𝑞′𝐽}, (3) where 𝐼, 𝐽 run on all quarks, including VLQs, 𝑇₃=±1/2 is the weak isospin of top or bottom in the SM, and 𝑓_𝐿,𝑅={0,±1/2,±1} are parameters which depend on the VLQ representation and satisfy the relation 𝑇^𝑞′₃=𝑇₃+𝑓_𝐿=𝑓_𝑅; they are listed in Table 2 for each representation.

Table 2 

Neutral current parameters 𝑓_𝐿 and 𝑓_𝑅.

From (3) two consequences can be inferred: (1)FCNCs are present between the new state and SM quarks but can also be induced between SM quarks themselves, if mixing with light families is allowed;(2)even flavour conserving neutral currents (𝐼=𝐽) are modified by the presence of VLQs.

Constraints on FCNCs coming from a large number of observations can therefore provide strong bounds on mixing parameters.

Charged currents are modified too. The general form of 𝑊𝑞₁𝑞₂ couplings with the presence of VLQs is 𝑔^𝐼𝐽_𝑊𝐿=𝑔√2𝑉^𝐿_𝐶𝐾𝑀^𝐼𝐽=𝑔√2𝑉^𝑡_𝐿^†⋅𝛿_𝐿⋅𝑉^∼𝐿_𝐶𝐾𝑀⋅𝑉^𝑏_𝐿,𝑔^𝐼𝐽_𝑊𝑅=𝑔√2𝑉^𝑅_𝐶𝐾𝑀^𝐼𝐽=𝑔√2𝑉^𝑡_𝑅^†⋅𝛿_𝑅⋅𝑉^∼𝑅_𝐶𝐾𝑀⋅𝑉^𝑏_𝑅, (4) where 𝐼,𝐽=1,2,3(,4) and the matrices 𝑉^𝑡,𝑏 may or may not be present depending on the scenario considered. The matrices 𝛿_𝐿,𝑅 are defined as 𝛿_𝐿=1111,𝛿_𝑅=0001, (5) where the lines mean that the size of the matrices depends on the chosen scenario; in particular, 𝑔_𝑊𝑅 exists only if both an up- and down-type VLQs are present simultaneously. The matrices 𝑉^∼𝐿,𝑅_𝐶𝐾𝑀 represent the misalignment between SM quarks in the left- and right-handed sector; 𝑉^∼𝐿_𝐶𝐾𝑀 corresponds to the measured 𝐶𝐾𝑀 matrix in the absence of VLQs. Two 𝐶𝐾𝑀 matrices can thus be defined in the presence of VLQs, for the left- and right-handed sectors. If VLQs exist, the measured 𝐶𝐾𝑀 matrix corresponds to the 3×3 block (𝑉^𝐿_𝐶𝐾𝑀)^𝑖𝑗, with 𝑖,𝑗=1,3. A further consequence of the introduction of VLQs is that the measured 3×3𝐶𝐾𝑀 block is not unitary, and it is possible to check that deviations from unitary are proportional to the mixing between SM quarks and VL states.

Charged currents may also be present between the exotic states {𝑋_5/3,𝑌_−4/3} and up- or down-type quark, respectively. The couplings are 𝑔_𝑊^𝑋𝐼=𝑔√2𝑉^𝑡_𝐿^4𝐼+𝑉^𝑡_𝑅^4𝐼,𝑔_𝑊^𝑌𝐼=𝑔√2𝑉^𝑏_𝐿^4𝐼+𝑉^𝑏_𝑅^4𝐼. (6)

Finally, the couplings to the Higgs bosons can be written as 𝐶_𝑢^𝐼𝐽=1𝑣𝑚_𝑢𝑚_𝑐𝑚_𝑡𝑚^′_𝑡−𝑀𝑣𝑉^𝑡_𝐿^∗,4𝐼𝑉^𝑡_𝑅^4𝐽,𝐶_𝑑^𝐼𝐽=1𝑣𝑚_𝑑𝑚_𝑠𝑚_𝑏𝑚^′_𝑏−𝑀𝑣𝑉^𝑏_𝐿^∗,4𝐼𝑉^𝑏_𝑅^4𝐽. (7) From these expressions it can be inferred that the presence of VLQ can modify the mechanism of production and decay of the Higgs boson with respect to SM predictions.

2.2. Constraints on Model Parameters

The presence of new states induces corrections to precisely measured observables of the SM both at tree level and at loop level. Tree-level modifications are robust, in the sense that they can affect observables which in the SM are generated only at loop level and because they only depend on mixing parameters and new particles representations. Loop corrections are more model dependent; however, the presence of new heavy states can result in cancellations between diagrams which can sensibly change loop-level observables. In the following a short review of the main observables which can provide constraints on the mixing parameters of VLQs is provided, considering the most recent experimental measurements; more details on analyses and formulas can be found in [36–40] for the singlet or SM-doublet scenarios or in [35] for the non-SM doublet (𝑋_5/3𝑡^′) scenario.

2.2.1. Tree-Level Constraints

Allowing a mixing between VLQ and SM quarks means that couplings of the type 𝑉𝑞₁𝑞₂, where 𝑉=𝑊,𝑍 and 𝑞_1,2 are SM quarks, receive deviations which can be observable in experimental searches. Such deviations depend on the mixing parameters of the new states and on their representations, allowing the possibility to pose strong bounds on the coupling between VLQs and SM particles.

If the VLQs mix only with third generation SM quarks, the only affected observables are 𝑊𝑡𝑏 and 𝑍𝑏𝑏; since either the top or bottom quarks are mixed with the new states in all representations, the CC coupling 𝑊𝑡𝑏 is always affected at tree level by the presence of VLQ, while the NC coupling 𝑍𝑏𝑏 is modified at tree level only if a 𝑏^′ VLQ is present.

If the VLQs mix with lighter generations, a number of observables are affected: FCNC can contribute at tree level to SM observables that otherwise would receive only loop-level contributions. The main observables which can be modified at tree level by the presence of new VLQs are listed in the following.

Rare FCNC Top Decays

FCNC processes describing top decays in the SM and in a VLQ scenario are represented in Figure 1. Current experimental bounds are set by the CMS experiment, which has performed a study of rare top decay with an integrated luminosity of 5.0fb⁻¹ [41], finding a limit BR(𝑡→𝑍𝑞)<0.24%, whereas the SM prediction is BR(𝑡→𝑍𝑞)=𝒪(10⁻¹⁴). This limit can be translated into bounds on combinations of nondiagonal mixing matrix elements in both of the left- and right-handed sectors.

Figure 1 

Feynman diagrams for FCNC rare top decays in the SM and induced at tree level by the presence of VLQs.

𝑍𝑞𝑞 Couplings

As already stated, flavour conserving couplings are also affected by the presence of new states. The left- and right-handed couplings 𝑍𝑞𝑞 have been measured at LEP1 [42] and the strongest bounds come from the charm and bottom quarks: 𝑔^𝑐_𝑍𝐿𝑔=0.3453±0.0036,_𝑐𝑍𝑅𝑔=−0.1580±0.0051,_𝑏𝑍𝐿𝑔=−0.4182±0.00315,_𝑏𝑍𝑅=0.0962±0.0063. (8) Deviations from SM predictions can also be parametrised through the quantities: 𝑅_𝑞=Γ𝑍⟶𝑞𝑞Γ(𝑍⟶hadrons)=𝑅^SM_𝑞1+𝛿𝑅_𝑞,𝐴_𝑞=𝑔^𝑞_𝑍𝐿²−𝑔^𝑞_𝑍𝑅²𝑔^𝑞_𝑍𝐿²+𝑔^𝑞_𝑍𝑅²=𝐴^SM_𝑞1+𝛿𝐴_𝑞 (9) with 𝑞=𝑐, 𝑏 and 𝑅^SM_𝑞 and 𝐴^SM_𝑞 are the SM predictions. The observed and predicted values are [43] 𝑅_𝑐^exp𝑅=0.1721±0.0030,_SM𝑐𝑅=0.17223±0.00006,_𝑏exp𝑅=0.21629±0.00066,_SM𝑏𝐴=0.21474±0.00003,_𝑐exp𝐴=0.670±0.027,_SM𝑐=0.6680^+0.00025_−0.00038,𝐴_𝑏^exp𝐴=0.923±0.020,_SM𝑏=0.93464^+0.00004_−0.00007. (10)

Bounds on matrix elements (𝑉^𝑡,𝑏_𝐿,𝑅)^4𝑖 can be obtained evaluating the contributions induced by VLQs to the measured quantities. The contributions are at tree level only if there is mixing between the VLQ and the considered quark. The contribution to the coupling is at loop level if there is no mixing (e.g., the contribution of a 𝑡^′ singlet to 𝑍𝑏𝑏).

Meson Mixing and Decays

FCNCs induced by the presence of VLQs can play a relevant role in meson mixing and decay. Some processes which in the SM can only occur at loop level may be generated at tree level through FCNCs. Mixing parameters and branching ratios for a large number of mesons have been measured accurately, providing strong constraints on VLQ mixing parameters. The Feynman diagrams of 𝐷⁰ mixing and decay in the SM and with the contribution of VLQs are shown in Figure 2.

Figure 2 

Feynman diagrams for 𝐷0 mixing and decay at loop level in the SM (first row) and at tree level with the presence of VLQs (second row).

Meson mixing and decays have been widely studied in the literature, and an analytical description of the contributions of VLQs for specific processes is beyond the purposes of this analysis. Detailed studies for specific scenarios can be found in [35, 44–46]. It can be noticed, however, that observables in the down sector have been measured with much more precision, with respect to the up sector: the contribution of down-type VLQs with mixing to light generation can be therefore strongly constrained by bounds coming from the flavour sector.

Atomic Parity Violation

A strong bound on mixing parameters between VLQs and the first quark generation comes from measurements of the atomic parity violation, which provides information about 𝑍𝑢𝑢 and 𝑍𝑑𝑑 couplings. The weak charge of a nucleus is defined as [47] 𝑄_𝑊=2𝑐_𝑊𝑔(2𝑍+𝑁)𝑔^𝑢_𝑍𝐿+𝑔^𝑢_𝑍𝑅+(𝑍+2𝑁)𝑔^𝑑_𝑍𝐿+𝑔^𝑑_𝑍𝑅, (11) where 𝑔^𝑢,𝑑_{𝑍𝐿,𝑍𝑅} are the left- and right-handed couplings of light quarks with the 𝑍⁰ boson and 𝑍 and 𝑁 are the number of protons and neutrons in the nucleus, respectively. The most precise test on atomic parity violation is in Cesium 133Cs and Thallium 204 Tl [48]: 𝑄_𝑊¹³³Cs_exp.𝑄=−73.20±0.35,_𝑊133Cs_SM𝑄=−73.15±0.02,_𝑊204Tl_exp.𝑄=−116.4±3.6,_𝑊204Tl_SM=−116.76±0.04. (12)

Deviations on flavour conserving neutral couplings given by the contribution of VLQs, defined in (3), provide bounds on a combination of the matrix elements (𝑉^𝑡,𝑏_𝐿,𝑅)⁴¹: 𝛿𝑄_𝑊^𝑉𝐿=2(2𝑍+𝑁)𝑇^𝑡′₃−12𝑉^𝑡_𝐿⁴¹²+𝑇^𝑡′₃𝑉^𝑡_𝑅⁴¹²+(𝑍+2𝑁)𝑇^𝑏′₃+12𝑉^𝑏_𝐿⁴¹²+𝑇^𝑏′₃𝑉^𝑏_𝑅⁴¹². (13)

𝐶𝐾𝑀 Matrix

𝐶𝐾𝑀 matrix entries have been measured very precisely both at tree and loop levels. Deviations from the standard 3×3 unitary 𝑉_𝐶𝐾𝑀 have also been studied extensively in the context of new physics scenarios. The contribution of VLQs strongly depends on the scenario considered. The very presence of a 𝐶𝐾𝑀 matrix in the right-handed sector is linked to the existence of both a top and a bottom VL partners, as evident from (5). The 𝐶𝐾𝑀 matrix can also contain new phases, which can induce CP violations.

2.2.2. Loop-Level Constraints

Loop constraints are more model dependent: deviations from SM predictions may occur only if specific particles circulate in loops, but the particle content of the theory depends on which representation the VLQs belong to, and in many cases, SM quantities are not affected at all. The main observables which can be affected by VLQs at loop level are shortly described in the following.

EW Precision Tests

Regardless of the representation the VLQ belongs to, the new states induce modification at loop level to the vacuum polarizations of electroweak gauge bosons, which are parametrised by the oblique parameters 𝑆, 𝑇, and  𝑈 [49]. The impact of VLQs in the case of mixing only with third generation has been first analysed in [37], while a more recent analysis for all VLQ representations mixing with third generation is in [34]. In [50] a study for a specific scenario with the presence of both a singlet and a doublet is presented, and an analysis of the 𝑆, 𝑇, and  𝑈 parameters for the singlet and SM-doublet representations taking into account variations of the Higgs mass and emphasizing the decoupling properties of VLQs is in [51].

Rare Top Decay

VLQs may contribute at loop level to FCNC top decays which are GIM suppressed in the SM, as the decay 𝑡→𝑔𝑞 shown in Figure 3. The presence of modified couplings can be competitive with the SM diagram. The strongest bounds on 𝑡→𝑔𝑞 decay have been set by ATLAS [52] using a sample with integrated luminosity of 2.05 fb ⁻¹. The obtained branching ratios are BR𝑡⟶𝑔𝑢<5.7×10⁻⁵,BR𝑡⟶𝑔𝑐<2.7×10⁻⁴, (14) whereas the SM prediction is BR(𝑡→𝑔𝑞)=𝒪(10⁻¹⁴).

Figure 3 

Feynman diagrams for FCNC top decays into 𝑔𝑞 in the SM (left) and induced at loop level by the presence of VLQs (centre and right). In the diagrams, 𝑢𝑖=𝑢,𝑐,𝑡,𝑡′ and 𝑑𝑖=𝑑,𝑠,𝑏,𝑏′.

Flavour Physics

VLQs can also play a role in flavour physics: new states can circulate in loops together with SM particles, and even small corrections can spoil cancellations within loop diagrams, producing observable effects. Such phenomena can be particularly relevant for meson mixing, especially if VLQs belong to a representation for which tree-level diagrams such as those of Figure 2 are not allowed. A 𝑡^′ can contribute to the mixing of mesons in the down sector, as in Figure 4, and if it belongs to a singlet or non-SM doublet representation, this is the only contribution of the new state to the mixing. Analogous considerations can be done for the other VLQs.

Figure 4 

Feynman diagrams for 𝐾0 mixing with the presence of a VLQ 𝑡′ in the loops.

VLQ contributions to meson mixing at loop level are strongly model dependent; a general analysis of their contribution is beyond the aims of this study. Detailed computations in specific models are present in the literature, though. In [53] the role of a VL top singlet, mixing dominantly with the top quark, in the rare decays 𝐾→𝜋𝜈𝜈, 𝐵→𝜋(𝐾)𝜈𝜈 and 𝐵_𝑠,𝑑→𝜇⁺𝜇⁻ is considered, finding corrections from 20% for 𝐾 and 𝐵 rare decays up to 50% for 𝐵_𝑠,𝑑 decays. Analogous conclusions have been obtained in [35], where corrections to the Δ𝐹=2 mixings in the 𝐾⁰ and 𝐵⁰ sectors given by the presence of a 𝑡^′ in the non-SM doublet with mixing to all quark families have been considered, finding sizable contributions, up to 60%, only for the phase of the 𝐵⁰_𝑠−𝐵⁰_𝑠 mixing.

3. Past and Current Searches

Various searches of new heavy states have been undertaken both at Tevatron and at the LHC, though no evidence for the existence of other quarks, beside those of the SM, has been obtained. Direct bounds on heavy chiral quarks can be interpreted as bound on VLQs, but it must be stressed that decay channels of VLQs are different from decay channels of heavy chiral quarks. For VLQs charged and neutral currents can have similar branching ratios; therefore searches performed with specific assumptions on the heavy state decay channel can give a rough idea of the bounds on VLQ mass, once rescaled with the actual branching ratios in the specific channel. In the following sections an overview will be given of all available searches of heavy quarks at Tevatron and at the LHC, both chiral and vector-like, focusing on the assumptions that have been made to obtain the bounds on the heavy quark masses. Searches of chiral quarks have been included only for reference purpose: a reinterpretation of bounds considering VLQ branching ratios is beyond the scope of this paper, but limits coming from searches of chiral quarks can only apply to VLQ scenarios only after appropriate rescaling. More details on single searches (kinematic cuts, detector parameters, etc.) can be found in the original publications.

3.1. Tevatron

The studies refer to the Tevatron Run II with a center of mass energy of 1.96 TeV. The bounds are presented for each experiment with increasing integrated luminosity.

3.1.1. CDF @ 1.06fb⁻¹

In [54], a search for 𝑏^′ pair production is performed. The 𝑏^′ is expected to decay 100% in 𝑍𝑏 and one 𝑍 is then required to decay leptonically. The analysis select events with one reconstructed 𝑍 and ≥3 jets. The obtained bound is 𝑚_𝑏′>268GeVat95%C.L.,BR𝑏^′⟶𝑍𝑏=100%. (15)

3.1.2. CDF @ 2.7fb⁻¹

In [55], a search for pair production of a heavy quark 𝑄 which promptly decays 100% into 𝑊𝑡 is performed. The signal considered is ^{𝑙±𝑙±𝑏𝑗}/^𝐸_𝑇. The results have been interpreted in terms of bounds on 𝑏^′ mass or on the mass of an exotic 𝑇_5/3 state (this bound implies the existence of a further heavy 𝐵 quark): 𝑚_𝑏′,𝑚_𝐵>338GeVor𝑚_𝑇5/3>365GeVat95%C.L.,BR𝑄⟶𝑊^±𝑡=100%. (16)

3.1.3. CDF @ 4.8fb⁻¹

For this integrated luminosity two analyses are available.

In [56], a search for pair production of 𝑏^′ decaying promptly to 𝑊𝑡 is performed. One 𝑊 is then required to decay leptonically and the analysis looks for events with one lepton (𝑒 or 𝜇), ≥5 jets (of which at least one b-jet), and missing transverse energy. The obtained bound is 𝑚_𝑏′>372GeVat95%C.L.,BR𝑏^′⟶𝑊𝑡=100%. (17)

In [57], a search for pair production of a heavy particle 𝑇^′ decaying to 𝑡𝑋, where 𝑋 is an invisible (DM) particle is performed. The analysis considers the lepton + jets channel, requiring one of the 𝑊s coming from the tops to decay leptonically. The search is analogous to top pair production, but for the presence of missing transverse momentum. Bounds are given for the combination of 𝑇^′ and 𝑋 masses, and in particular, the analysis excludes the presence of a 𝑇^′ with 𝑚_𝑇′≤360 GeV for 𝑚_𝑋≤100 GeV.

3.1.4. CDF @ 5.6fb⁻¹

In [58], a search for 𝑡^′ pair production is performed. The 𝑡^′ is expected to decay 100% in 𝑊𝑞, where 𝑞 can be a light quark or a bottom quark, and one 𝑊 is then required to decay leptonically. The signal under consideration is therefore 𝑡^′𝑡^′→𝑊𝑞𝑊𝑞→𝑙𝜈𝑞𝑞𝑞𝑞. This analysis considers events with one high-𝑝_𝑇 lepton (𝑒 or 𝜇), large missing transverse energy, and ≥4 jets; for the 𝑡→𝑊𝑏 search at least one b-jet must be identified. The obtained bound is 𝑚_𝑡′>358GeVat95%C.L.,BR𝑡^′𝑚⟶𝑊𝑏=100%,_𝑡′>340GeVat95%C.L.,BR𝑡^′⟶𝑊𝑞=100%. (18)

3.1.5. CDF @ 5.7fb⁻¹

For this integrated luminosity two analyses are available.

In [59], a search for pair production of a heavy particle 𝑇^′ decaying to 𝑡𝑋, where 𝑋 is an invisible (DM) particle is performed. The search considers events in the full hadronic channel, requiring 5≤ jets ≤10 and missing transverse energy. Bounds are given for the combination of 𝑇^′ and 𝑋 masses, and in particular, the analysis excludes the presence of a 𝑇^′ with 𝑚_𝑇′≤400 GeV for 𝑚_𝑋≤70 GeV.

In [60], a search for single production of heavy quarks is performed. The heavy quarks are expected to decay 100% in 𝑊𝑞, where 𝑞 is an SM quark of the first generation. The signal event has the topology 𝑊+2𝑗, where the 𝑊 is required to decay leptonically. Due to the fact that single production is model dependent, the bounds on the cross section and couplings of the heavy quarks with SM quarks are given for different masses of the heavy quarks, ranging from 300 GeV to 600 GeV.

3.1.6. D0 @ 5.3fb⁻¹

In [61] a search for 𝑡^′ pair production is performed. The 𝑡^′ is supposed to decay 100% to 𝑊𝑞, where 𝑞 is a light quark. The analysis selects final states with one isolated lepton, ≥4 jets, and missing transverse energy, corresponding to one 𝑊 decaying leptonically and the other hadronically. Combining the 𝑒+jets and 𝜇+jets channels, the obtained bound is 𝑚_𝑡′>285GeVat95%C.L.,BR𝑡^′⟶𝑊𝑞=100%. (19)

3.1.7. D0 @ 5.4fb⁻¹

In [62] a search for single production of VLQs is performed. A specific model is considered [63], in which there are two degenerate VL doublets, with hypercharge 7/6 and 1/6, which interact only with the first generation of SM quarks. The analysis searches for final states with either a 𝑊 or 𝑍 boson and two jets. One jet comes from the VLQ decay and the other is produced in association with the VLQ. The gauge boson is then required to decay leptonically (𝑒 or 𝜇) and events with exactly one lepton (case of 𝑊) or exactly two leptons (case of 𝑍) and ≥2 jets are selected. Results are given for different choices of the coupling parameters and assumptions on BRs: 𝑚_𝑏′𝑏>693GeVat95%C.L.BR^′𝑚⟶𝑊𝑞=100%_𝑡′𝑡>551GeVat95%C.L.BR^′𝑚⟶𝑍𝑞=100%nocouplingwithdownquark_𝑡′𝑡>403GeVat95%C.L.BR^′𝑚⟶𝑊𝑞=100%_𝑏′𝑏>430GeVat95%C.L.BR^′⟶𝑍𝑞=100%nocouplingwithupquark. (20)

3.2. LHC

The studies have been performed for a center of mass energy of 7 TeV. The bounds are presented for each experiment with increasing integrated luminosity.

3.2.1. ATLAS @ 1.04fb⁻¹

For this integrated luminosity several analyses are available.

In [64], a search for pair production of a heavy particle 𝑇 decaying to 𝑡𝐴₀, where 𝐴₀ is an invisible (DM) particle is performed. The search is performed in the 𝑡𝑡+𝑀𝐸𝑇 channel, where one of the 𝑊s coming from top decays leptonically and the other hadronically. The final state analysed contains one isolated lepton with large 𝑝_𝑇, ≥4 jets and missing transverse energy. Bounds are given for combinations of 𝑇 and 𝐴₀ masses, excluding heavy quarks up to 𝑀_𝑇=420 GeV for stable neutral states up to 𝑀_𝐴0=140 GeV.

In [65] a search for pair production of 𝑡^′ with subsequent decay into 𝑊𝑏 is performed. One of the 𝑊s is then required to decay leptonically. This search is conducted on final states containing one isolated lepton (𝑒 or 𝜇) with high transverse momentum, high missing transverse momentum, and ≥3 jets. The obtained bound is 𝑚_𝑡′>404GeVat95%C.L.,BR𝑡^′⟶𝑊𝑏=100%. (21)

In [66] a search for pair production of a fourth generation quark 𝑄 decaying 100% in 𝑊𝑞, where 𝑞=𝑢,𝑑,𝑐,𝑠,and𝑏 and with subsequent decay of both 𝑊𝑠 into leptons is performed. The analysis considers a final state with 2 opposite-sign leptons, ≥2 jets, and missing energy. The obtained bound on the new state, applicable to all heavy quarks decaying to 𝑊𝑞 is 𝑚_𝑄>350GeVat95%C.L.,BR𝑄⟶𝑊𝑞=100%. (22)

In [67] a search for pair production of 𝑏^′ decaying 100% to 𝑊𝑡 is performed. Two of the 4 𝑊s after top decay are then required to decay leptonically and the analysis considers final states containing two isolated same-sign leptons, ≥2 jets, and large missing transverse momentum. The obtained bound is 𝑚_𝑏′>450GeVat95%C.L.,BR𝑏^′⟶𝑊𝑡=100%. (23)

In [68] a search for pair production of 𝑏^′ decaying 100% to 𝑊𝑡 is performed. This search is very similar to [67], but in this case only one of the 4 𝑊s after top decay is then required to decay leptonically and the analysis considers final states containing exactly one lepton, ≥6 jets, and large missing transverse momentum. The bound is however very close to the one obtained in [67]: 𝑚_𝑏′>480GeVat95%C.L.,BR𝑏^′⟶𝑊𝑡=100%. (24)

This search has been reinterpreted in [69] to compute bounds on a VL top partner mixing only with the third SM generation: the obtained bounds are 𝑚_𝑇>415 GeV or 𝑚_𝑇>557 GeV for BR(𝑇→𝑊𝑏)=0% or BR(𝑇→𝑊𝑏)=100%, respectively.

3.2.2. ATLAS @ 2fb⁻¹

In [70] a search for pair production of 𝑏^′ is performed. At least one 𝑏^′ is then required to decay into 𝑍𝑏, while the other can decay either to 𝑍𝑏 or 𝑊𝑡. A parameter which describes the fraction of events with at least one 𝑏^′ decaying to 𝑍𝑏 depending on the BR is defined: 𝛽=2×BR(𝑏^′→𝑍𝑏)−BR(𝑏^′→𝑍𝑏)². The case 𝛽=1 corresponds to 100% decay into 𝑍𝑏. The parameter 𝛽 is also computed for the case of a VL 𝑏^′ mixing to third generation in the mass range 𝑚_𝑏′=200−700 GeV, obtaining 𝛽=0.9−0.5. The final states considered in this search contain ≥2 opposite-sign leptons and one b-tagged jet. Limits are given both for 100% decay assumption and for a specific VL scenario: 𝑚_𝑏′>400GeVat95%C.L.,BR𝑏^′𝑚⟶𝑍𝑏=100%,_𝑏′>358GeVat95%C.L.,forVLsingletmixingonlywiththirdgeneration. (25)

3.2.3. ATLAS @ 4.64fb⁻¹

In [71] a search for single production of VLQs coupling only to light generations is presented. The final state consists in a reconstructed vector boson (𝑊 or 𝑍) decaying leptonically and 2 jets. The obtained bounds (which depend on the assumption on the VLQ couplings) are 𝑚_𝑏′>1120GeVat95%C.L.,BR𝑏^′𝑚⟶𝑊𝑞=100%,_𝑋5/3>1420GeVat95%C.L.,BR𝑋_5/3𝑚⟶𝑊𝑞=100%,_𝑡′>1080GeVat95%C.L.,BR𝑡^′⟶𝑍𝑡=100%. (26)

3.2.4. ATLAS @ 4.7fb⁻¹

In [72], a search for pair production of a heavy particle 𝑇 decaying to 𝑡𝐴₀, where 𝐴₀ is an invisible (DM) particle is performed. The search is performed in the 𝑡𝑡+𝑀𝐸𝑇 channel, where both of the 𝑊s coming from top decays leptonically. The final state considered in the analysis contains two leptons and missing transverse energy. Bounds are given for combinations of 𝑇 and 𝐴₀ masses, excluding heavy quarks up with masses 380GeV<𝑀_𝑇<420GeV for stable neutral states with masses below 100 GeV.

In [73] a search for pair production of 𝑡^′ is performed. Depending on its branching ratios, the 𝑡^′ is assumed either to belong to a chiral fourth generation or to be vector-like. The search looks for final states containing one isolated lepton with high 𝑝_𝑇, at least 3 jets and large missing energy. Results are given either assuming BR(𝑡^′→𝑊𝑏)=100%, corresponding to the fourth generation scenario or considering BR(𝑡^′→𝑊𝑏) and BR(𝑡^′→𝐻𝑡) as independent parameters, with the relation BR(𝑡^′→𝑍𝑡)=1−BR(𝑡^′→𝑊𝑏)−BR(𝑡^′→𝐻𝑡). The obtained bounds are 𝑚_𝑡′>656GeVat95%C.L.,BR𝑡^′𝑚⟶𝑊𝑏=100%,_𝑡′𝑡>500GeVat95%C.L.,forVLsingletwithBR^′𝑡⟶𝑊𝑏=50%,BR^′⟶𝐻𝑡=33%, (27) while the search is not sensitive to vector-like doublet scenarios.

In [74] a search in the same-sign dilepton channel is interpreted in terms of pair production of 𝑏^′ and single or pair production of the exotic 𝑋_5/3. Besides the 2 same-sign leptons, the final state is required to contain at least 2 jets, with at least one b-jet, large missing energy, and large 𝐻_𝑇. The bounds considering only pair production processes are 𝑚_{𝑏′,𝑋5/3}𝑏>670GeVat95%C.L.,BR^′,𝑋_5/3⟶𝑊𝑡=100%. (28) While adding the single production of 𝑋_5/3 with different assumptions on its coupling with 𝑊𝑡, the bounds are: 𝑚_𝑋5/3𝑋>680−700GeVat95%C.L.,BR_5/3⟶𝑊𝑡=100%. (29)

3.2.5. CMS @ 1.14fb⁻¹

In [75] a search for pair production of a VL 𝑡^′ quark is performed. The 𝑡^′ is assumed to decay 100% into 𝑍𝑡, whereas the decay into 𝑡𝐻 is supposed to be kinematically forbidden. The final state must contain ≥3 leptons and ≥2 jets. The obtained bound is 𝑚_𝑡′>475GeVat95%C.L.,BR𝑡^′⟶𝑍𝑡=100%. (30)

3.2.6. CMS @ 4.9fb⁻¹

In [76] a search for 𝑏^′ pair production is performed. The 𝑏^′ is then supposed to decay exclusively to 𝑊𝑡. The analysis searches for final states containing ≥2 electrons or at least one muon and ≥4 (≥2) jets for same-sign dilepton (trilepton) events. The obtained bound is 𝑚_𝑏′>611GeVat95%C.L.,BR𝑏^′⟶𝑊𝑡=100%. (31)

In [77] a search for 𝑏^′ pair production with subsequent 𝑏^′→𝑍𝑏 decay is performed. The decay branching ratio is assumed to be 100% and the search focuses on final states with a pair of opposite charged leptons (to reconstruct the 𝑍 boson) and at least one 𝑏-tagged jet. The obtained bound is 𝑚_𝑏′>550GeVat95%C.L.,BR𝑏^′⟶𝑍𝑏=100%. (32)

3.2.7. CMS @ 5fb⁻¹

In [78] a search for pair production of 𝑡^′ is performed. The 𝑡^′ decays exclusively to 𝑊𝑏 and the 𝑊 bosons are both required to decay leptonically. Events are required to have two opposite-sign leptons, ≥2 jets, of which exactly two come from bottom fragmentation. The obtained bound is 𝑚_𝑡′>557GeVat95%C.L.,BR𝑡^′⟶𝑊𝑏=100%. (33)

In [79] a search for pair production of exotic 𝑋_5/3 is performed. The analysis considers final states composed of exactly 2 same-sign leptons, at least 4 jets, and large 𝐻_𝑇. The obtained bound is 𝑚_𝑋5/3>645GeVat95%C.L.,BR𝑋_5/3⟶𝑊𝑡=100%, (34)

Two searches have been performed on the same final state, containing a single isolated lepton (𝑒 or 𝜇), large missing transverse energy, and ≥4 jets, one of which originates from the fragmentation of a bottom quark, though considering different kinematical cuts. In [80] a search for 𝑡^′ pair production is performed, where the 𝑡^′ is supposed to decay 100% to 𝑊𝑏, while in [81] a search of pair production of heavy quarks decaying either to 𝑍𝑡 or 𝑊𝑡 is presented. The combined bounds are 𝑚_𝑡′>560GeVat95%C.L.,BR𝑡^′𝑚⟶𝑊𝑏=100%,_𝑡′>625GeVat95%C.L.,BR𝑡^′𝑚⟶𝑍𝑡=100%,_𝑏′>675GeVat95%C.L.,BR𝑏^′⟶𝑊𝑡=100%. (35)

4. Signatures of Vector-Like Quarks at LHC

4.1. A General Picture

The identification of the channels which may lead to the discovery of VLQs at the LHC depends on the scenario under consideration. In general, processes dominated by QCD, such as pair production, have the advantage of being model independent, while single production is driven by model-dependent processes. However, pair production suffers from a larger phase-space suppression with respect to single production, and if the VLQ mass is large enough, single production dominates over pair production. The VLQ mass corresponding to the equivalence between pair and single production cross sections depends on the specific model. Excluding purely QCD processes, the production of VLQs is related to the interaction of the new states with SM particles. If VLQs interact with SM quarks through Yukawa couplings, a mixing is induced between quarks of different families, giving rise to FCNCs. On the other hand, in scenarios such as minimal universal extradimensions, the KK-odd VLQs do not mix with SM quarks, and therefore they can only be produced in pairs or together with another KK-odd state.

The Feynman diagrams for pair and single production of VLQs are shown in Figures 5 and 6.

Figure 5 

Feynman diagrams for pair production of a generic VLQ. Above the dominant and model-independent QCD contributions, below the subdominant and model-dependent EW contributions. Arrows on fermion lines have been removed to account for both particles and antiparticles, when necessary. Notice the possibility to have FCNCs between SM quarks in the 𝑉 and 𝑆 s-channel diagram, which is peculiar to VL scenarios.

Figure 6 

Feynman diagrams for single production of a generic VLQ. VLQs can interact with SM quarks both through charged currents and neutral currents, allowing FCNCs also within SM states in diagrams with 𝑞𝑖−𝑞𝑗−{𝑉,𝑆} interactions. Arrows on fermion lines have been removed to account for both particles and antiparticles, when necessary. Notice that not all diagrams are allowed for a specific VL quark (e.g., neutral currents are not allowed for quarks with exotic electric charges).

The decay channels of VLQs are model dependent too, and this is the most relevant problem when trying to interpret experimental bounds on new heavy quarks, due to the fact that these bounds are generally obtained under strong assumptions on the branching ratios of the new states. In the following, the decay channels for each VLQ will be analysed to find which final states are possible if VLQs are produced at the LHC. Of course this analysis cannot be completely general, because VLQ couplings are model dependent. VLQs are therefore assumed to interact with SM quarks of all flavours through Yukawa couplings. This is the minimal scenario of new physics with VLQs, in which they are the only new states besides SM particles. Next-to-minimal scenarios with the addition of more than one VLQ representation or in which VLQs interact with SM particles and another invisible particle (as in UED scenarios) will not be considered.

4.1.1. 𝑡^′ and 𝑏^′

Being partners of SM quarks, the {𝑡^′,𝑏^′} can be produced exactly in the same way as any SM quark, but for the presence of FCNC channels. On the other hand, depending on their interactions with other SM quarks and on the representation they belongs to, the {𝑡^′,𝑏^′} has different decay channels: 𝑡^′⟶𝑑_𝑖𝑊⁺,𝑋_5/3𝑊⁻with𝑑_𝑖=𝑑,𝑠,𝑏,𝑏^′𝑢𝐶𝐶,_𝑖𝑍,𝑢_𝑖𝐻with𝑢_𝑖𝑏=𝑢,𝑐,𝑡𝑁𝐶,_′⟶𝑢_𝑖𝑊⁻,𝑌_−4/3𝑊⁺with𝑢_𝑖=𝑢,𝑐,𝑡,𝑡^′𝑑𝐶𝐶,_𝑖𝑍,𝑑_𝑖𝐻with𝑑_𝑖=𝑑,𝑠,𝑏𝑁𝐶, (36) of course not all decays may be kinematically allowed for a given scenario but will depend on masses and couplings of the VLQs under consideration. A key point which has not always been considered in experimental searches of top or bottom partners is the possibility for VLQs to mix with all SM families: VLQs can decay in different channels, with branching ratios which depend on the relative strength of the mixing between VLQs and SM quarks. The variation of the BRs of 𝑡^′ decay into 𝑉𝑞 is shown in Figure 7, which refers to a scenario in which the 𝑡^′ belongs to a non-SM doublet (𝑋_5/3,𝑡^′), analysed in detail in [35]. The assumption that the 𝑡^′ mixes only with the top quark is therefore very strong from an experimental point of view: cuts optimized for scenarios with BR(𝑡^′→𝑍𝑡)=100% or BR(𝑡^′→𝑊𝑏)=100% may completely reject events coming from different channels, thus overestimating the bounds.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 7 

Branching ratios for 𝑡′ (first column) and 𝑋5/3 (second column) belonging to the non-SM doublet (𝑋5/3,𝑡′) for different mixing hypotheses. From top to bottom: mixing only with top; mixing with top and charm; mixing only with charm. The mixing parameters have been saturated according to the bounds obtained in [35]. Notice that the BR of 𝑋5/3 in the case of mixing only with top or charm is not identically 1: this is due to the presence of three-body decays, which have not been included in the plot.

Limiting ourselves to the production of two particle states, it is possible to identify all the allowed channels for {𝑡^′,𝑏^′} production and decay. The full list is shown in Table 3, where the channels are ordered in terms of the possible charge combinations allowed by a proton-proton interaction.

Table 3 

Production and decay channels for 𝑡^′ and 𝑏^′. Only configurations with 𝑄≥0 have been shown for simplicity. Throughout the table, 𝑢_𝑖=𝑢,𝑐,𝑡(,𝑡^′) and 𝑑_𝑖=𝑑,𝑠,𝑏(,𝑏^′).

Even if the list is limited to two particle intermediate states, it is still possible to notice that if the {𝑡^′,𝑏^′} is heavy enough to decay into a top quark or to other VLQs, there are many combinations which can result in multileptonic final states, allowing an easy identification of a {𝑡^′,𝑏^′} signal against the SM background. The multileptonic final states can be also enhanced by the presence of neutral currents, which are forbidden for a sequential chiral fourth family.

4.1.2. 𝑋_5/3 and 𝑌_−4/3

VLQs with exotic charges can only interact with other states through charged currents. They can be produced singly or in pairs, but the allowed diagrams and decay channels are limited, with respect to the {𝑡^′,𝑏^′} case, due to the smaller number of interactions. VLQs with exotic charges always belong to multiplets which contain also one SM VL partner (non-SM doublets) or two SM VL partners (triplets); therefore they can be produced together with a 𝑡^′ or 𝑏^′. All the possible combinations are listed in Table 4.

Table 4 

Production and decay channels for 𝑋_5/3 and 𝑌_−4/3. Only configurations with Q ≥ 0 have been shown for simplicity. Throughout the table, 𝑢_𝑖=𝑢,𝑐,𝑡(,𝑡^′) and 𝑑_𝑖=𝑑,𝑠,𝑏(,𝑏^′).

The allowed decays for the 𝑋_5/3,𝑌_−4/3 VLQs are 𝑋_5/3⟶𝑢_𝑖𝑊⁺with𝑢_𝑖=𝑢,𝑐,𝑡,𝑡^′,𝑌_−4/3⟶𝑑_𝑖𝑊⁻with𝑑_𝑖=𝑑,𝑠,𝑏,𝑏^′. (37) Again, not all possibilities may be allowed for a given scenario, especially decays into 𝑡^′ and 𝑏^′, which depend on the mass gaps inside the multiplets. The variation of the branching ratios for an 𝑋_5/3 belonging to the non-SM doublet (𝑋_5/3,𝑡^′)  is shown in Figure 7. It is still possible to notice that assuming mixing only with third family can be a quite strong assumption, which may lead to the misinterpretation of experimental results and overestimating mass bounds.

4.2. Results from Specific Phenomenological Analyses

LHC signatures of VLQs have been analysed in many phenomenological studies, both in specific scenarios and in model-independent ways. In most analyses it is commonly assumed that VLQs mix only with third generation quarks, while some analyses consider the general mixing case. If VLQs mix mostly with third generation quarks, a reinterpretation of many experimental searches for top or bottom partners, even under explicit chiral assumptions, is possible, since the favourite channels involve the presence of top quark decay products, which can be obtained also in VLQs decays. The scenario in which the VLQs do not mix with at all with the third generation, but only with lighter generations, has also been considered, and its main advantage is the presence of energetic jets in the final state, due to decays of the type 𝑄→𝑉𝑗. This scenario has been searched experimentally, and therefore predictions can be directly compared with data. Finally, for scenarios with general mixing, a reinterpretation of experimental bounds is not straightforward since acceptances for different channels may differ significantly.

In the following, a brief overview of phenomenological analyses is presented. The large amount of studies in the literature makes it impossible to analyse all of them in a single review; therefore a selection must be made, considering only the following(i)studies which have been published on peer-reviewed journals at the time of submission of the present paper; (ii)analyses of minimal scenarios, that is, signatures coming from single or pair production of VLQs, which then directly decay into SM states. This choice has been made to keep the overview as model independent as possible and to be as close as possible to the minimal framework described in Section 2; furthermore, model-independent predictions can be easily compared with current experimental searches. The analyses are presented in chronological order; descriptions of the main assumptions on VLQ properties and of the proposed discovery channels are provided, but more details can be found in the original publications.

In [82] the pair production of 𝑋_5/3 and of 𝑏^′ is considered. The heavy states are then required to decay 100% into 𝑊^±𝑡, depending on the case. The analysis then focuses on signatures with same-sign dileptons in the final state; that is, 𝑝𝑝⟶𝑋_5/3𝑋_5/3,𝑏^′𝑏^′⟶𝑙^±𝜈𝑙^±𝜈𝑏𝑏𝑞𝑞𝑞𝑞. (38) The detailed analysis shows how the same-sign dilepton channel can be extremely promising for the discovery of heavy states which mainly mix to third family quarks. The same-sign dilepton channel has been considered also in [83, 84], where methods for the reconstruction of the 𝑋_5/3 mass are proposed.

In [85] a thorough systematic analysis of signatures of all possible VLQs states, mixing mainly with third generation, is undertaken. All singlet and doublet scenarios are analysed and benchmark points for mixing parameters are considered. Final states with different number of leptons are combined to obtain discovery potentials for each state at LHC with a center of mass energy of 14 TeV.

In [86] the single production of VL quarks through the process 𝑞𝑞−−→^′𝑉∗𝑞₁𝑄 with 𝑉=𝑍,𝑊 is considered for LHC at both 7 and 14 TeV. The analysis is performed factorizing out the model dependence in the coupling parameters and considering 𝑄=𝑋_5/3,𝑡^′,𝑏^′,𝑌_−4/3. The VLQs are assumed to decay through CC and NC to 𝑉𝑗, but decays to ℎ𝑗 are not considered, and to reduce the background, leptonic decays of the gauge bosons are considered. The considered processes are therefore ^{𝑙𝑝𝑝⟶𝑄⟶𝑉𝑗𝑗with𝑉⟶±𝑙∓,𝑙±}/^𝐸_𝑇^,/^𝐸_𝑇^. (39) Different scenarios, with constraints on coupling parameters, are considered. The analysis shows that despite that in the first 7 TeV run with 1 fb⁻¹ luminosity the reach of the LHC is similar to the Tevatron reach with a 10 fb⁻¹ luminosity, the reach greatly improves in the long run configuration with √𝑠=14 TeV and 𝐿=100 fb⁻¹, with the possibility to probe masses as high as ∼3.7 TeV.

In [87] the pair and single productions of 𝑏^′ at the LHC with a center of mass energy of 14 TeV are studied, focusing on 𝑍𝑏 and 𝑏𝐻 decays with leptonic and semileptonic final states. The needed luminosity for discovery of a 𝑏^′ is plotted against the 𝑏^′ mass up to 1250 GeV.

In [35] signatures at LHC with √𝑠=7 TeV for single production of a 𝑡^′ belonging to a non-SM VLQ doublet {𝑋_5/3,𝑡^′} are studied. The processes are studied for 𝑚_𝑡′=350−500 GeV, a range around the value for which single production becomes dominant over pair production. FCNCs decays to 𝑍𝑡 and 𝑡ℎ are considered, but since the 𝑡^′ is allowed to mix with all SM families, relations between BRs for different masses have been considered. The analysis focuses on the following signatures: 𝑝𝑝⟶𝑡^′⟶𝑍𝑡𝑗with𝑍⟶𝑙⁺𝑙⁻,𝜈𝑡𝜈,𝑗𝑗,𝑝𝑝⟶^′⟶𝑡ℎ𝑗withℎ⟶𝑏𝑏. (40) Also, a signature under the hypothesis of no mixing with third family is considered; namely, 𝑝𝑝⟶𝑡^′⟶𝑗ℎ𝑗withℎ⟶𝑏𝑏. (41) The analysis shows that such signatures are difficult to observe at LHC with a center of mass energy of 7 TeV, since SM backgrounds have very similar kinematical features.

In [88] signatures at LHC with √𝑠=14 TeV for pair production of a VL singlet labelled 𝑡₂, in a model which contains also an SM-like VL doublet, are studied. One of the 𝑡₂ is required to decay to 𝑡ℎ, while the other is free to decay to 𝑍𝑡, 𝑡ℎ, or 𝑊𝑏. Depending on the considered Higgs mass (125 or >200 GeV), Higgs decays ℎ→𝛾𝛾 or ℎ→𝑍𝑍→4𝑙 are considered. The processes under consideration are therefore 𝑝𝑝⟶𝑡₂𝑡₂⟶𝑡ℎ𝑡ℎ𝑡ℎ𝑍𝑡withℎ⟶𝛾𝛾orℎ⟶𝑍𝑍⟶4𝑙.𝑡ℎ𝑊𝑏 (42) The analysis shows that these channels can be observed at 14 TeV for a luminosity between ~20 fb⁻¹ and ~200 fb⁻¹ for 120GeV≲𝑚_ℎ≲550GeV, and the definition of new variables is proposed, to allow the estimation of the heavy top mass.

In [89] processes of production and decay of a singlet top partner are considered for LHC with a center of mass energy of 8 TeV and integrated luminosity of 15 fb⁻¹. The study focuses on the 𝑡𝐻 decay channel, which is enhanced by the presence of a dimension 5 operator in the effective Lagrangian. Considering final states with multiple b-jets, bounds on the top partner mass and mixing angles parameter space are provided.

5. Contribution of Vector-Like Quarks to Other Processes at LHC

5.1. Higgs Production and Decay

VLQs can contribute to processes of Higgs production and decay: 𝑡^′ and 𝑏^′ quarks mix with SM states through Yukawa couplings, and therefore they can circulate in the loops of gluon fusion processes and ℎ→𝛾𝛾 decays, as depicted in Figure 8. In minimal pictures, adding only one VLQ representation, exotic VLQs do not play any role at LO but can provide corrections to these processes at higher orders. Many studies have dealt with the role of VLQs in Higgs production processes [35, 90], finding that adding just one VL multiplet, the corrections to gluon fusion and 𝛾𝛾 decays are always negligibly small. The same result applies also at NNLO [51].

Figure 8 

Feynman diagrams for processes with VLQs contributions. From left to right: Higgs production through gluon fusion, Higgs to two-photon decay, Higgs pair production, and FCNC same-sign top production.

Other studies have considered Higgs signatures given by VLQ decays, which can be considered together with standard Higgs production and decay channels. In [91] processes of Higgs production driven by the decay of a 𝑡^′ singlet are considered. The 𝑡^′ is allowed to mix only with the top quark and the analysis focuses on pair production at 14 TeV, where one of the two top partners decays to 𝑡ℎ and the other into 𝑍𝑡 or 𝑊𝑏. The search is then conducted looking for boosted Higgs bosons which then decay into 𝑏𝑏. Though lacking a realistic detector simulation, the analysis describes a scenario in which the Higgs signal can be enhanced by the presence of 𝑡^′ in the mass range 400–800 GeV. In this framework, the Higgs can thus be observed with a 5σ significance at a luminosity of 10 fb⁻¹.

In [92] corrections from new physics to the trilinear Higgs coupling and to Higgs pair production are studied. In the case of VLQs, an example with a singlet top partner is considered: the analysis shows that the contribution of VLQs is small, of the order of few percents, and this is due to decoupling properties of the heavy state.

5.2. Same-Sign Top Production

The process of production of same-sign tops at the LHC can be driven by the presence of VLQs due to the possibility of FCNCs. The Feynman diagram is shown in Figure 8. The analysis in [45] shows that, in a Littlest Higgs scenario with one top-partner VL quark, the cross section is however very small, around 0.01 fb at LHC with a center of mass energy of 14 TeV, below the experimental sensitivity.

6. Conclusion

The aim of this paper has been to provide a broad, though necessarily incomplete, overview on the searches and perspectives of heavy vector-like quarks at the LHC. Vector-like quarks are predicted by many models of new physics. Recent observations strongly point towards the existence of the Higgs boson, thus completing the SM picture: among the next steps of the LHC, there will be therefore the search for new BSM states. A minimal extension of the SM with the presence of vector-like quarks has a huge and interesting range of possible signatures, some of which have already been tested both at Tevatron and at the LHC. Current bounds on the mass of vector-like quarks are around 400–600 GeV, depending on assumptions on their mixing and decay channels. If vector-like quarks mix with all SM families, many searches must be reinterpreted while dedicated, optimized searches may be in order. A complete list of possible final states for production of any possible vector-like quark in the minimal picture has been provided, together with a short description of the main phenomenological analyses present in the literature. The discovery of a new fermionic state would certainly be a major and exciting event at the LHC; thus a detailed understanding of its properties, if it turns out to be vector-like, will be extremely useful for future analyses.

Acknowledgments

The research of Y. Okada is supported in part by the Grant-in-Aid for Science Research, Japan Society for the Promotion of Science (JSPS), no. 20244037 and no. 22244031.