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
A fermion is defined to be vector-like if its left- and right-handed chiralities belong to the same representation of the symmetry group
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: 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 [ extra dimensions: excited partners of SM quarks belonging to heavier tiers of universal extra-dimensional scenarios are vector-like; gauging of the flavour group: VL fermions are required for anomaly cancellation and can play a role in the mechanisms of quark mass generation [ little Higgs models: VL states appear as partners of SM fermions in larger representations of the symmetry group [ 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 [
VLQs can also appear in models which try to explain measured asymmetries in different processes: in [ the forward-backward asymmetry
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
Some of the results reported here were published in [
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
Allowed representations for VLQs, with quantum numbers under
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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
Neutral current parameters
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From ( 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; even flavour conserving neutral currents (
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
Charged currents may also be present between the exotic states
Finally, the couplings to the Higgs bosons can be written as
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 [
Allowing a mixing between VLQ and SM quarks means that couplings of the type
If the VLQs mix only with third generation SM quarks, the only affected observables are
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.
FCNC processes describing top decays in the SM and in a VLQ scenario are represented in Figure
Feynman diagrams for FCNC rare top decays in the SM and induced at tree level by the presence of VLQs.
As already stated, flavour conserving couplings are also affected by the presence of new states. The left- and right-handed couplings
Bounds on matrix elements
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
Feynman diagrams for
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 [
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
Deviations on flavour conserving neutral couplings given by the contribution of VLQs, defined in (
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.
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
VLQs may contribute at loop level to FCNC top decays which are GIM suppressed in the SM, as the decay
Feynman diagrams for FCNC top decays into
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
Feynman diagrams for
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 [
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.
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.
In [
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For this integrated luminosity two analyses are available.
In [
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For this integrated luminosity two analyses are available.
In [
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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.
For this integrated luminosity several analyses are available.
In [
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This search has been reinterpreted in [
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Two searches have been performed on the same final state, containing a single isolated lepton (
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
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
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
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.
Being partners of SM quarks, the
Branching ratios for
Limiting ourselves to the production of two particle states, it is possible to identify all the allowed channels for
Production and decay channels for
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Even if the list is limited to two particle intermediate states, it is still possible to notice that if the
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
Production and decay channels for
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The allowed decays for the
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
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 studies which have been published on peer-reviewed journals at the time of submission of the present paper; 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
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 [
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VLQs can contribute to processes of Higgs production and decay:
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 [
In [
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
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.
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.