Abstract
We study the process (where and and ) through the anomalous interactions of the new heavy quarks at the LHC. Considering the present limits on the masses and mixings, the signatures of the heavy quark anomalous interactions are discussed and analysed at the LHC for the center of mass energy of 13 TeV. An important sensitivity to anomalous couplings TeV−1, TeV−1, TeV−1 and TeV−1, TeV−1, TeV−1 for the mass of 750 GeV of the new heavy quarks and can be reached for an integrated luminosity of fb−1.
1. Introduction
The standard model (SM) of the strong and electroweak interactions describes successfully the phenomena of particle physics. However, there are many unanswered questions suggesting the SM to be an effective theory. In order to answer some of the problems with the SM, additional new fermions can be accommodated in many models beyond the SM (see [1–9] and references therein). The new heavy quarks could also be produced in pairs at the LHC with center of mass energy of 13 TeV. However, due to the expected smallness of the mixing between the new heavy quarks and known quarks, the decay modes can be quite different from the one relevant to charged weak interactions. A new symmetry beyond the SM is expected to explain the smallness of these mixings. The arguments given in [10] for anomalous interactions of the top quark are more valid for the new heavy quarks and due to their expected larger masses than the top quark.
The ATLAS experiment [11] and CMS experiment [12] have searched for the fourth generation of quarks and set limits on the mass of GeV and GeV at TeV. The pair production of new heavy quarks has been searched by the ATLAS experiment [13, 14] and the GeV mass limits are set at TeV. The CMS experiment has excluded masses below 557 GeV [15]. The vector-like quarks have been searched by the ATLAS experiment [16, 17] and set bounds as 900 GeV for charged current channel and 760 GeV for neutral current channel at TeV. The CMS experiment [18] has set the lower bounds on the mass of 685 GeV at TeV. Some of the final states in the searches of new phenomena can also be considered in relation with the new heavy quarks.
The anomalous resonant productions of the fourth family quarks have been studied in [19, 20] at the LHC with TeV. The possible single productions of fourth generation quarks via anomalous interactions at Tevatron have also been studied in [21]. The parameter space for the mixing of the fourth generation quarks has been presented in [22]. The CP violating flavor changing neutral current processes of the fourth generation quarks have been analyzed in [23], and the large mixing between fourth generation and first three generations has been excluded under the proposed fit conditions. Investigation of the parameter space favored by the precision electroweak data has been performed for the fourth SM family fermions in [24].
In this work, we present the analysis of anomalous productions and decay of new heavy quarks and at the LHC. We have performed the fast simulation for the signal and background. Any observations of the invariant mass peak in the range of 500–1000 GeV and excess in the events with the final states originating from and can be interpreted as the signal for the new heavy quarks and via the anomalous interactions.
2. New Heavy Quarks Anomalous Interactions
A general theory that includes the standard model (SM) as its low energy limit can be written as an expansion series in powers of with operators obeying the required symmetries. The dimension six gauge invariant operators can be built from the SM fields and they can induce dimension five operators after spontaneous symmetry breaking. The coefficients of the dimension five terms are related to those of dimension six operators, and they can lead to sizable effects in the heavy quark associated production in high energy collisions [25]. For our study, the effective Lagrangian with dimension five terms for the anomalous interactions among the new heavy quarks ( or ), ordinary quarks , and the gauge bosons can be written explicitly:where , , and are the field strength tensors of the gauge bosons; ; are the Gell-Mann matrices; is the electric charge of the quark (); , , and are the electromagnetic, neutral weak, and strong coupling constants, respectively. , where is the weak mixing angle. is the anomalous coupling with photon; is for the boson, and is the coupling with gluon. Finally, is the cutoff scale for the new interactions.
3. Decay Widths and Branchings
For the decay channels where , , and , we use the effective Lagrangian to calculate the anomalous decay widths:with
The anomalous decay widths in different channels are proportional to , and they are assumed to be dominant for TeV−1 over the charged current channels. In this case, if we take all the anomalous coupling equal then the branching ratios will be nearly independent of . We have used three parametrization sets entitled PI, PII, and PIII. For the PI parametrization, we assume the constant value TeV−1, and PII has the parameters TeV−1 with . For PIII we take the couplings TeV−1 with the same value of . The index is the generation number.
Tables 1 and 2 present the decay width and branching ratios of the new heavy quark through anomalous interactions for the parametrization PI, PII, and PIII, respectively. Taking the anomalous coupling TeV−1 we calculate the decay width GeV and 1.90 GeV for GeV and 1000 GeV, respectively. The branching into channel is the largest and branching into channel is the smallest for equal anomalous couplings with the parametrization PI. On the other hand, PII and PIII parametrization give higher branching ratios into () than () channels due to factor in the parametrization.
For the new heavy quark the decay width and branching ratios are presented in Tables 3 and 4 for the parametrizations PI, PII, and PIII, respectively. We calculate the decay width, by taking the anomalous couplings TeV−1, GeV, and 1.92 GeV for GeV and 1000 GeV, respectively. The branching for is the largest (30%) and it is the smallest for (0.2%) channel for equal anomalous couplings with the parametrization PI. For PII and PIII parametrization the branching ratios into () are larger than () channels. The and decay widths are about the same values for PII and PIII parametrization.
4. The Cross Sections
In order to study the new heavy quark productions at the LHC, we have used effective anomalous interaction vertices and implemented these vertices into the CalcHEP package [26]. In all of the numerical calculations, the parton distribution functions are set to the CTEQ6L parametrization [27]. The new heavy quarks can be produced through their anomalous couplings to the ordinary quarks and neutral vector bosons as shown in Figure 1.
(a)
(b)
Total cross sections for the productions of new heavy quarks and are given in Tables 5 and 6 for the parametrizations PI, PII, and PIII, at the center of mass energy of 8 TeV and 13 TeV. For an illustration, taking the mass of new heavy quarks as 700 GeV the cross section of production is calculated as 8.50 pb (10.03 pb) for the parametrization PIII at TeV. It can be seen from Tables 5 and 6 that the cross section decreases while the mass of the new heavy quark increases. The cross section for production is larger than the production with a factor of 1.2–1.8 (0.7–1.0) for PI (PII and PIII) parametrization depending on the considered mass range at TeV. The general behaviour of the production cross sections depending on the mass of new heavy quarks is presented in Figures 2 and 3 for different parametrizations.
4.1. Analysis of the Process for Signal
The signal process () includes the exchange in both the -channel and -channel. The -channel contribution to the signal process would appear itself as resonance around the mass value in the invariant mass. The -channel gives the nonresonant contribution. We consider that the boson decays into lepton + missing transverse momentum with the branching ratio of 21% and boson decays into dilepton with the branching ratio of 6.7%. In our analyses, we consider the signal in the , , and channels, where . However, if one takes the hadronic decay, the signal will be enhanced by a factor of .
We have obtained the cross sections by using the cuts pseudorapidity and transverse momentum GeV for jets and photon, in Table 7 (Tables 8 and 9) for PI (PII, PIII) parametrization, respectively. Invariant mass distribution of the (where , , and ) system is shown in Figure 4 for PI parametrization of the signal with TeV−1 and GeV at the center of mass energy TeV. It appears from signal significance calculations that the optimized transverse momentum cut is GeV for analyses.
The backgrounds for the final state (where , jet, and boson) are given in Table 10. We apply the following cuts to the final state photon and jets as and GeV. For the background cross section estimates, we assume the efficiency for -tagging to be and the rejection ratios to be 10% for quark jets and 1% for light quark jets since they are assumed to be mistagged as -jets.
In order to find the discovery limits we use the statistical significance [28] defined aswhere and are the numbers of the signal and background events, respectively. In Figures 5–7, the integrated luminosity required to reach significance for the signal of anomalous interactions is shown for parametrizations PI, PII, and PIII at the LHC with TeV. It is seen from these figures that the channel requires more integrated luminosity than the other channels. By requiring the signal significance , the contour plots of and mass of quark are presented in Figure 8. The results show that one can discover the quark anomalous couplings down to 0.1 TeV−1 in the channel for GeV.
4.1.1. Simulation for Signal
In order to include detector effects in the simulation, we have generated (where , , and ) signal events for each subprocess and they are mixed using the “event_mixer” script which can be found within the CALCHEP package [26]. For further decay and hadronization these events are passed to PYTHIA [29] and simulated with the PGS4 program [30] using generic LHC detector parameters. This fast simulation includes the important detector effects such as tracking, smearing effects of the calorimeters, resolution, and tag efficiencies. The EXROOTANALYSIS package [31] is used for the simulated events and the output is analyzed and histogrammed with the ROOT [32] macros. We consider jets (up to five), leptons (electrons or muons), photons, and missing transverse momentum within the simulated events for the , , and events generation. The typical kinematical distributions are shown in Figures 9-10.
In the analysis, the signal (with TeV−1 and GeV) and the corresponding background () are taken into account. The -channel contribution to the signal process appears as a resonance around the mass value in the reconstructed invariant mass . The reconstructed mass distribution for the signal (reconstructed from a top quark and a vector boson) is shown in Figure 11.
Similar to the single top processes, the top quark in the final state is reconstructed from a leading jet (commonly ) and a boson (which can be reconstructed from its leptonic or hadronic decay). For the production we require systematically the large transverse momentum of photon ( GeV), minimum jet transverse momentum ( GeV), and the pseudorapidity range () in addition to the requirements on mass reconstruction of -boson and top quark. The large and the requirement of single -tagging allow a better separation of the signal (for channel) from the background. Other channels for and productions are more challenging due to a large number of jets, which require additional discriminators such as angular and/or total transverse energy variables. However, in order to get rid of the backgrounds from and production (for a similar framework the production cross sections are about 25 pb and pb, resp.), one can consider the channel for a distinctive signal from the . An analysis of the investigation of single top production with similar backgrounds at the LHC can be found in [33–35].
4.2. Analysis of the Process for Signal
The signal process () includes the new heavy quark exchange in both the -channel and the -channel. The -channel contributes to the signal process as resonance around the mass value in the invariant mass, while the -channel contributes to the nonresonant behaviour. For this process, we consider the leptonic decay of boson. In the analyses, we consider the signal to be , , and .
We have obtained the cross sections by using the pseudorapidity cuts and transverse momentum cuts GeV for jets and photon, in Table 11 (Tables 12 and 13) for PI (PII, PIII) parametrizations, respectively. Invariant mass distribution of the (where , , and ) system is shown in Figure 12 for PI parametrization of the signal with TeV−1 and GeV at the center of mass energy TeV. It appears from signal significance calculation that the optimized transverse momentum cut is GeV for analyses.
The backgrounds for the final state (where photon, jet, and boson) are given in Table 14. We apply the following cuts to the final state photon and jets as and GeV. It can be noted that the background cross section decreases as the cuts increase. We assume the efficiency for -tagging to be and the rejection ratios to be 10% for quark jets and 1% for light quark jets.
In order to reach significance for the signal of anomalous interactions the required integrated luminosity is shown in Figures 13–15 for parametrizations PI, PII, and PIII at the LHC with TeV. The channel requires more integrated luminosity than the other channels. By requiring the signal significance , the contour plots of and mass of quark are presented in Figure 16. The results show that one can discover the quark anomalous couplings down to 0.1 in the channel for GeV.
4.2.1. Simulation for Signal
In the simulation, we have generated (where , , and ) events for each subprocess and these events are simulated using generic detector parameters to include detector effects such as tracking, tagging efficiencies, and smearing effects. After the simulation, the typical kinematical distributions are shown in Figures 17-18.
In the analysis, the signal (with TeV−1 and GeV) and the corresponding background are taken into account. The invariant mass of the new heavy quark can be reconstructed from a and a neutral gauge boson (where the boson can also be reconstructed from its dilepton or hadronic decay). For the production, we require a large (>100 GeV) for photon and large (>100 GeV) for jet and pseudorapidity (<2.5). For the signal channel, the invariant mass distributions for signal and background events are shown in Figure 19. The large and the requirement of single -tagging allow a better separation of the signal (for channel) from the background, and then we find a precise limit for the anomalous coupling in this channel. For the and production, we require two high jets (one -jet) and a high jet in addition to the reconstructed mass , respectively. The main character of the signal is the high and/or and single -tagged jet. We calculate the signal and background events in the range GeV and we find a similar significance as shown in Figure 16.
5. Conclusion
The new heavy quarks of up-type and down-type can be produced with large numbers at the LHC if they have the anomalous couplings (via flavor changing neutral current) that well dominate over the charged current interactions. The single production of new heavy quarks can be achieved through the anomalous interactions at the LHC with TeV. The anomalous vertices could appear significantly at leading order processes due to the possibility of new heavy quarks. From the results of signal significance calculations for () anomalous productions, the sensitivity to the anomalous couplings () can be reached down to 0.10 TeV−1 (0.15 TeV−1) in the ( + jet) channel at TeV, assuming a dynamical parametrization for the anomalous couplings and the mass of 750 GeV for the new heavy quarks. The observability limits on the anomalous couplings obtained after the simulation are comparable with the partonic level analysis in the photon and boson associated channels, whereas the productions and are less comparable due to the fast simulation method. In any case the single tagging will play an important role in probing new heavy quarks and reducing the background.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgment
This work was supported in part by Turkish Atomic Energy Authority (TAEA) under Project Grant no. 2011TAEKCERN-A5.H2.P1.01-19.