Extra Quarks and Bileptons in BSM Physics in a $331$ Model

We describe some salient features of the $331_F$ (Frampton-Pisano-Pleitez) bilepton model, in which the constraints of anomaly cancelation require the number of generations to be three. In a class of six models, four of which characterised by a $\beta$ parameter describing the embedding of the hypercharge in the $SU(3)_L$ symmetry, a specific choice for $\beta$ allows bileptons in the spectrum, i.e. vectors and scalars of lepton numbers $\pm 2$. At the same time the model allows exotic quarks, with the third quark generation treated asymmetrically respect to the other two. Bileptons generate specific signatures in the form of multilepton final states in Drell-Yan like processes, with and without associated jets, which can be searched for at the LHC.


Introduction
At the beginning of June 2018 the ATLAS collaboration reported the measurement of the coupling of the top quark to the Higgs boson [1]. At the same time the CMS collaboration published the results of a similar analysis [2]. From their common results it is established that the coupling of the top quark to the Higgs boson is compatible with the prediction of the Standard Model (SM), confirming that the mechanism of mass generation of the heaviest known quark is similar to that of the lighter ones [3,4]. These findings secure the mechanism of spontaneous symmetry breaking (SSB) -induced by a scalar sector and associated Yukawa couplings -as a general feature of the SM. If we consider BSM (beyond the SM) models, in particular models with multiple SSB steps, by the same token, it is natural to expect that extra fermionic states will be generated, widely distributed in their mass. Their charges are directly linked to the underlying patterns of anomaly cancellation, which, in some cases, take to electric charges which differ by those typical of the three generations of the SM, and are classified as exotics.

GUT's and 331's
The idea that the gauge symmetry (S U(3) C × S U(2) L × U(1) Y ≡ 321) of the SM is part of a larger one has been pursued since the 70's, after that it was noticed that the unification of the gauge couplings could be achieved, provided that the underlying gauge group was simple or a product of simple factors  (see [7] for an overview). Such symmetries with multiple simple groups can be obtained by the sequential breakings of simple groups of higher rank, most notably within E 6 and S O(10) scenarios realized at a large scale, the grand unification scale or GUT. Among these, we mention the left-right which can be derived from the breaking of S O (10). Other examples are models based on S U(3) c × S U(3) L , later extended by an extra U(1) X in order to get the correct fermion masses. Tree level considerations on the structure of the couplings on the 331 models suggest that the breaking 331 → 321 could take place at the TeV scale, rather than at the usual GUT scale of 10 13 − 10 15 GeV, which has been the motivation for studying such class of models, especially in the flavour sector ( see [12,13]). There are various realization of such models since the embeddings of 321 into 331 can be quite different.

whereas the third family is
D, S and T are extra (exotic) quarks. In this respect, the number of generations is underwritten by the contraints of anomaly cancellation, which single out this model as unique respect to the general class of BSM scenarios. The lepton sector is assigned to the representation3 of the same gauge group. Universality is instead respected in the lepton sector, where the three lepton generations are ordinarily arranged into triplets of S U(3) L , The presence of exotic particles in the spectrum of the 331 model is due to the specific embedding of the hypercharge Y in the S U(3) L × U(1) X gauge symmetry, which is defined by for the 3 and the3 representations of S U(3) L , respectively, with generators corresponding to the Gell-Mann matrices, and . The charge operator is given by in the fundamental and anti-fundamental representations of of S U(3) L , respectively, where

Family embedding with exotics
and denote by q X the U(1) X charges, the breaking of the symmetry and for the3 The X-charge is fixed by the condition that the first two components of the Q 1 and Q 2 triplets carry the same hypercharge as the quark doublets Q L = (u, d) L of the Standard Model, yielding The minimal version of the 331 F model, in our conventions, is obtained by β = √ 3, resulting in with two exotic quarks D and S of charge -4/3 whereas The exotic quark T carries electric charge 5/3. For the leptons we have the ususal charge assignments and the three generations are treated symmetrically with Both left-and right-handed components of the SM leptons are fitted into the same S U(3) L multiplet. The condition of absence of colorless fractionally charged fermions fixes the value of β to 4 possible values (± √ 3, ±1/ √ 3), of which the FPP model is one, plus two additional models. The first is a flipped 331 version [8], with all the quarks in the same representation and the leptons in different ones; while the second is embedded in E 6 and there is family replication for both leptons and quarks. Among these models states with bilepton charges are present only in 331 F and in the E 6 version [9].  Figure 2. Bilepton signal from quark-gluon fusion and gluon-gluon fusion.

The scalars of 331 F
The scalars of the 331 F model, responsible for the electroweak symmetry breaking (EWSB), come in three triplets of The breaking S U(3) L × U(1) X → U(1) em is obtained in two steps. The vacuum expectation value of the neutral component of ρ causes the breaking from S U(3) L × U(1) X to S U(2) L × U(1) Y . Then the usual spontaneous symmetry breaking mechanism from S U(2) L × U(1) Y to U(1) em is obtained through the vevs of the neutral components of η and χ. Exotic quarks play an important role in the production of vector bileptons (B ± ) in qq annihilaton channels, as shown in Fig. 1. Compared to an ordinary Drell-Yan process where the coupling of the final state leptons to the intermediate gauge bosons is direct, in this case it is mediated by the bilepton pairs, each decaying to same sign leptons with a distinct signature of multi-lepton final states. At the same time, respect to an ordinary Drell-Yan process, an extra contribution is generated by a t-channel exchange of an exotic quark (Q) at Born level ( Fig. 1 c). Amplitudes with no associated jets can be generated also via the sextet scalars, by replacing Y ± with H ± .

The triplet sector
Coming to the electroweak SSB mechanism, this is realised in the 331 F model by giving a vev to the neutral component of the triplets ρ, η and χ, with Yukawa interactions where y i d , y i u and y i E are the Yukawa couplings for down-, up-type and exotic quarks, respectively. The masses of the exotic quarks are related to the vev of the neutral component of ρ = (0, 0, v ρ ). In this case the invariants are, in their representation content, If the relation y i E ∼ 1 is satisfied, using v ρ v η,χ , it is clear that the masses of the exotics are O(TeV), which is of particular interest for searches of such states at the LHC. Notice that the model has the appealing feature that the condition of reality of the gauge couplings sets a constraint on the location of the extra vacua, which is limited to the TeV region.

The sextet sector
The triplet sector is not sufficient to account for the masses of the leptons of the SM. This is the reason for introducing a scalar sextet. A typical Dirac mass term for the leptons in the SM is associated with the operatorl L He R , with l L = (v eL , e L ) being the S U(2) L doublet. The representation content is (2, 1/2) × (2, 1/2) × (1, −1) (for l, H and e R , respectively) in S U(2) L × U(1) Y . In the 331 the L and R components of the lepton (e) are in the same multiplet and therefore the identification of an S O(1, 3) × S U(3) L singlet needs two leptons in the same representation. The flavour structure of the Yukawa terms is given by the trilinear terms where a and b are flavour indices while i, j, k belong to the 3 of S U(3) L . Some considerations on the gauge charges and fermion statistics of this interaction imply that G η ab is antisymmetric in flavour space and as such it is not sufficient to account for the masses of all the leptons. This problem is overcome by the introduction of a scalar sector, sextet of S U(3) L , denoted as σ leading to the Yukawa term with G σ ab which is symmetric in flavour space. This allows to singlet out the representation 6 of S U(3) L , contained in l i a · l j b , by combining it with the flavour-symmetric σ * , i.e.6. Multi-lepton final states are a specific feature of the model generated by the decay of doubly charged vectors and scalars.

Quark exotics in Drell-Yan like distributions
We show in Fig. 2  (more complex) generalization of that process, with the total p T of the 4 leptons from the decay of Y ± vectors balanced by those of the two extra jets. The number of amplitudes which contribute to such final states is quite large and results have been presented in [10], to which we refer for more details. Such processes can equally be generated by a pair of H ± states if the contribution of the scalar sextet is included. The inclusion of the sextet representation in the potential V(ρ, η, χ, σ) enlarges the number of physical states in the spectrum, allowing a richer scenario. In fact we now have, after electroweak SSB five scalar Higgses, three pseudoscalar Higgses, four charged Higgses and three doubly-charged Higgses. For instance, the physical doubly-charged Higgs states are expressed in terms of the gauge eigenstates and the elements of the rotation matrix R C as [11] In [10] the study has been focused only on processes involving intermediate vectors rather than scalars, by considering benchmark points where the scalar bileptons are much heavier than the vector ones.
In [11], on the other hand, the study has been focused on the Drell-Yan like contributions shown in Fig. 1, which provide the golden plated mode for the study of bileptons at the LHC. In this second study the H ± and Y ± states have been chosen to be close in mass. In this case the analysis has been focused on observables of the final state leptons which may allow to distinguish between processes mediated either by the Y ± or by the H ± . Setting a distinction between the scalar (H ± ) and vector (Y ± ) contributions to the 4-lepton channel is an important experimental challenge, since searches for doubly-charged scalars are performed in a model-independent way, which differ from the scenario offered by this specific model, due to the presence of vector bileptons. This and the presence of exotics are peculiarities of the model which we hope will be addressed in direct experimental searches at the LHC.

Conclusions
In the class of models models with a 331 symmetry, the FPP model has a special status. It carries specific signatures in the form of scalar and vector bileptons which can be searched for at the LHC. Drell-Yan like processes are the golden plated modes for the discovery of such realizations. We have briefly overviewed their spectra and the the specific embedding of the hypercharge in the S U(3) L symmetry which take to exotic quarks in the spectrum. The asymmetric treatment of the 3 generations is a crucial signature of many 331 models, in which the number of families is underwritten by the cancellation of the gauge anomalies. At the same time, they are constrained to lay at the TeV scale.