Current status on pair-produced muon-philic vectorlike leptons in multilepton channels at the LHC

In this work, we obtain the current limits on the pair production of vectorlike leptons decaying to a Standard Model gauge boson and a lepton in the second generation using the Run-2 data at the LHC. Since there is no dedicated search out of Run-2 data, we recast the ATLAS analyses searching for the type-III seesaw heavy leptons in the multi-lepton channels. There is no limit for the SU(2)L singlet vectorlike lepton beyond about 100 GeV, while the limit is about 780 GeV for the doublet one. Thus, dedicated searches for the vectorlike leptons are necessary, especially for the singlet one. We also study the general cases of the vectorlike lepton decays and future sensitivities at the HL-LHC.

In this paper, we study pair-productions of the VLLs, through the Drell-Yan process, decaying to the second generation lepton, namely muon-philic VLL.Such VLL is well motivated to explain the experimental anomalies in the muon g − 2 [69,79,80] and the semi-leptonic B decays [81]. 3In this work, we obtain the current limits using the Run-2 data at √ s = 13 TeV by simply recasting the ATLAS analyses searching for the triplet lepton in the type-III seesaw [84,85].We then estimate expected sensitivities at the HL-LHC using the same channels.
This paper is organized as follows.We briefly explain the VLLs in Sec. 2 and discuss the analysis strategy in Sec. 3. Our main results are shown in Sec. 4. Finally, we summarize the paper in Sec. 5.

Vectorlike lepton scenario
In this work, we consider the two kinds of VLLs whose gauge quantum numbers are given by where r Y is a representation r under SU (2) L and the index Y is the hypercharge under U (1) Y .
Here the electric charge is given by Q = T 3 + Y , with T 3 being isospin.The doublet L has two components denoted by (L 0 , L − ), where the superscript is the electric charge.These VLLs can be considered as the fourth generation leptons since L and E have the same quantum numbers as the SM leptons.
For simplicity, we assume that one of the VLLs is heavy enough so that the lightest charged VLL is almost either singlet or doublet 4 .Under this assumption, the mass of the neutral VL lepton L 0 is the same as that of the charged counterpart L − approximately.We further assume that the VLLs exclusively couple to the second generation of the SM leptons to avoid lepton flavor violations strongly constrained by the experiments.In Fig. 1, we show the next-to-leading order (NLO) cross sections of the VLL pair production, pp → EE or LL, at √ s = 13 TeV.The cross sections at the fixed-order NLO are calculated by using MadGraph5 [87] based on the UFO model file [88] developed in Ref. [89].
The lightest charged VLL decays to a SM boson and a lepton in the second generation E − /L − → W − ν µ , Zµ − , hµ − if there is no new particle lighter than the VLL.The neutral one L 0 decays as L 0 → W + µ −5 .If the mass of the lightest charged VLL is large enough compared to the SM boson masses, the branching ratios are given by BR as expected from the Goldstone boson equivalence theorem.Nevertheless, we shall allow other values of the branching ratios since the above patterns can be broken when some of the new Yukawa couplings have a certain hierarchical structure [32,75].

Analysis
In this section, we summarize our strategy to recast the ATLAS analyses searching for the triplet leptons in the type-III seesaw model [84,85].In Ref. [84], the signals are composed of two light leptons, i.e. e or µ, with at least two jets and large missing energy, where the two jets are from a Z/W boson decay.Both opposite sign (OS) and same sign (SS) leptons are searched in the analysis, but in our case the signal will not contribute to the signal regions (SRs) with the SS leptons because our neutral VLL, L 0 , is a Dirac but not a Majorana fermion.We also note that the SRs containing muons will be the most important to identify the muon-philic VLL.In Ref. [85], the signals with 3 or 4 leptons are studied.Overall, our final states should be either di-leptons with a hadronic Z/W boson or 3/4 charged leptons involving muons.
We simulate the signal events by using MadGraph5 [87] based on the UFO model file generated by FeynRules [90,91].The decays of the VLLs are handled by MadSpin [92], and then the parton-level events are showered and hadronized by PYTHIA8 [93].The pair productions of the VLLs are simulated up to one additional parton using the MLM matching [94] with xqcut = m VLL /10.The fast detector simulation is performed by Delphes3.4.2 [95] with the default ATLAS card.Jets are reconstructed using the anti-k T algorithm [96,97] with ∆R = 0.4.The same cut conditions are applied for the generated events as the ATLAS analyses [84,85], but the object-based missing transverse momentum significance S(E miss T ) is calculated by the approximated one S(E miss H T , where E miss T is the missing transverse momentum and H T is the sum of transverse momenta of visible particles [98].Note that the Higgs decays are irrelevant for the SRs where the b-tagged jets are vetoed. 6e shall study the pair productions of the VLLs: followed by the decays of the VLLs to a lepton in the second generation and a Z or W boson.We label the processes as XY -V V ′ , where X, Y are pair-produced VLLs.In this labeling, X, Y = F ± , L 0 , where F ± = E ± , L ± .The kinetic distributions will be common for E ± and L ± , while the production cross sections are different.V (V ′ ) is a SM EW gauge boson from the decay of X (Y ).The processes labeled by F + F − -W W will not contribute to the SRs because the leptons produced from the VLL decays are neutrinos, and hence the numbers of leptons are not enough to pass the cuts.Altogether, the relevant processes are so we simulate these 5 processes.We use the statistic variable q µ defined as [99], where the likelihood function is given by Here, n i , s i , b 0 i and σ i are respectively the number of observed, signal, background events and the error of the number of backgrounds in the bin labeled by i.Note that the SRs in the analysis are exclusive with each other because these have the different number of leptons.In Eq. ( 5), b is the number of backgrounds which maximizes L for a given µ, and (μ, b) are the values of (µ, b) which maximizes L. We only consider the uncertainties from the backgrounds which are typically the dominant sources for the errors.The 95% C.L. limit is defined as [100] CL where Φ is the cumulative distribution function of the normal distribution.Here, q A µ is the test statistics in Eq. ( 5) by replacing n i → b 0 i .For the future limits, the significance is given by [99] The number of signal and background events (its error) are rescaled as R L ( √ R L ), where R L is the ratio of the integrated luminosity L. The number of observed events and the estimated backgrounds are shown in the ATLAS papers [84,85].The number of signal events is calculated as where P = F − F + , L 0 F ± , L 0 L 0 labels the production of the VLL pairs whose cross section is σ P , and D = ZZ, W W, W Z labels the decays whose branching fraction is Br D given by BR , where ℓ 2 = µ, ν µ .ϵ P,D i is the number of events passing the cut in the bin i, per the number of events generated.We obtain the values of ϵ P,D i by the simulation.
σ upper limits

Results
In this section, we explain our analysis results on the signal efficiencies, the current limits, and the future limits after the full running of the HL-LHC.Figure 2, except the bottom-right panel, shows the efficiencies of the processes in the relevant SRs: eµ-OS and µµ-OS for the two lepton final states defined in Table 2 of Ref. [84], and 3ℓ-ZL, 3ℓ-ZLveto, 3ℓ-JNLow, 4ℓ-Q0 and 4ℓ-Q2, defined in Tables 2 and 3 of Ref. [85].Here, the label ZL represents leptonically decaying Z boson, and it is required to exist in 3ℓ-ZL and 3ℓ-JNLow, while it is vetoed in 3ℓ-ZLveto.The jet multiplicity is required to be less than one in 3ℓ-JNLow.For the 4ℓ SRs, Q is the absolute value of the sum of the lepton charges in final states and it is required to be zero or two.Note that the 4ℓ-Q2 SR is possible only when some of the leptons are missing and hence the corresponding efficiencies are lower than the others.The efficiencies are smaller than 10 −3 in the other SRs, namely ee-OS and ℓℓ ′ -SS (ℓ, ℓ ′ = e, µ), because the VLLs decay to the second generation leptons and they preserve the lepton numbers.Note that the efficiencies in the 2ℓ SRs decrease for the heavier VLL mass since the event selection requirement 60 < m jj < 100 GeV in Ref. [84] is less likely to be satisfied.Whereas, those in the SRs with 3 or 4 leptons increase for heavier VLL due to larger lepton transverse momentum.All of the efficiencies drop for light VLL where m VLL ≲ 200 GeV, due to the requirement of two leptons with p T > 40GeV.We point out that the 4ℓ-Q0 SR and µµ-OS are the dominant event selection category for the F + F − -ZZ channel where the even numbers of leptons are predicted.For the channels involving a W boson, the 3ℓ-JNLow SR is the most important, particularly for heavier VLL with m VLL ≳ 700 GeV.There are three leptons if a W boson decays leptonically with about 20% BR, and the cuts for the invariant masses of 2-4 leptons systems and H T + E miss T are not applied in the 3ℓ-JNLow.The tighter cut for m T (ℓ 1,2 ) than the other 3ℓ-SRs are easily satisfied for heavier VLLs, and thus the efficiency increases for heavier VLLs in this SR.
In addition to the efficiencies, we show the 95% C.L. upper bounds on the production cross sections based on the individual SRs on the bottom-right panel of Fig. 2. The total cross sections of the charged VLL pair-productions are shown for comparison.The limits can be obtained by multiplying the factor from the branching fractions to the SM gauge bosons, i.e.Br D in Eq. (9).Note that the limits are from the individual processes, and the actual limits on the VLLs shown in the following will be obtained by combining these processes.
We obtain the current limits on the VLLs with the signal efficiencies.Figure 3 shows the 95% C.L. lower limits on the VLL mass in the two dimensional plane of the branching ratios into W boson and Z boson.The VLL is a SU (2) L singlet (doublet) in the left (middle and right) panel.In the middle panel, only the charged VLL production is taken into account, which can be applied to the scenarios with large mass splitting between the neutral and charged VLLs, m L 0 ≫ m L ± , in a theoretical set-up such as mixing with additional neutral particles [29].If the masses of charged and neutral leptons are sufficiently degenerate, the results on the right panel are applied.
In the left panel of Fig. 3, we see that the current limit on the singlet VLL mass reaches about 400 GeV for large BR(E → Zµ) ∼ 1 due to the leptonic decay modes of Z boson.However, there is no limit for BR(E → Zµ) ≲ 0.5 due to the small production cross sections of pp → EE.In particular, no limit beyond about 100 GeV exists in the case of the minimal singlet VLL model shown in Eq. ( 2), pointed by the orange marker.On the other hand, the limit is stronger for the doublet case because of the larger cross sections.Without the production of the neutral VLL the limit is about m VLL ≳ 500 GeV for BR (L → Zµ) ∼ 1 and m VLL ≳ 150 GeV up to BR (L → Zµ) ≳ 0.3.With the production of the neutral VLL, we obtain the lower limit of VLL mass at least 620 GeV, dominantly determined by L 0 L 0 -W W .The limit reaches to 800 GeV for BR (L → Zµ) ∼ 1, and the limit for the minimal doublet VLL scenario in Eq. ( 3) is about 750 GeV.Note that the sensitivities are mostly determined by the final states belonging to 3ℓ-ZNLow or 4ℓ-Q0 SRs as seen in Fig. 2, requiring high lepton multiplicity.Therefore, the contours in Fig. 3 depend more on BR(E/L → Zµ).
Figure 4 shows the same figure as Fig. 3 but with the 3 ab −1 data at the future HL-LHC.Interestingly, we expect the full running of the HL-LHC can probe a much wider range of the singlet VLL, as shown in the left panel of the figure.The expected sensitivity on the lower limit of m V LL is about 650 GeV for BR (E → Zµ) ∼ 1, and it reduces to 100 GeV for BR (E → Zµ) ∼ 0.1.It is remarkable that the minimal scenario in Eq. ( 3) can be constrained (discovered) up to about 420 (250) GeV.From the middle panel, without including the neutral VLL productions, the limit is at most 750 GeV for BR (L → Zµ) ∼ 1 and the limit decreases to 100 GeV as BR (L → Zµ) decreases up to about 0.1-0.2depending on BR (L → W ν). With the neutral component productions, from the right panel, the expected limit is about 1050 GeV for BR (L → Zµ) ∼ 1, and decreases to 880 GeV for BR (L → Zµ) ∼ 0.

Summary
In this work, we studied the LHC searches for the pair productions of the fourth generation VLLs which decay to a SM EW boson and a lepton in the second generation.We recast the ATLAS analyses searching for the triplet lepton in the type-III seesaw [84,85].In general, the limits for the VLLs are weaker than those for the triplets because the production cross sections are smaller and our VLLs are Dirac fermions not producing the lepton number violating signals.
In the minimal scenario, shown in Eqs. ( 2) and (3), there is no limit beyond about 100 GeV on the singlet VLL even with the Run-2 data, while the limit is at about 750 GeV for the doublet case.To obtain the limits for the singlet case using the Run-2 data, we should consider more dedicated analysis to overcome the small production cross sections, e.g. by lowering the threshold for lepton p T 's, to be sensitive for the VLL masses within 100-200 GeV, and searching for a 3ℓ resonance decayed from a charged VLL.For the singlet case, it would also be efficient to search for the decays via the SM Higgs boson which dominantly decays to a pair of bottom quarks.
We also obtained the expected sensitivities at the HL-LHC with 3 ab −1 data and found the future limits would reach to 420 (950) GeV for the singlet (doublet) case.It is remarkable that the future experiment will put the limit on the minimal scenario of the singlet VLL.Note that our analysis covers the general cases where the branching fractions can be different from those in Eqs. ( 2) and (3).The most significant decay mode is E ± , L ± → Zµ ± , and hence the limits become the most stringent for BR (E, L → Zµ) ∼ 1, and are weaker for smaller BR (E, L → Zµ).
The muon-philic VLLs are known to be a good candidate to explain the muon g −2 anomaly.In such a case, the chiral enhancement of the muon g − 2 by the muon-philic VLLs is correlated to the rate for h → µ + µ − , and the VLLs lighter than about 500 GeV may be excluded [60,61,86].Our searches can constrain the scenarios of explaining the muon g−2 by the chiral enhancement of light VLL correlated with the rate for h → µ + µ − as well.The comprehensive study for the VLL explanation of the muon g − 2 is our future work.

Figure 2 :
Figure 2: Efficiencies from the processes studied in this work.Here, F ± = E ± , L ± is one of the charged VLLs.In addition to the efficiencies, we show the 95% C.L. upper bounds on the production cross sections based on the individual SRs on the bottom-right panel.The gray lines show the production cross sections of the VLL pairs.

Figure 3 :
Figure 3: Current 95% C.L. limits on the VLL masses for the singlet VLL (left), doublet without L 0 (middle) and doublet with L 0 (right).There is no limits on the mass in the white region where the corresponding BRs are too small.The orange points indicate the predictions in the minimal scenarios.

Figure 4 :
Figure 4: The same figures as Fig. 4, but showing the future exclusion limits at the HL-LHC.