Effects of the FCNC couplings in production of new heavy quarks within Z' models at the LHC

We study the flavor changing neutral current couplings of new heavy quarks through the Z' models at the LHC. We calculate the cross sections for the signal and the corresponding standard model background processes. Considering the present limits on the mass of new heavy quarks and the Z' boson, we performed an analysis to investigate the parameter space (mixing and mass) through different Z' models. For an FCNC mixing parameter x=0.1 and the Z' mass M_{Z'}=2000 GeV, and new heavy quark mass m_{t'}=700 GeV at the LHC with \sqrt{s}=13 TeV, we find the cross section for single production of new heavy quarks associated with top quarks as 5.8 fb, 3.3 fb, 1.5 fb and 1.2 fb within the Z'_{\eta} , Z'_{\psi} , Z'_{LP} and Z'_{\chi} models, respectively. It is shown that the sensitivity would benefit from the flavor tagging.


I. INTRODUCTION
Addition of new heavy quarks would require the extension of the flavor mixing in charged current interactions as well as the extension of Higgs sector in the standard model (SM). A large number of new heavy quark pairs can be produced through their colour charges at the Large Hadron Collider (LHC). However, due to the expected smallness of the mixing between the new heavy quarks and known quarks through charged current interactions, the production and decay modes can be effected by the flavor changing neutral current (FCNC) interactions. A new symmetry beyond the SM is expected to explain the smallness of these mixings. We may anticipate the new physics discovery by observing large anomalous couplings in the heavy quark sector. The couplings of the new heavy quarks can be enhanced to observable levels within some new physics models. In numerous phenomenological studies (see [1] and references therein), a lot of extensions of the SM foresee the extra gauge bosons, the Z ′ -boson in particular. Flavor changing neutral currents can be induced by an extra U (1) ′ gauge boson Z ′ . The Z ′ boson in the models using an extra U (1) ′ group can have tree-level or an effective Z ′ qq ′ (where q and q ′ both can be the up-type quarks or down-type quarks) couplings. The Z ′ η , Z ′ χ and Z ′ ψ models corresponding to the specific values of the mixing angle in the E 6 model with different couplings to the fermions, and the leptophobic Z ′ LP model with the couplings to quarks but no couplings to leptons are among the special names of the Z ′ models [2].
The ATLAS and CMS collaborations have performed extensive searches of new vector resonances at the LHC. We summarize briefly these searches, that exploited data from the pp run at √ s = 7 TeV and √ s = 8 TeV, as well as the corresponding constraints on Z ′ boson masses. The most stringent limits come from searches with leptonic final states (Z ′ → l + l − ): M Z ′ χ > 2620 GeV [3] and M Z ′ η > 1870 GeV [4], M Z ′ ψ > 2260 GeV [5] (more recently M Z ′ ψ > 2510 GeV [3]) for the Z ′ boson predicted by the U (1) ′ extensions, also extending to the mass limit of M Z ′ S > 2900 GeV [3,6] for a gauge boson with sequential couplings. The results from ATLAS experiment exclude a leptophobic Z ′ decaying to tt with a mass less than 1740 GeV at 95% C.L. [7], while the CMS experiment excludes a top-color Z ′ decaying to tt with a mass less than 2100 GeV at 95% C.L. [8]. These searches assume rather narrow width for the Z ′ boson (Γ Z ′ /M Z ′ = 0.012). From the electroweak precision data analysis, the improved lower limits on the Z ′ mass are given in the range 1100 − 1500 GeV, which gives a limit on the Z − Z ′ mixing about 10 −3 [2]. The limits on the Z ′ boson mass favors higher center of mass energy collisions for direct observation of the signal. Using dilepton searches with LHC data, the dark matter constraints have been analysed in Ref. [9,10] in the regime M Z ′ > 2m DM .
A work performed in Ref. [11,12] presents the effects of FCNC interactions induced by an additional Z ′ boson on the single top quark and top quark pair production at the LHC ( √ s = 14 TeV). The relevant signal cross sections have been calculated and especially the benefit from flavor tagging to identify the signal has been discussed. Considering an existence of sizeable couplings to the new heavy quarks, the Z ′ boson decay width and branchings, as well as the production rates, can be quite different from the expectations of usual search scenarios.
In the models of interest new heavy quarks can have some mixing with the SM quarks. For example, in composite Higgs model [13] the lightest new heavy quark couples predominantly to the heavier SM quarks (top and bottom quarks). In the models of vector-like quarks (VLQ) [14] they are expected to couple preferentially to third-generation quarks and they can have flavour-changing neutral current couplings, in addition to the charged-current decays characteristic of chiral quarks. Within the E 6 model the isosinglet quarks [15] are predicted and they can decay to the quarks of the SM. The new heavy quarks can be produced dominantly in pairs through strong interactions for masses around 1 TeV in the pp collisions of the LHC with a center of mass energy of 13 TeV. The single production of new heavy quarks would only be dominant over pair production for the large quark masses [16], it is model dependent, and it could be suppressed if the mixing with SM quarks is small.
There are searches for pair production and single production of new heavy quarks at the LHC. The ATLAS and CMS collaborations focused on decay modes of new heavy quarks into a massive vector boson and a third generation quark assuming a 100% branching ratio, based on L int ≈ 20 fb −1 of pp collision data at √ s = 8 TeV, and set lower mass limit for up type new heavy quark as m t ′ > 700 GeV [17] and m t ′ > 735 GeV [18].
In this work, we investigate the single production of new heavy quarks via FCNC interactions through Z ′ boson exchange at the LHC. This paper aims at studying the signal and background in detail within the same MC framework, and the relevant interaction vertices are implemented into the MC software. Analyzing the signal observability (via contour plots) for different mass values of the Z ′ boson and new heavy quarks as well as the mixing parameter through FCNC interactions are another feature of the work. In section II, we calculate the decay widths and branching ratios of Z ′ boson for the mass range 1500 − 3000 GeV in the framework of different Z ′ models. An analysis of the parameter space of mass and coupling strength is given for the single production of new heavy quarks at the LHC in section III. We analyzed the signal observability for the Z ′ qq ′ FCNC interactions. We consider both t ′t andt ′ t single new heavy quark productions for the purpose of enriching the signal statistics even at the small couplings. The analysis for the signal significance is given in section IV and the work ends up with the conclusions as given in section V.

II. FCNC INTERACTIONS
In the gauge eigenstate basis, following the formalism given in Ref. [11,19,20], the additional neutral current Lagrangian associated with the U (1) ′ gauge symmetry can be written as where ǫ L,R (f f ′ ) are the chiral couplings of Z ′ boson with fermions f and f ′ . The g ′ is the gauge coupling of the U (1) ′ , and P R,L = (1 ± γ 5 )/2. Here, we assume that there is no mixing between the Z and Z ′ bosons as favored by the precision data. Flavor changing neutral currents (FCNCs) arise if the chiral couplings are nondiagonal matrices. In case the Z ′ couplings are diagonal but nonuniversal, flavor changing couplings are emerged by fermion mixing. In the interaction basis the FCNC for the up-type quarks are given by where the chiral couplings are given by In general, the effects of these FCNCs may occur both in the up-type sector and down-type sector after diagonalizing their mass matrices. For the right-handed up-sector and down-sector one assumes that the neutral current couplings to Z ′ are family universal and flavor diagonal in the interaction basis. In this case, unitary rotations (V f L,R ) can keep the right handed couplings flavor diagonal, and left handed sector becomes nondiagonal. The chiral couplings of Z ′ in the fermion mass eigenstate basis are given by Here the matrix can be written as V ′ = V u L V d † L with the assumption that the down-sector has no mixing. The flavor mixing in the left-handed quark fields is simply related to V ′ , assuming the up sector diagonalization and unitarity of the CKM matrix one can find the couplings where the generation index i runs from 1 to 3.
In our model, the chiral couplings can be written as The values of the matrix elements |A 14 | = 3.2, |A 24 | = 2.0 and |A 34 | = 3.0 are used as given in Ref. [37] by taking into account λ = 0.22. For a comparison, we also calculate the cross sections using the scenario of equal parameters |A i4 | = 2.0 (where i runs from 1 to 3).
For the FCNC constraints from D 0 −D 0 mixing with parameter x D ≈ 6 × 10 −3 , we follow the calculations performed in Ref. [11], and find that the contribution from Z ′ boson (through FCNC effects) can be obtained as With the given parametrizations above, this is translated into the result that as long as the combination |C u L (x − 1)| is less than about 0.3, the experimental bounds can be well satisfied in different Z ′ models that we have studied in this work.  We use the value of masses of new heavy quarks m Q ′ = 700 GeV, and the masses of new heavy leptons m l ′ = 200 GeV and m ν ′ = 100 GeV. For numerical calculations we have implemented the Z ′ qq ′ interaction vertices into the CalcHEP program package [38]. The decay widths of Z ′ boson for different mass values within different Z ′ models are given in Table II. For the parameter x = 1, both the left-handed and right-handed couplings become universal, and family diagonal. In this case we cannot see the FCNC effects on the decay widths and cross sections. For the FCNC effects on the decay width, we take the parameter x = 0.1 as shown in Fig. 1. All these scenarios of Z ′ models predict a narrow decay width ranging from 0.6% to 3% for Γ Z ′ /M Z ′ depending on the mass of Z ′ boson foreseen by different models, for the considered set of parameters. The effect of the FCNC reduces the decay width in the relevant mass range. The decay widths are compared with the similar results from Ref. [11,12] for x = 0.1 to prove the implementation. Unless otherwise stated thoughout this work, we use the FCNC mixing parameter x = 0.1 and the mass value of t ′ quark m t ′ = 700 GeV, and the mass value of new heavy charged lepton m l ′ = 200 GeV and new heavy neutrino m ν ′ = 100 GeV. The branching ratios of Z ′ boson decays depending on its mass predicted by different Z ′ models are given in Fig. 2 -Fig.  9, specifically they are given in Fig. 2, Fig. 4 and Fig. 6 for the diagonal couplings to quarks and leptons, while they are given in Fig. 3, Fig. 5 and Fig. 7 for the FCNC couplings to different flavors of up sector quarks within the Z ′ η , Z ′ χ and Z ′ ψ models, respectively. In Fig. 8 and Fig. 9, the branchings for a leptophobic Z ′ LP boson decays to pair of quarks with diagonal couplings and FCNC couplings are presented depending on its mass.
The cross sections for the process pp → (t ′t +t ′ t) + X depending on the Z ′ boson mass at the LHC ( √ s =13 TeV) are given in Fig. 10 and Fig. 11 by using parton distribution function library CTEQ6L [39]. Here, the Z ′ boson contributes through the s-and t-channel diagrams, and the cross sections of associated production of single top quarks and single new heavy quarks (t ′t andt ′ t) in the final state are summed. For this process the cross section at √ s = 13 TeV is about 8 times larger than the case at √ s = 8 TeV. Fig. 12 shows the p T distributions of the b-quark in the signal process with M Z ′ = 1500 GeV for the parameter x = 0.1 at the pp center of mass energy of 13 TeV. A high p T cut reduces the background significantly without affecting much the signal cross section in the interested Z ′ mass range. The rapidity distribution of the bottom quarks (b andb) from the signal are shown in Fig. 13 at the collision energy of 13 TeV. In order to enhance the statistics we sum up the b andb distributions. There is a peak in the b-quark rapidity distribution η b ≃ 0 with the tails extending to |η b | ≃ 2.5.     well above the top quark mass. We also apply invariant mass cut (for to make analysis with the signal and background. The signal cross sections (σ S ) in the invariant mass interval of M Z ′ − 4Γ Z ′ < m W bt < M Z ′ + 4Γ, for the process pp → W + bt + W −b t + X are given in Table III, Table IV, Table V and Table VI for Table VII, Table VIII, Table IX and Table X, respectively. The cross section for the corresponding background are given in Table XI for the chosen invariant mass interval.           We plot the invariant mass distribution of the W bt system for the signal (with x = 0.1 and m t ′ = 700 GeV) and background at the LHC with √ s = 13 TeV in Fig. 14, Fig. 15, Fig. 16 and Fig. 17 for different Z ′ models.
decay widths corresponding to the parameters explained in the text.

IV. ANALYSIS
Here, we consider two types of backgrounds for the analysis. The first one has the same final state (W bt) as expected for the signal processes and the other one (pair production of top quarks both associated with b-jets) is the irreducible background and contributes to the similar final state. The ratio of the cross sections for pair production of top quarks at the √ s = 13 TeV and √ s = 8 TeV is about 3.5. The ratio of the cross sections for process pp → (t ′t + tt ′ ) + X is found to be about 8 for considered Z ′ models. It is expected that an improvement in the statistical significance (for the center of mass energy √ s = 13 TeV when compared to the case of √ s = 8 TeV) will be obtained. For the analysis, one can apply a high transverse momentum (p T ) cut for the b-jets and the other jets. Employing the variable p T cuts such that p T > 100 GeV for different Z ′ mass values and the rapidity cuts |η| < 2 for the central detector coverage, the results are given in Table XII, Table XIII, Table XIV and Table XV, we give the number of signal (S) and background (B) events by assuming integrated luminosity of L int = 10 5 pb −1 per year. For the FCNC coupling parameter x = 0.1, the LHC is able to measure the Z ′ mass up to about 3000 GeV with the associated productions of the new heavy quark t ′ and top quark. The statistical significance (SS) values for the final state are given in Table  XII -Table XV for different Z ′ boson masses.
In the analysis, we reconstruct the invariant mass of W bt system around the Z ′ boson mass which are shown in Fig. 14, Fig. 15, Fig. 16, Fig. 17. We assume top quark decay t(t) → W + b(W −b ), where the W boson can decay leptonically or hadronically. In the final state W + W − bb, we assume the b-tagging efficiency as 50% for each of the  b-quarks. We take into account the channel in which one of the W bosons decay leptonically, while the other decays hadronically. We calculate the cross section of the background in the mass bin widths for each M Z ′ value; as an example of the Z ′ η model, for the M Z ′ = 1500 GeV we take the invariant mass interval ∆m W bt ≃ 40 GeV, and we find the background cross section σ B = 6.60 × 10 −3 pb for process pp → (W −b t + W + bt) + X.
We plot the observability contours in the plane of model parameters (x − M Z ′ ), for different Z ′ models as shown in Fig. 18 at the LHC with √ s = 13 TeV and L int = 100 fb −1 . The curves with labels Z ′ LP , Z ′ χ , Z ′ ψ and Z ′ η show the accessible regions (below the curves) of the model parameters at the LHC. For the Z ′ η model, the FCNC parameter bounds from x = 0.6 − 0.4 can be searched for the mass range of M Z ′ = 1500 − 3000 GeV.      We consider the associated productions of new heavy quark t ′ and top quark (with the subsequent decay channel t ′ → W + b) through the Z ′ exchange diagrams at the LHC. We find the discovery regions of the parameter space for the single productions of new heavy quarks through FCNC interactions with the new Z ′ boson. In the models considered in this paper, the single production of new heavy quarks at the LHC can have the contributions from the couplings of Z ′ qq and the FCNC couplings of Z ′ qq ′ (where q, q ′ = u, c, t, t ′ ). For the FCNC parameter range (0 < x < 1 means maximal to minimal FCNC) the LHC can have the potential to produce new heavy quarks which couple to the Z ′ boson predicted by specific models.