Probing a new decay of vector-like top partner mediated by heavy Majorana neutrino via single production

Models beyond the Standard Model have been proposed to simultaneously solve the problems of naturalness and neutrino mass, in which heavy Majorana neutrinos and vector-like top partners are usually predicted. A new decay channel of the top partner mediated by the heavy Majorana neutrino can thus appear: $T\to b\,W^{+}\to b\,\ell^{+}\ell^{+}q\bar{q'}$. We study in this paper the observability of this decay process through single production of the top partner at the 14 TeV LHC: $pp\to T/\bar{T}$+jets$\to b/\bar{b}+\mu^{\pm}\mu^{\pm}$+jets. $2\sigma$ exclusion bounds on the top partner mass and mixing parameters are given by Monte-Carlo simulation, which surpass those from the search through VLT pair production in the mass range of $m_{T}>1.3$ TeV.


I. INTRODUCTION
The discovery of the 125 GeV Higgs boson at the LHC in 2012 [1,2] marks a great success of the Standard Model (SM) and deepens our understanding of the electroweak symmetry breaking. With a mass at the electroweak scale (∼ 10 2 GeV), the observed Higgs boson causes the so-called naturalness problem: the Higgs mass receives loop corrections from heavy particles like the SM top quark, which can lead the Higgs mass to Planck scale unless new physics is present to cancel out the quadratical divergence. The naturalness problem motivates a variety of new models beyond SM (BSM), such as the composite Higgs [3][4][5][6] and the little Higgs models [7,8], through the introduction of a spontaneously broken global symmetry that leads the Higgs boson to be a pseudo Goldstone boson. Vector-like top partners (VLT) are usually present in these models and play an important role in the cancelling of the quadratical divergence in the Higgs mass from the SM top loop. Therefore, VLTs have been widely studied and searched for at hadron colliders through both single and pair production, with subsequent decays into a SM quark and a gauge boson or Higgs boson [9][10][11][12][13][14][15][16][17]. ATLAS and CMS collaborations at the LHC excluded VLT with mass lower than 740 ∼ 1370 GeV, depending on its SU (2) representation and different branching ratios assumed [18,19].
Models have been proposed to solve the above two BSM issues simultaneously by incorporating neutrino mass into scenarios with VLT. For example, LNV interaction between triplet scalar and doublet lepton can be included within the Littlest Higgs scenario [83].
Other examples include Little Higgs models [84][85][86][87][88][89][90][91][92][93][94], Composite Higgs models [95][96][97][98][99], Higgs Inflation models [100], Top Seesaw models [101][102][103], etc [104,105]. VLT and heavy Majorana neutrinos are what these BSM models have in common and hence a new decay channel of VLT will be present through a mediating heavy Majorana neutrino. As mentioned above, VLTs and heavy Majorana neutrinos can both be searched for at the LHC, we thus propose a model-independent search strategy for the new decay channel of VLT in a scenario that includes three RH Majorana neutrinos and a singlet top partner T . As the mass of VLT increases, the cross section of its single production will surpass pair production at the LHC, as a result of the collinear enhancement of the light quark emitting a W boson [106].
Besides, the single production of VLT also has a unique event topology that can be used to suppress the SM backgrounds. Therefore, we focus on the VLT single production as a complementary study of the search by pair production [107]. We will demonstrate in the rest of the paper that with GeV-scale Majorana neutrinos, the new decay channel of VLT can be probed at the LHC by searching for final same-sign dileptons [108]. In the next section we will introduce relative effective Lagrangian of the present scenario. Section III is our analysis by Monte-Carlo simulation of the search at the 14 TeV LHC and exclusion limits will be given on the VLT couplings and Majorana neutrino mixings. Section IV is our conclusion. 3

II. THE NEW DECAY MODE OF VLT AND THE RELEVANT LAGRANGIAN
As a phenomenological investigation and without losing general features, we parameterize the low-scale Type-I seesaw by a single right-handed Majorana neutrino mass m N and a mixing parameter between the light and heavy neutrinos V N . Introduction of interactions between VLT and gauge bosons will lead to a new decay mode of T through mediating heavy Majorana neutrino, ending up with a pair of same-sign leptons (FIG. 1(a)): T → b W + → b + + qq . We will show in the next section that the same-sign dilepton in the final state can serve as a special signature at the LHC to search for this new decay mode. The effective interactions relevant to the VLT decay process are   will be enhanced as the result of on-shell production of W boson from N decay, but the enhancement is not that large and the rare decay branching ratio (∼ 10 −8 ) is still lower than that in the light mass range (m N m W ). Therefore in the next section we focus on this mass range of the heavy Majorana neutrino and study the search at the LHC for the VLT new decay mode. Note that the rare decay mode of the SM top quark t → b + + jj, comparing with the one of the top partner T , can actually be a more frequent possibility and be used to study the light-heavy neutrino mixings [76]. While in the present scenario that accommodates neutrino masses and naturalness, the search for T decay T → b + + jj can provide information for both the seesaw mechanism and the top partner simultaneously.
It should also be noted that large neutrino mixings can be inconsistent with small neutrino masses and a Majorana singlet of m N m W , but this can be resolved by introducing two bi-spinors per family [81]. Fine-tuning should also be required to cancel out the radiative corrections, but for the above mass range below electroweak scale, the lepton number violating signature can be observable at the LHC without fine-tuning as the result of destructive interference between contributions from different neutrinos [82].

III. SEARCH FOR THE NEW DECAY AT THE LHC
The SU(2) singlet VLT can be produced singly through proton-proton collision at the LHC via electroweak interactions: pp → T q /Tq /T W , among which the W -exchange production (qb → T q) has the largest cross section. The singly produced VLT can then go through the new decay mode T → b + + jj. If the W boson accompanied with VLT decays hadronically, we will have the signal of a same-sign dilepton and multijets including a b-tagged one: pp → T q /Tq /T W − → b + + + + multijets. Given the fact that e-flavor mixing with heavy neutrino |V eN | 2 has been strictly bounded below ∼ 10 −8 in the mass range from GeV to 10 2 GeV by GERDA experiments [80] and that high efficiency and accuracy of τ -tagging are necessary for limiting τ -flavor mixing, which are beyond the ability of current collider simulation, we focus on the dimuon channel in the mass range of heavy Majorana neutrino (m N m W ) that is kinematically accessible at the LHC for its resonant production. The contribution from CP-conjugation of the above process is also included in 5 the simulation below. Therefore our signal process can be expressed as in which we consider mainly the W -exchange single production. Besides, a diagonalized mixing matrix between light-flavor and heavy neutrinos V N is adopted and hence for the dimuon channel in our case, the mediated heavy Majorana neutrino is N 2 that couples exclusively to µ-flavor.
As for the SM backgrounds for the signal consisting of a same-sign dimuon plus multijets, the major ones come from events with fake leptons (such as top pair production tt and single production t/t+jets) and prompt multileptons (such as tt W ± and W ± W ± +jets). Therefore the following four kinds of processes are considered as backgrounds We did not include events with opposite-sign dimuons, which may also contribute to the background if one of the dimuon's charge is mismeasured, as the mismeasurement rate of muon charge is generally low. Note that the top decay mediated by the heavy Majorana neutrinos: will also be present in our scenario and contribute in the backgrounds tt, ttW ± and t/t+jets.
in which m N stands for the mass of N 2 for simplicity, while for N 1 (N 3 ) that couples solely to e (τ ), we assume a kinematically inaccessible mass 300 GeV (1 TeV). Signal and background events are generated at parton level using MadGraph5_aMC@NLO [109] (version 2.6.7) with the NN23LO1 PDF [110], and then by checkmate2 (version 2.0.26) [111], go through parton showering and hadronization with pythia-8.2 [112] as well as detector simulation with tuned delphes-3.4.1 [113]. Jet-clustering is done using fastjet [114] with anti-k t algorithm [115]. B-tagging efficiency is assumed to be 70% with MV2c20 algorithm [116] in benchmark points for our signal, we can find that a larger VLT mass will be reflected in the more flat distribution of / E T . Distributions of relative distance between final dimuon are displayed in FIG. 2(c), where for the signal events ∆R µµ is smaller than that for the backgrounds, since the dimuon comes from the same parent particle T in the former case while final muons come from different parent particles in the latter case. In FIG. 2(d) we present distributions for rapidity of the leading jet (non-b-tagged). In the single VLT production, the jet from splitting of a valence quark with W boson emission is always of strong forward nature which can be seen in the rapidity distributions. But cutflows with cuts on rapidity of the forward jet show that it is not effective if other cuts, such as ones on / E T and ∆R µµ , are first applied. Thus in the following cuts we do not include this one. According to the above distributions and analysis, the following cuts are applied that can well distinguish signal from the SM backgrounds: • Cut 1: Two muons of same sign are required and each of them should satisfy p T (µ) > 10 GeV and |η(µ)| < 2.8.
• Cut 2: At least 4 jets in the final states are required with p T (j) > 15 GeV and |η(j)| < 3.0.
• Cut 3: We require a large missing transverse energy as / E T > 160 GeV.
• Cut 4: Relative distances are required for the dimuon separation as 0.4 < ∆R µµ < 1.0, for jets separation as ∆R jj > 0.4 and for jet-muon separation as ∆R µj > 0.4.
• Cut 5: At least one of the final jets is required to be a b-tagged one, which also should have p T > 210 GeV. Signal cross section at 2σ in the range of 10 GeV m N m W from the DELPHI Collaboration [77], as well as the searches at the LHC for same-sign dilepton [78] and trilepton events [79], which, as seen from FIG. 3(a), can be well improved in our case for a wide range of m T from 800 to 2000 GeV. In FIG. 3(b), the contours are displayed on the plane of VLT-SM coupling V T b versus m T for cases of V µN = 0.002, 0.004, 0.01 corresponding to solid lines from top to bottom. In the given mass region, V T b can be excluded at 2σ down to 0.26 ∼ 0.39 for the above three settings of V µN with the best point at m T ∼ 1.05 TeV. We can also find from FIG. 3(a) 1(b)).
Finally we comment on the pileup effects in our discussion, which, although need proper removal techniques [119][120][121] for a fully realistic simulation, have limited effects on our results since the event selection is based on hard same-sign dileptons.

IV. CONCLUSION
We study in this paper the search for the new decay mode of a vector-like top partner mediated by the heavy Majorana neutrino (T → b + + jj) in a model-independent scenario that includes a singlet VLT into the low-energy Type-I seesaw, through the VLT single