Hunting scalar leptoquarks with boosted tops and light leptons
Kushagra Chandak Tanumoy Mandal Subhadip Mitra
hep-ph hep-ex

0.95




kushagra.chandak@research.iiit.ac.in
Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad 500 032, India


tanumoy.mandal@physics.uu.se
Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden


subhadip.mitra@iiit.ac.in
Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Hyderabad 500 032, India




The LHC search strategies for leptoquarks that couple dominantly to a top quark are different than for the ones that couple mostly to the
light quarks. We consider charge 1/3 (ϕ_1) and 5/3 (ϕ_5) scalar leptoquarks that can
decay to a top quark and a charged lepton (tℓ) giving rise to a resonance system of a boosted top and a 
high-p_ T lepton. We introduce simple phenomenological models suitable for bottom-up studies and explicitly map them to all possible scalar leptoquark models within
the Buchmüller-Rückl-Wyler classifications that can have the desired decays. We study pair and single productions of these leptoquarks.
Contrary to the common perception, we find that the single production of top-philic leptoquarks ϕ = {ϕ_1,
ϕ_5} in association with a lepton and jets could be significant for order one ϕ tℓ coupling in certain scenarios. 
We propose a strategy of selecting events with at least one hadronic-top and two high-p_ T same flavour opposite sign leptons. This captures events from
both pair and single productions. Our strategy can significantly enhance the LHC discovery potential
especially in the high-mass region where single productions become more prominent.
Our estimation shows that a scalar leptoquark as heavy as ∼1.7 TeV can be discovered at the 14 TeV LHC with 
3 ab^-1 of integrated luminosity in the tℓℓ+X channel for 100% branching ratio in the ϕ→ tℓ decay mode. 
However, in some scenarios, the discovery reach can 
increase beyond 2 TeV even though the branching ratio comes down to about 50%.




Hunting scalar leptoquarks with boosted tops and light leptons
    Subhadip Mitra
    December 30, 2023
==============================================================







§ INTRODUCTION



So far, the predictions of the Standard Model (SM) have been verified to a
remarkable degree of accuracy. But some persistent deviations in rare B-meson decays
observed in several independent experiments hint towards new physics. 
In particular, a significant excess in the R_D^(*) observables was first reported by the BaBar
collaboration in 2012 <cit.>. Later, this excess was also seen in the 
LHCb <cit.> and Belle <cit.>
measurements (though its significance reduced). The current combined deviation in the R_D and R_D^* observables, as computed by the
HFLAV group <cit.>, is still about 3.1 away from the SM 
prediction <cit.>. 
In the R_K^(*) observables, a deviation of about 2.5 from the corresponding SM 
predictions <cit.> have been observed by the LHCb 
collaboration <cit.>. Altogether, 
these deviations indicate towards lepton universality violation and suggest that the
underlying new physics, if that really is the origin of these anomalies, has strong affinity
towards the third generation SM fermions.


A popular explanation of the rare B-decay anomalies is the existence of TeV-scale scalar
leptoquarks (LQ or ℓ_q) that has large couplings to the third generation quarks.
LQs  appear in different scenarios like 
Pati-Salam  models <cit.>, SU(5) grand unified theories <cit.>, 
the models with quark lepton compositeness <cit.>,  R-parity violating supersymmetric models 
<cit.> or coloured Zee-Babu model <cit.> etc. Their phenomenology has also 
been studied in great detail (see, for example, Refs. <cit.> 
for some phenomenological studies).


The LHC is actively looking for the signatures of scalar LQs that couple with third generation fermions for some time and has put direct 
bounds on them. Among the various possible signatures, the 
pp→ℓ_qℓ_q→ ttττ mode is already extensively searched for by the ATLAS and the CMS collaborations. Assuming 100% branching ratio (BR) in the ℓ_q→ t τ decay mode, the latest scalar LQ pair production 
search at the CMS detector has excluded masses below 900 GeV <cit.>. CMS has also put bounds 
on scalar LQs that decay to a b-quark and a neutrino at about 1.1 TeV assuming 100% BR in this decay mode <cit.>.
Similar limits are also available from the ATLAS searches <cit.>.


In this paper, we consider scalar LQs with a non-standard decay to a top quark and a light charged lepton (ℓ={e,}). In light of the observed B-decay anomalies, such non-standard decay modes have started getting some attention. For example, the CMS collaboration has recently published their first analysis of LQ pair production searches in the ttμμ channel <cit.>. 
They have also done a prospect study for this channel at the HL-LHC based on the 13 TeV data collected in 2016 <cit.>. Generally,  it is possible to
have LQs with large cross-generational couplings i.e. a LQ that couples to quarks and leptons
of different generations <cit.>. However, large cross-generational couplings would introduce 
flavour changing neutral currents which are strongly constrained from precision experiments except for the cases where LQs couple with third generation quarks. 
For the light  lepton we consider either an electron or a muon but not both at the same time.
This is because, the scenarios with comparable couplings of a LQ to leptons of different generations simultaneously 
(and hence comparable BRs to those modes) would be constrained by the lepton number/flavour violation experiments. 
With this, pair production of such LQs would have either of the two possible signatures viz. ttμμ and ttee.  

 
In this paper, we look beyond the pair production process of scalar LQs and  consider their single productions also. 
The motivation for this is twofold. First, as the LQ mass increases, the pair production cross section falls of faster than the single 
production cross sections due to the extra phase space suppression it receives. Second, the recent B-decay anomalies indicate
towards the presence of large cross-generational couplings of LQs – a necessary condition to search for the single production 
processes. However, the common perception is that LQs that couple with third generation quarks exclusively would have tiny 
single production cross sections for perturbative new couplings because of the small b-quark parton density function (PDF) 
(t-PDF is absent). Here, we implement a search strategy <cit.> by 
combining events of pair and single productions of scalar LQs  in the signal. 
We use a publicly available dedicated top-tagger to tag hadronically decaying boosted tops in the final states 
and estimate the LHC discovery potential of LQs in the  tℓℓ +X mode.
Contrary to the  common perception, we find that if the unknown couplings controlling the single production processes are not 
very small but perturbative (i.e. order one), such a strategy can enhance the discovery prospect of LQs at the LHC 
significantly.

The rest of the paper is organized as follows. In Section <ref>, we introduce the 
leptoquark models. In Section <ref> we discuss the LHC phenomenology and  our search strategy 
and present our results in Section <ref>. Finally, we summarise and conclude in Section <ref>.






§ LEPTOQUARK MODELS



Electromagnetic charge conservation forces the LQs that
decay to a top quark and a charged lepton to have electromagnetic 
charge ± 1/3 or ± 5/3. From the classification of possible LQ states in 
Refs. <cit.>, we see that only S_1, R_2 and S_3 have
the desired decay modes, ℓ_q→ tℓ (where ℓ={e,μ}). 
Below, we show these three types of LQs Lagrangians following the notations of Ref. <cit.>. To avoid proton decay constraints, we ignore the diquark operators.




 §.§ Existing Models


▪S_1=(3,1,1/3):

For S_1, one can write the following two renormalizable operators invariant under the SM gauge group (G_SM):

    ℒ⊃     y^LL_1 ijQ̅_L^C i S_1 iτ^2 L_L^j+y^RR_1 iju̅_R^C i S_1 e_R^j+h.c.,

where Q_L and L_L are the SM left-handed quark and lepton doublets, respectively. The superscript C  denotes  
charge conjugation. The Pauli 
matrices are represented by τ^k with k={1, 2, 3}. Here, the generation indices are denoted 
by i,j={1, 2, 3}.  
This can be written explicitly as,

    ℒ⊃   -(y^LL_1 U)_ijd̅_L^C i S_1ν_L^j+(V^T y^LL_1)_iju̅_L^C i S_1 e_L^j
       +y^RR_1 iju̅_R^C i S_1 e_R^j+h.c..

where U and V represent the  Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing matrix and the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix, respectively. Since the neutrino flavours cannot be distinguished at the LHC, we denote them by just ν. Similarly, for LHC phenomenology in general, and in particular for our analysis, the small off-diagonal terms of the CKM matrix play negligible role. Hence, we assume a diagonal CKM matrix for simplicity. We identify the terms relevant for our analysis,

    ℒ⊃    y^LL_1 3j(-b̅_L^C ν_L+t̅_L^Cℓ_L^j)S_1
    +y^RR_1 3j t̅_R^Cℓ_R^j S_1+h.c.,

where j={1, 2}.


▪S_3= (3,3,1/3):

There is only one type of G_SM-invariant renormalizable operator one can write for S_3:


    ℒ⊃    y^LL_3 ijQ̅_L^C i,aϵ^ab (τ^k S^k_3)^bc L_L^j,c + h.c.,


Here, the SU(2) indices are denoted 
by a,b,c={1, 2}.  Expanding this we get,

    ℒ⊃   -(y^LL_3U)_ijd̅_L^C i S^1/3_3ν_L^j-√(2) y^LL_3 ijd̅_L^C i S^4/3_3 e_L^j
       +√(2) (V^Ty^LL_3U)_iju̅_L^C i S^-2/3_3ν_L^j
       -(V^Ty^LL_3)_iju̅_L^C i S^1/3_3 e_L^j+h.c.,

The relevant interaction terms can be written as,

    ℒ⊃    -y^LL_3 3j[(b̅_L^Cν_L+t̅_L^Cℓ_L^j) S^1/3+√(2)( b̅_L^Cℓ_L^jS^4/3_3..
       -
    ..t̅_L^Cν_LS^-2/3)]+h.c.,

with j={1, 2}.



▪R_2=(3,2,7/6):
Similarly, for R_2 we have the following terms,

    ℒ   ⊃   -y^RL_2 iju̅_R^i R_2^aϵ^abL_L^j,b+y^LR_2 jie̅_R^j R_2^a *Q_L^i,a +h.c.,

which, after expansion, can be written as,

    ℒ   ⊃     - y^RL_2 iju̅^i_R e^j_L R_2^5/3+  (y^RL_2
      U)_iju̅^i_R 
      ν^j_L R_2^2/3
          +(y^LR_2 V^†)_jie̅^j_R 
      u^i_L R_2^5/3 * +y^LR_2 jie̅^j_R d^i_L R_2^2/3 * +  h.c..

We identify the terms relevant for us as,

    ℒ   ⊃     - y^RL_2 3j t̅_R ℓ^j_L R_2^5/3+  y^RL_2 3j t̅_R 
      ν_L R_2^2/3
          +y^LR_2 j3 ℓ̅^j_R 
      t_L R_2^5/3 * +y^LR_2 j3 ℓ̅^j_R b_L R_2^2/3 * + h.c.,

with j={1, 2}.




 §.§ Simplified Models and Benchmark Scenarios




Following Ref. <cit.>, we write a simplified phenomenological Lagrangian for the  models above,

    L   ⊃   _ℓ(√(η_L)t̅_L^Cℓ_L
     + √(η_R)t̅_R^Cℓ_R)ϕ_1+_νb̅_L^Cν_Lϕ_1+ h.c.,    
    L   ⊃   _ℓ(√(η_L)t̅_Rℓ_L + √(η_R)t̅_Lℓ_R)ϕ_5+h.c..

In this notation, a charge 1/3 (5/3) scalar LQ is generically represented by ϕ_1 (ϕ_5). Here, η_L and η_R = (1 - η_L) are the
fractions of leptons coming from LQ decays that are left-handed and right-handed, respectively.
The simplified Lagrangian does not include any charge 2/3 or 4/3 LQ as such LQs would not couple  with just a top quark and a charged lepton simultaneously.

For our analysis, we consider four benchmark coupling scenarios.

    
  * Left-handed Couplings with Same Sign (LCSS): In this scenario, we set _ℓ=_=, _ℓ=0 and η_R=0, i.e., we have a ϕ_1 LQ that couples to the left-handed leptons. As a result, it couples to both tℓ and bν pairs with equal strength and hence decays to either of the pairs with about 50% BRs. In this scenario, the ϕ_1 behaves like the charge 1/3 component of S_3 (with -y^LL_3 3j=).
    
    
  * Left-handed Couplings with Opposite Sign (LCOS): We set _ℓ=-_=, _ℓ=0 and η_R=0. In this scenario too a ϕ_1 LQ couples with the left-handed leptons equally but with opposite signs. However, since it couples to both t and bν pairs with equal (absolute) strength, it still decays to either a tℓ or a bν pair with about 50% BRs. In this scenario, it behaves like an S_1 with y_1 3j^LL= and y_1 3j^RR=0.
    
    
  * Right-handed Coupling (RC): In this scenario, the LQ has no weak charge and couples with only right handed leptons.  This scenario is common to both ϕ_1 and ϕ_5 as we do not use the charge of leptoquark in our analysis. Here, we set  _ℓ=_ℓ=, _=0 and η_L=0. It decays to a tℓ  pair with  100% BR. In this scenario, the LQ is either of S_1 type with y_1 3j^LL=0 and y_1 3j^RR= or it is R_2^5/3 with y^LR_2 j3=.
    
     
  * Left-handed Coupling (LC): In this scenario the LQ couples with only left handed charged leptons.  This scenario is exclusive to ϕ_5. Here, we set -y^RL_2 3j=_ℓ=, _ℓ=_=0 and η_R=0. It decays to a tℓ  pair with  100% BR. 

We have summarized these four scenarios in Table <ref>.




§ LHC PHENOMENOLOGY & SEARCH STRATEGY



We have used various publicly available packages for our analysis. We implement the Lagrangian of Eqs. (<ref>) and (<ref>) in FeynRules <cit.> to create the UFO <cit.>
model files. Both the signal and the background events are generated in the event generator MadGraph5 <cit.> at the leading order (LO). The 
higher-order corrections are included by multiplying appropriate QCD K-factors wherever available. 
We use NNPDF2.3LO <cit.> parton distribution 
functions (PDFs) for event generation by setting default dynamical renormalization and factorization scales used in
MadGraph5. Events are passed through Pythia6 <cit.> to perform showering and 
hadronization and matched up to two additional jets using MLM matching 
scheme <cit.> with virtuality-ordered Pythia showers to remove the double counting 
of the matrix element partons with parton showers. Detector effects are simulated using 
Delphes3 <cit.> with the default CMS card.
Fatjets are reconstructed using the FastJet <cit.> package by clustering Delphes 
tower objects. We employ Cambridge-Achen <cit.> algorithm with radius parameter R = 1.5
for fatjet clustering. To reconstruct hadronic tops from fatjets, we use a popular top tagger, namely the HEPTopTagger <cit.>.




 §.§ Production at the LHC




As indicated in the [sec:intro]introduction section, LQs are produced resonantly at the LHC through pair and single
production channels.  
The  pair production  is mostly model independent [depends only on the universal QCD
coupling, see e.g. Fig. <ref>] and proceeds through the gg and qq initiated processes. In the LCOS and the LCSS models, the process bb→ϕ_1ϕ_1 through
the t-channel neutrino exchange is dependent on model coupling  [see Fig. <ref>]. However, this contribution is small
in the total pair production cross section. The pair production process leads to the following final state,


    pp→ϕϕ→ (tℓ)(tℓ)

where a ϕ stands for either a ϕ_1 or a ϕ_5.
Single production channels, where a LQ is produced in association with a lepton and either a jet or a top-quark, are given as, 

    .[      pp       →   ϕ t ℓ       →  (tℓ)tℓ;      pp       →    ϕℓ j       → (tℓ)ℓ j ]}.



In Fig. <ref>, we show the parton level cross sections of different production processes of ϕ_1 [Fig. <ref>] and ϕ_5 [Fig. <ref>]. The single productions are computed for  =1.
We see that for ϕ_1, the single production processes depend heavily on whether it is an S_1 with  LCOS/RC type couplings or an S_3 with LCSS coupling. In the LCSS scenario, the pp→ϕ_1ℓ j becomes the dominant process beyond M_ϕ≳ 1 TeV whereas in the LCOS scenario, it overtakes the pair production only for M_ϕ>2.2 TeV. This difference happens since in the LCOS scenario, some single production diagrams [see e.g. Figs. <ref> & <ref>] interfere destructively because of the opposite relative sign of the _ℓ and _ couplings, whereas in case of LCSS, they interfere constructively. In the RC scenario, ϕ_1 does not couple to a b-quark or a left handed top quark (that can be produced from a W boson and a b-quark interaction) and hence we do not expect (pp→ϕ_1ℓ j) to be large. We see that (pp→ϕ_1ℓ j)<(pp→ϕ_1ϕ_1) for M_ϕ_1 < 3 TeV in this scenario. For ϕ_5, the cross section of pp→ϕ_5ℓ j processes in the LC scenario is smaller than that in the RC scenario, as ϕ_5 couples exclusively to a right handed top quark in this case. 

It is clear from the cross section plots that for order one , it is important to consider single productions while estimating the discovery prospects. Before we move on, we note that the cross section plots do not show the full picture, as one has to consider the branching ratios and the detector effects. In the LCOS and LCSS scenarios,  BR(ϕ→ tℓ) ∼ 50% whereas it is 100% in the RC and LC scenarios. 




 §.§ Signal Topology

In our analysis, we only consider the hadronic decays of tops to reconstruct them in the final states. The characteristic of our signal is the presence of one or two boosted top quarks forming one/two top-like fatjets and two high-p_ T leptons. From Eqs. (<ref>) and (<ref>), we see that if we define our signal as events containing exactly two high-p_ T  same flavour opposite sign (SFOS) leptons and at least one hadronic top-like fatjet in the final state then it would include both single and pair productions and enhance the sensitivity. 

There is some overlap between the pair and the single production processes. For example, at the parton level, a tℓ  tℓ final state can be produced from both the pair production process as well as the pp→ϕ tℓ processes. Hence one has to be careful to avoid double counting while computing single productions <cit.>. In our simulations we achieve this by ensuring that for any single production process both ϕ and ϕ^† are never on-shell simultaneously.









 §.§ The SM Backgrounds

The main SM background processes for this signal topology would be those which give two high-p_ T leptons and
a top-like jet originating from an actual top quark or other jets (which can come from hadronic decays of the SM particles or from QCD jets). We see that the single Z and t t processes contribute dominantly.
Processes with large cross section containing single lepton can also act as a background if the
second lepton appear due to a jet misidentified as a lepton. However, due to very small misidentification rate, these
class of processes contribute negligibly to the total background. 

Although some backgrounds are seemingly huge (see Table <ref>), events that would satisfy the final signal selection criterion
used in our analysis would actually come from a very specific kinematic region.
With this in mind, we generate the background processes with 
some strong generation level cuts, for better statistics and saving computation time,

Generation level cuts:


  * p_ T(ℓ_1)> 250 GeV,

  * the invariant mass of the lepton pair M(ℓ_1,ℓ_2) > 115 GeV (the Z-mass veto).

Here, ℓ_1 and ℓ_2 denote the leptons with the highest and the second highest p_ T, respectively.
We discuss the different background processes in more detail below.



  * V + jets:

Inclusive single vector boson (V=Z,W) production processes in the SM have very large cross sections and
therefore, can act as potential backgrounds for our signal even if the cut efficiencies are extremely small.
There are two types of single vector boson processes that we consider as potential backgrounds. 




  * Z/γ^* + jets:
This background is generated by simulating the process, pp→  Z/γ^* + (0,1,2,3)-jets→ℓℓ+jets 
matched up to three extra partons. Here, the two high-p_ T leptons can arise from the leptonic decays of the
Z-boson and a top-like fatjet can originate from the QCD jets. Since the invariant mass of the two 
leptons peaks at Z-mass, this background is controlled by the Z-mass veto. 



  * W + jets:
This process also has huge cross section like the previous one, but it is a reducible background. 
We generate it by simulating the process, pp→  W + (0,1,2,3)-jets→ℓν+jets matched up to three extra partons. 
Requirement of a top-like jet can be fulfilled if the QCD jets mimic as a top-jet. 

However, as we demand the second lepton also to have high p_ T where the 
lepton misidentification efficiency becomes small, we found this background to be negligible.



  * VV + jets:

There are four types of diboson processes viz. Z_ℓ Z_h, W_h Z_ℓ, W_ℓ W_ℓ and Z_ℓ H_h that can act as sources of two high-p_ T leptons. The subscripts “ℓ” and “h” represent leptonic and hadronic decay modes
respectively. In these cases, the required top-like jet can arise from the hadronic decay products of bosons or from
the QCD jets. Processes containing leptonically decaying Z can be drastically reduced by applying Z mass veto on
the invariant mass of the lepton pair. We do not consider the case where one lepton come from the vector boson decays
and the other appear due to jets misidentified as leptons. We generate matched event samples including up to two jets 
of these processes.  


  * tt + jets:

The SM top pair production at the LHC can provide us two high-p_ T leptons when both the tops decay leptonically.
Additionally, a top-like jet which arise from the QCD jets together with those two leptons can mimic our signal.
We find that, like the Z background, this contribution is also significant in our case. A priori, the t_ℓ t_h process where one top decays leptonically and the other
hadronically can also contribute to the background. We generate this events by matching up to two additional jets.


  * ttV:

The SM processes with a top pair associated with a vector boson can act as backgrounds for our signal.  We consider
the following four cases viz. t_ℓ t_ℓ Z_h, t_ℓ t_ℓ W_h, t_h t_h Z_ℓ, t_h t_ℓ W_ℓ depending on 
the decays of tops and vector bosons. We generate these event samples without adding extra jets in the final state. 


  * tW:

The SM pp→ t_ℓ W_ℓ process contains two leptons in the final state and contribute to the background for our 
signal. We generate this process using matching by adding up to two extra jets.


In Table <ref> we collect the total cross sections of the background processes computed at various orders of QCD available in the literature. From these we compute the K-factors and, as mentioned, scale the corresponding LO cross sections  in our analysis.









 §.§ Event selection


We apply the following sets of cuts on the signal and background events sequentially.







  * (a) At least one top-jet (obtained from HEPTopTagger) with p_ T(t_h) > 135 GeV.

(b) Two SFOS leptons with p_ T(ℓ_1)> 400 GeV and p_ T(ℓ_2)> 200 GeV 
and pseudorapidity |η(ℓ)|<2.5. For electron we consider the barrel-endcap cut on η between 1.37 and 1.52.

(c) Invariant mass of lepton pair M(ℓ_1,ℓ_2) > 120 GeV to avoid Z-peak.

(d) The missing energy E_T < 200 GeV.





  * The scalar sum of the transverse p_T of all visible objects, S_T>1.2× Min( M_ϕ, 1750) GeV.


  * M(ℓ_1,t) OR M(ℓ_2,t) > 0.8× Min(M_ϕ,1750) GeV.

In Fig. <ref> we show the final signal selection efficiencies (ε) for different coupling hypotheses. We define ε as,
ε= C_1+C_2+C_3/.
Since the M_ϕ dependent cuts (i.e., C_2 and C_3) get frozen beyond M_ϕ=1750 GeV, we see the kink-like shapes at 1750 GeV. 





















§ DISCOVERY POTENTIAL



With the number of signal (N_S) and background (N_B) events surviving the selection cuts defined in Section <ref>, we estimate the expected significance (Z) using the 
following formula:


    Z =√(2(N_S+N_B)ln(N_S+N_B/N_B)-2N_S)  .

In Fig. <ref>, we show the expected  significances for observing the ϕ_1 and ϕ_2 signals in the benchmark coupling scenarios (Section <ref>) over the SM backgrounds in the muon mode as functions of their masses for  3 ab^-1 of integrated luminosity at the 14 TeV LHC. 
As explained, we have used the combined signal (i.e.
pair and single production events together) to estimate the significances in the LCOS, LCSS, RC and LC scenarios with =1. For the LCOS and LCSS scenarios, the BR of 
LQ to te mode is 50% whereas for the RC and LC scenarios it is 100%. For comparison, we also show the expected significance for only the pair production 
(i.e. → 0) with 50% and 100% BR cases. In Table <ref> we explicitly show the mass values corresponding to 5 (discovery), 3 and 
2 (exclusion) significances for different coupling hypotheses in both e and μ channels.






As already mentioned, the CMS collaboration has projected the expected significance for scalar LQs decaying into tμ pairs in the pair production channel at the 14 TeV HL-LHC <cit.>. There, with 100% BR in the tμ mode, the 5 discovery reach goes to about 1.8 TeV (considering statistical uncertainty only). Our estimate is quite close, ∼1.7 TeV if we consider only pair production with 100% BR in the ϕ_1→ t decay
mode (see Table. <ref>). This reach can decrease to 1.4 TeV if the BR falls by 50%. However, if we include single productions, the 5 reach goes up to 2.1 TeV in the LCSS scenario (where the ϕ_1 behaves like the charge 1/3 component of S_3). This drastic enhancement of 700 GeV in the discovery reach happens because of the (relatively) large pp→ϕ_1ℓ j cross section in the high mass region leading to a substantial number of events surviving the applied selection cuts. However, in the LCOS scenario where a ϕ_1 behaves like an S_1, this increment is minor, just about 50 GeV, as destructive interference reduces the single production cross sections.

In the RC scenario, the total single production cross section of ϕ_1 is small compared to the pair production one. Hence, the discovery reach is almost identical to that in the pair production only case. A similar situation is observed in the LC scenario for ϕ_5. As explained in Section <ref>, in both the RC scenario for ϕ_1 and the LC scenario for ϕ_5, leptoquarks couple to the right-handed tops. As a result, single productions in these cases have small cross sections as right-handed tops can  couple to
the charged current only via chirality flipping. 

For any M_ϕ our signal cross section depends on  as,
_signal ≈_pair(M_ϕ) + ^2 _single(=1,M_ϕ), 
i.e., for any M_ϕ if  increases the signal increases. Using this relation one can recast the plots in Fig. <ref> in the -M_ϕ plane, as we have done in Fig. <ref>. These plots show the lowest  needed to observe  ϕ_1 and ϕ_5 signals with 5 significance for a range of M_ϕ with 3 ab^-1 of integrated luminosity. For all the points below a curve, the expected significance would be less than 5. In Fig. <ref> we show the corresponding plots for 2 significance. In other words, these plot give us the lowest couplings that can be excluded at the HL-LHC.








§ SUMMARY AND CONCLUSIONS


In this paper, we have studied the HL-LHC reach for discovering scalar LQs that
decay to a top quark and a charged lepton. In particular, we have focused on
charge 1/3 (ϕ_1) and 5/3 (ϕ_5) scalar LQs that produce a resonance system with hadronically decaying boosted top quark and an electron or a muon. 
According to the classification given in Refs. <cit.>, only
 S_1, S_3 (charge 1/3 component of the triplet) and R_2 (charge 5/3 component of the doublet) scalar LQs can produce the specific signatures we consider. We have also introduced
a simplified Lagrangian for ϕ={ϕ_1,ϕ_5} suitable for bottom-up searches. We have shown how these simplified models connect to the actual models for different
coupling configurations. 

LQs can be produced in pairs or singly (pp→ϕℓ j,ϕℓ t) at the LHC. When a LQ couples mostly with 
the third generation quarks, usually the pair production channels are considered for their discovery assuming the single
productions to be suppressed because of small b-PDF. Interestingly, we find that for order one couplings, cross section of
some single production channels can be larger than the pair production cross section. Hence, it is natural to expect that 
the inclusion of these single production channels would, therefore, increase their discovery prospects beyond the pair
production searches. However, this 
depends on the underlying model; 
the pp→ϕ_1 ℓ j single production cross sections can differ drastically depending on the representation in which 
ϕ_1 belongs to.
In particular,
for the charge 1/3 component of S_3 (the LCSS scenario, see Section <ref>), pp→ϕℓ j has larger cross section than the pair production in the heavier mass region. This also happens for R_2^5/3 (with y^LR type coupling
 the RC scenario). 
However, for S_1 (the LCOS scenario), the single productions have smaller cross sections because of  destructive 
interference between certain diagrams [which is caused by the opposite signs of the left handed charged lepton and neutrino couplings, see Eq. (<ref>)].

We have proposed a selection criterion that would retain events from both pair and single production processes so that the 
search becomes a combined one with increased reach. Our signal topology is defined by at least one hadronically decaying
boosted top and two opposite sign same flavour leptons. 
With this, we have found that the 5σ discovery reach for ϕ_1 in LCSS scenario with =1 is about 2.1 TeV at the 14 TeV LHC with 3 ab^-1 integrated
luminosity. In the LCSS scenario, the BR ϕ→ tℓ mode is 50% and the reach for the pair production is only about 1.4 TeV. This significant improvement is due to constructive 
interference among certain single production diagrams. This increases the pp→ϕℓ j cross section about one order
in magnitude compared to the LCOS case where destructive interference  makes single production less important.
Finally we note that the enhancements of discovery reach due to the single production channels would increase further if the new couplings are more than one as the single production cross sections scale as square of the coupling involved. 


T.M. is grateful to the Royal
Society of Arts and Sciences of Uppsala for financial support as a guest researcher at Uppsala University during the initial stage of this project. S.M. acknowledges support from the Science and
Engineering Research Board (SERB), DST, India under grant number ECR/2017/000517. We thank R. Arvind Bhaskar for reading and commenting on the manuscript.



JHEPCust

