Search For a Leptoquark and Vector-like Lepton in a Muon Collider

The proposal for a high-energy muon collider offers many opportunities in the search for physics beyond the Standard Model (BSM). The collider by construction is likely to be more sensitive to the muon-philic models, primarily motivated by the BSM explanation of muon $(g-2)$ excess and quark flavor anomalies. In this work, we explore the potential of the proposed muon collider in the context of such models and focus on one such model that extends the Standard Model (SM) with a leptoquark, a vector-like lepton, and a real scalar. In this model, we propose searches for TeV scale leptoquarks in $2\mu+2b+mET$ channel. Notably, the leptoquark can be produced singly at the muon collider with a large cross-section. We have shown that a significant signal in this channel can be detected at a 3~TeV muon collider even with an integrated luminosity as low as $\sim 10$~fb$^{-1}$


I. INTRODUCTION
In the high energy frontier, the highest energies have been achieved in the hadron colliders since the protons could be accelerated to much higher energies than the electrons.
The Large Hadron Collider (LHC) has achieved an impressively high beam energy of 6.8 TeV for each colliding proton, making it the highest ever for any collider.The available hard scattering energy would be much more in a hadron machine compared to a machine containing electron or positron beams.The hadron machines, however are unable to use the full energy of the colliding protons due to their composite nature.Moreover, while having several advantages in the energy frontier, the hadron collider is plagued by a noisy environment in the form of unwanted hadronic activity and smearing effects from the parton distribution functions (PDFs), which compromises the precision studies.On the other hand, a much higher energy of the muon beams is achievable through a circular collider due to its significantly smaller synchrotron radiation compared to an electron beam.The muon, being an elementary particle, can, therefore, give high centre-of-mass energies in the hard collisions with a very little energy spread due to the suppressed radiative effects of bremsstrahlung and beamsstrahlung [1,2].This, in turn, helps in the precision measurement of observables and particle properties.Another interesting possibility at these very highenergy muon colliders would be the generation of electroweak gauge bosons as partons of the beam through collinear radiation.These will emerge as electroweak PDFs [3][4][5][6], that can have implications in the study of vector boson fusion (VBF) processes.It is for this reason that the muon collider is also advocated as a "VBF collider" [7].So, to some extent, a muon collider combines the advantages of pp and ee colliders, i.e. the benefits of high energy and high precision [3,4,[8][9][10][11].Thus, the proposal for a high-energy muon collider by the International Muon Collider Collaboration (IMCC) is an important development and a recent growing interest in collider physics [12][13][14][15].
The muon collider will mark a new frontier in collider physics, with high luminosity and beam intensity, including 1 ab −1 for a 3 TeV machine and 10 ab −1 for a 10 TeV machine [3,8].
Its uniqueness lies in the muon beams themselves and it will be the first time in human history that a particle collider will be built with a second-generation particle.Therefore, it offers opportunities to directly study muon-related physics [16][17][18][19][20][21][22].The potential of physics searches of the proposed muon collider has been explored over the last few years.In most studies, the investigations were primarily aimed at the center of mass energy of 10 TeV or more [14].Furthermore, one expects that the integrated luminosity achievable in this 3 TeV machine will be nearly 1 ab −1 , comparable to the luminosity achievable at the 14 TeV LHC.
Therefore, the early stages of the muon collider could prove crucial in identifying new physics signals that LHC might not be able to probe even with its high luminosity option.
The broad classes of physics studies at the muon collider consist of precision measurement of electroweak interactions [23][24][25], Higgs properties [17,19,20,[26][27][28][29][30], exploration of new physics sensitivity via higher dimensional effective operators [31], and new physics searches for well-motivated models beyond the SM (BSM) [32][33][34][35][36][37][38][39][40][41][42][43].The 'muon-specific' BSM models have an additional advantage in the muon collider [44,45] as they would lead to direct interactions of the new physics sector with the primary colliding beams.The 'muon-philic' (µ-philic) BSM models have been of wide interest, primarily because of the observed excess in the anomalous magnetic moment of the muon, namely (g − 2) µ [18].The latest measurement by the 'Muon G-2' collaboration at Fermi National Laboratory (FNAL) combined with the E989 experiment at the Brookhaven National Laboratory (BNL) stands at 5.1σ from its prediction by the Standard Model 1 .In addition, one can also contemplate scenarios where non-trivial physics may be lurking at electroweak energies.These scenarios are likely to stay hidden because they do not interact with the first generation of the SM fermions which have made up almost all the high energy collider primary beams.The proposed muon collider can be a perfect opportunity to search for such µ-philic models.
In this work, we study a new physics scenario containing a leptoquark, a real scalar, and a pair of vector-like leptons (VLL) in the context of a 3 TeV muon collider.This model was proposed to address various flavor anomalies in the quark sector.Its phenomenological implications and collider studies have been discussed in Refs.[62][63][64][65].The model gives rise to non-universal couplings for different generations of leptons (quarks) to the VLLs and real scalar (leptoquark).With an appropriate choice, these non-universal couplings help in explaining the excess in both the quark flavor violation [66][67][68][69][70] and muon magnetic moment, while the lepton flavor violating (LFV) processes remain within the existing experimental bounds.We note that interesting phenomenological studies may exist when the model contains vector-like quarks in addition to VLLs [71][72][73][74].We however restrict ourselves to a model containing only VLLs in this work.
We note that there have been recent works on leptoquark [8,[75][76][77][78] and VLL [41,79] searches in a muon collider.In our study, we perform a search for leptoquarks in the 2µ + 2b + / E T final state, extending our earlier study in the context of LHC in Ref. [64], where we mainly focused on the sub-TeV masses of the leptoquark, as LHC is not very sensitive to heavier masses.However, due to the µ-philic nature of the model and the absence of a huge QCD background, a better opportunity to search for such a scenario is easier in the muon collider.In this work, we show that the signature of this model in the same channel for leptoquark mass of around 2 TeV is within the discovery range with just a few fb −1 of integrated luminosity at the 3 TeV muon collider2 .However, as the mass of the leptoquark approaches the kinematic threshold of the collider, it will be difficult to carry out the search and require a higher center of mass energy at the muon collider.
The paper is organized as follows.In section II, we briefly discuss the model we study in this work.In section III, we examine how the theoretical and experimental constraints affect our model parameter space.In section IV, we discuss the possibility of probing the leptoquark at a 3 TeV muon collider and finally summarize and conclude in section V.

II. MODEL
The model is an extension of the SM particle content where we add new particles, namely, a real scalar (S), a pair of vector-like leptons (ℓ 4L , ℓ 4R ), and a scalar leptoquark (Φ).The only new symmetry introduced beyond the SM gauge symmetry is an additional Z 2 symmetry with an odd charge to all the new particles.
Under this new gauge group symmetry of transformation properties and charges of the new fields are given in Table I.
The gauge invariant Lagrangian density for the new fields and their interaction with the SM fields is given by The introduction of new neutral scalars generally affects the properties of the SM Higgs boson through mixing with these additional scalars.However, the mixing will be prohibited due to the unbroken Z 2 symmetry in the new sector, as it prevents all such mixing terms at the tree level.This is due to the fact that the new real scalar S is forbidden from getting vacuum expectation value (vev) owing to its Z 2 odd nature.So, the SM Higgs boson becomes massive after the spontaneous breaking of the electroweak symmetry.The masses of Φ and S on the other hand get additional contributions proportional to the electroweak vev which shifts their masses from µ Φ and √ 2µ S by the λ HΦ and λ HS terms, respectively.The masses then become and where v is the vev of the SM Higgs doublet.
Furthermore, the couplings of the SM Higgs boson with the other SM particles remain unchanged at the tree level.Additionally, the new particles are kept heavier than the SM Higgs boson in order to prevent the decay of the Higgs boson to any new modes.
All new contributions to the interaction terms of the SM particles come at the loop level.Note that the leptoquark (Φ) carries a non-zero hypercharge Y as well as color charge and will contribute to both the hgg and hγγ couplings at one loop.This change in coupling affects the Higgs signal strength [80].However, the contributions to the Higgs signal strength in the gluon-gluon fusion production mode and γγ decay channel are suppressed and are well within the 2σ limit, provided we keep the leptoquark mass sufficiently heavy [64].
The leptoquark and VLL also interact at the tree level with the SM fermions through the h i and h ′ j couplings.These two sets of couplings are crucial in addressing the excess observed in the experiments and affect the lepton and quark sector properties through the mediation of the new particles in the loop.These two couplings h i and h ′ j get modified after the mixing of quarks and leptons via Cabibbo-Kobayashi-Maskawa (CKM) and Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrices, respectively.The couplings of the leptoquarks and VLL's with the SM fermions in the physical (mass) basis become where U d and U ℓ are the unitary mixing matrices of down-type quarks and leptons, respectively.Non-observation of any significant anomaly in the K 0 -K 0 and B 0 -B 0 oscillations put restrictions on the couplings of the first two generations as h ph 1,2 ≃ 0 [63].On the other hand, the observed mass splitting between the physical states in the B 0 s -B 0 s sets a constraint |h ph 2 h ph 3 | ≲ 0.65 [63,81].The other coupling h ph 3 does not have strong upper bound from experiment and we have kept it below perturbativity limit [63].
One of the central features of this model is that it can account for the observed excess of the anomalous magnetic moment of muon (g − 2) µ .This excess is explained by introducing the VLLs ℓ 4 and the real scalar S at the one-loop.The lepton flavor violation in µ → eγ and τ → µγ can be kept under control by choosing h ′ 1 and h ′ 3 coupling small.The neutral scalar S can be chosen to be the lightest one among all the Z 2 -odd particles.Thus, the particle S can act as a dark matter (DM) candidate.The details of the new physics contribution of this model to (g − 2) µ , implications in flavor physics, and DM aspect of the model have already been studied and analyzed in Ref. [64], and this will be briefly discussed in the next section.

III. THEORETICAL AND EXPERIMENTAL CONSTRAINTS
We implement the model file in SARAH [82] and SPheno [83] is used to generate the spectrum files.We use SSP [84] for scanning the parameter space.For the scanning, we have varied the masses in the following range: The lower bound of 102.6 GeV on the mass of the charged lepton M ℓ 4 comes from Large Electron Positron collider (LEP) [85].As we will be analyzing the signal at 3 TeV muon collider, we have taken the maximum mass of the LQ to be 3 TeV.The scan range of the VLL is taken to be 500 GeV since it is favored by muon anomaly data.We will see this in the next subsection.As we want our scalar to be a dark matter candidate, for the scan we have taken M S < M ℓ 4 and to evade the h → invisible decay constraints, we have taken the lower bound on scalar mass to be 65 GeV.

A. Muon anomaly and Lepton Flavor Violation
In its recent report [46], the 'Muon G-2' collaboration at the Fermilab National Accelerator Laboratory (FNAL) has announced the experimental measurement of muons anomalous magnetic moment [48].This anomalous part a µ is defined in terms of the gyromagnetic ratio or Landé g-factor, which is expected to be 2 at the tree level, as a µ ≡ (g − 2)/2.After taking the effects of loop corrections, the value of a µ in the SM is expected to be more than zero, and its predicted value, calculated in the SM comes out to be [48-56, 86-97] On the other hand, the experimental uncertainty in the measurements has been brought down by the 'Muon G-2' collaboration at FNAL [98][99][100] and it has improved significantly to almost half of the uncertainty in the prediction from the SM.However, the measured central value of a µ in its Run-2 plus Run-3 [46] remained almost the same as the Run-1 [99,100].The new measurement of a µ reads as [46] a We note here that there are tensions in the SM prediction for the a µ in Eq. 5 mainly in the hadronic vacuum polarization (HVP) contribution.In the consensus prediction by Ref. [48], the HVP contributions are calculated using experimental e + e − annihilation data [49][50][51][52][53][54][55].An alternative ab initio calculation using lattice QCD techniques [56][57][58][59][60] for the HVP contribution weakens the tension between the theory prediction and experimental result.Furthermore, the recent e + e − → π + π − result from the CMD-3 experiment [61] disagrees with all previous measurements of this cross-section used in the 2020 White Paper [48] and leads to reduced tension with the experimental result.At present, any firm comparison of the muon (g − 2) measurement with the theory is hard to establish and we therefore choose to work in the paradigm that a 5.1σ excess exists, and a contribution from new physics is needed.
In our model, at one-loop, the new physics (NP) contribution to a µ comes from the scalar S and the VLL and the extra contribution can be expressed as [62,64] where m µ is the mass of muon and loop function A similar set of Feynman diagrams to muon anomaly will contribute to the LFV process.
We have plotted the allowed parameter space for muon anomaly and LFV in M S -M ℓ 4 and h ′ 2 -M ℓ 4 plane in Figs.1(a) and 1(b), respectively.From the figure, we find that the muon anomaly data favors M ℓ 4 ≲ 330 GeV and h ′ 2 ≳ 1.5.The constraints coming from the LFV processes can easily be satisfied by tuning the h ′ 1 and h ′ 3 couplings [64].We have kept the values of h ′ 1 and h ′ 3 couplings O(10 −5 ) and O(10 −2 ), respectively.Another point worth noticing here is that since the leptoquark is odd under Z 2 and has no direct interaction with any SM lepton (see Eq. 1), it will not contribute to the muon anomaly and any LFV processes at one loop.It, however, will have a role in quark flavor violation, which puts limits on the leptoquark mass-coupling plane.

B. Dark Matter
In our model, by virtue of Z 2 symmetry, the lightest BSM particle can act as a DM.In this work, the scalar S is assumed to be the lightest in the BSM sector.This scalar can, therefore, act as a DM candidate.In the present context, we avoid a detailed discussion of the DM aspect of the model.In what follows, we will treat the DM as a type of weakly interacting massive particle (WIMP) that was abundant in the early phase of the universe and was in thermal equilibrium with the other SM particles.As the universe cooled down and expanded, the lighter states did not have sufficient thermal energy to produce the heavier DM particles through interactions, and the DM number density became too low to support further interactions and subsequently 'froze out', becoming a persistent relic within the Universe.
The latest measurement of the DM relic density given by Planck [104] is Ω c h 2 = 0.1198 ± On the other hand, the indirect detection experiments constrain the thermally averaged DM annihilation cross-sections ⟨σv⟩.For the mass range in our work, the Fermi Large Area Telescope (Fermi-LAT) [106][107][108] and MAGIC collaboration [109,110] provide an upper limit at 95% C.L. on the DM annihilation cross-section to be ∼ 10 −25 cm 3 /s [111] in the µ + µ − channel.
We have performed a scan to satisfy these DM-related measurements, assuming S as the DM candidate.For the scan, we generated the CALCHEP [112] model file from SARAH [82] and pass it through MICROMEGAS [113], which calculates the DM observables like relic density Ω DM h 2 , spin-dependent (σ SD ) and spin-independent (σ SI ) cross-sections, and the thermally averaged annihilation cross-sections (⟨σv⟩).The direct detection constraints are easily satisfied in our model since the scalar S has no direct coupling with the nucleons.On the other hand, in indirect detection, the strongest limits on the parameter are expected from the µ + µ − channel because of the muon-philic nature of the model.For the parameter range considered in this work, the value of (⟨σv⟩) in this channel lies below the observed value, i.e. below 10 −25 cm 3 /s.For the relic density, we require that the DM should not be over-abundant in the present universe, i.e. the relic density should be below the observed value by the PLANCK [104].In Fig. 2, we show the allowed parameter space in M S -M ℓ 4 plane, which satisfies the DM constraints.In the same plane, the allowed point by the muon anomaly data has also been plotted in Fig. 2. We see that smaller mass differences between the DM and VLL are more favored from DM constraints.

C. EW and collider constraints
The high value of h ′ 2 needed for the explanation of the observed excess in the (g−2) µ affects the Zµ + µ − coupling the most.This coupling is measured to be well within SM prediction via electroweak precision observables (EWPO) at the LEP.The deviation allowed for new physics by the EWPO at 2σ is 0.8% [62], i.e.
The loop diagrams contributing to the g µ L coupling are similar to that of the (g−2) µ diagrams with the external γ being replaced by Z bosons.The NP contribution can be expressed as where and q is the momentum transfer, i.e. momentum carried by Z boson and For h ′ 2 = 3.0 and masses M S , M ℓ 4 > 100 GeV, the changes are less than 0.3% [64], which is well within the current limit.We have also checked with h ′ 2 = 3.52 and have obtained the maximum change to be ≈ 0.4%.
The above discussion on the consistency of the parameter space with experimental measurements indicates that the suitable range for relevant parameters could be With this note, we choose four benchmark points tabulated in Table II for our collider studies that will be described in the next section.

IV. COLLIDER SEARCHES
In this section, we discuss the possibility of producing the leptoquark (Φ) and VLL (ℓ 4 ) at the muon collider and study the signature of the associated production of these particles.As opposed to the hadron collider, the pair production of both the leptoquark and VLL at a 3 TeV muon collider will proceed via the photon and Z boson exchange which will have a large s-channel suppression.A more promising channel would be the single production of the leptoquark through the associated production with a VLL and a b quark.
This 2 → 3 process is found to generate a larger rate of production cross-section and also allows a significantly larger range of leptoquark mass that can be probed since the VLL mass is favored to be lighter than 330 GeV to satisfy the muon anomaly excess.Crucially, this process forces us to involve all the new particles of the model to participate in the interaction which would then require all the new model parameters to be included in the analysis.The VLL decays to a S and a muon and the final decay of the leptoquark gives rise to 2b + 2µ + / E T : A representative Feynman diagram is depicted in Fig. 3.As the leptoquark is produced in association with the VLL and the production of VLL is proportional to the h ′ 2 coupling, which is large (> 1.5) to satisfy the muon anomaly, it proves to be an advantage for the production cross-section.The muon-philic nature of this model is reflected in the large production of the above-mentioned signal (Table II).The SM processes that can give rise to similar final states are: E T , where jets are misidentified as b-jet.
For collider analysis, we have implemented the model file in SARAH [82] and have generated the UFO file to generate signal events at MADGRAPH [114].The spectrum files for the benchmark points are generated using SPheno [83].Both the signal and background events generated in MADGRAPH are passed through PHYTHIA8 [115] for showering and hadronization.Detector simulation is done in DELPHES-3.5.0 [116] by editing the default muon collider card accordingly [117].For generating SM backgrounds with hard jets, proper MLM matching [118] scheme has been taken into account.We impose the following kinematical acceptance cuts while generating events in MADGRAPH: Tagging b-jets in muon collider is not well studied yet as the detector components responsible for measuring impact parameters and displaced vertices are still under research and design.Therefore, we have not used any tagging of the final jets produced at the detector.
The jets initiated from the b quarks are treated as normal jets without any b-tagging.The cost we have to pay is that we need to consider the other light quark and gluon-initiated jets, which could be reduced greatly with b-tagging, in the background.
Furthermore, we note that the traditional search for leptoquark in 2ℓ + 2j channel at the hadron collider [119][120][121][122][123] does not constrain our model much [64].This is because traditional searches expect low missing energy in the final state, whereas our signal consists of high missing energy.[132].
We now provide the details of our cut-based analysis.On top of the preselection cuts discussed in Eq. 15, we employ the following selection cuts on the kinematic variables: • p T (µ): We portray the p T distribution of the leading and sub-leading muons in Fig. 4(a) and Fig. 4(b) respectively.To ensure there are exactly two muons, we put a veto on any third muon with p T > 10 GeV.As we see for backgrounds, the muons tend to populate the higher p T bins as they come from the hard scattering.We see that p T (µ 1 ) < 200 GeV and p T (µ 2 ) < 100 GeV helps to reduce the backgrounds.
• p T (j): Momentum distribution for the leading and sub-leading jets are depicted in Fig. 4(c) and Fig. 4(d).To ensure that the signal contains exactly 2 jets, we reject any third jet with p T (j) > 20 GeV.Compared to the backgrounds, the jets are more boosted for the signal as they come from heavier leptoquark and VLL.Putting cuts of p T (j 1 ) > 250 GeV and p T (j 2 ) > 150 GeV helps us to reject the backgrounds drastically.
• / E T : For the signal, the / E T comes from the scalar mass S (Fig. 4(e)) and hence tends to appear at higher / E T value.We optimize the cut / E T > 100 GeV to enhance the signal over the background.
We summarize the cut flow effects in Table III.We calculate the signal significance by using the formula [133] where S(B) represents the number of signals (background) events surviving after all the cuts are applied.
We see from Table III, that the three benchmark points with leptoquark mass < 2 TeV can be probed with 5σ significance with luminosity < 10 fb −1 .However, once the leptoquark mass approaches the kinetic threshold of the muon collider, the signal significance drops significantly and we need higher luminosity to probe the mass of Φ.We also note that the associated production mode allows the probe of the leptoquark with relatively large masses, whereas the pair production would have restricted the search limits to masses ≲ √ s/2.A larger center-of-mass energy would further enhance the reach for such leptoquark searches.
The DM scalar S also plays a significant role in this search as it mediates the 2 → 3 scattering process for leptoquark production.The simultaneous correlation between the flavor sector TeV muon collider and the required luminosity to probe with 5σ significance.
anomalies and the DM relic abundance also helps in suggesting the regions of parameter space for which this leptoquark production channel is important.We conclude this section with an optimistic outlook, that the muon collider, if built, will be an excellent opportunity to test such µ-philic models of new physics.

V. CONCLUSION
In this work, we have investigated the potential of a muon collider to search for a model with leptoquark, which carries an odd charge under a discrete Z 2 symmetry.The model we consider in this work extends the SM with a Z 2 symmetry along with a set of particles odd under this new discrete symmetry, viz. a VLL, a real scalar, and a leptoquark.The model offers a new physics explanation for the excess seen in the (g − 2) µ measurement where the new particles contribute to the loops.In this setup, for a substantial parameter space, we see that the muon anomaly is satisfied when the mass of the VLL M ℓ 4 < 330 GeV and h ′ 2 > 1.5.The constraint from LFV measurements is satisfied by keeping h ′ 1 and h ′ 3 coupling small.By virtue of the Z 2 symmetry in the BSM sector, the real scalar S can act as a DM, provided the mass difference with VLL is not too large.
Guided by the parameter space, which enables us to explain the experimental excesses as well as provide a DM alternative in the theory, we look at the prospect of observing the signatures of these new particles at a muon collider.We identify that the associated production of the Z 2 odd leptoquark with the VLL via the exchange of the DM scalar provides an interesting channel to search for these particles.The proposed search strategy in 2µ + 2b + / E T offers a significant signal at a 3 TeV muon collider.Discovery of leptoquarks of mass up to 2 TeV can be easily achieved with an integrated luminosity of around 10 fb −1 at the 3 TeV machine.This is a significant improvement compared to the LHC, where only a sub-TeV leptoquark could be searched for in the same channel [64].Due to the phase-space suppression, a 3 TeV muon collider is not suitable for leptoquark search beyond 2 TeV, for which 10 TeV or higher-energy machines will be more useful.

FIG. 1 .
FIG. 1. Parameter space allowed by muon anomaly data in (a) M S − M ℓ 4 plane and (b) h ′ 2 − M ℓ 4 plane.These points also satisfy constraints from LFV measurements.In panel (a), h ′ 2 is varied ∈ [1.0, 3.5], and, in panel (b), the scan takes M S ∈ [65, 400] GeV.So, different points would possibly have different values of h ′ 2 and M S in panels (a) and (b), respectively.

0. 0012 .
The other important measurements come from the DM (a) direct detection (DD) and (b) indirect detection experiments.Non-observation of any significant DM signal in any DD experiments puts an upper limit on the DM-nucleon cross-section.For the DM mass range considered in this work, the strongest constraint comes from XENON-1T[105].

FIG. 4 .
FIG. 4. Normalized distribution of the kinematic variables for the signal and SM backgrounds.

TABLE I .
Charges of the new fields under the gauge group G.All SM particles are even under Z 2 .where the SM Higgs doublet, quarks, and leptons are represented by H, Q Li , and L Lj (i, j = 1, 2, 3), respectively.The VLL doublet L 4 = (ν 4 , ℓ − 4 ) T consists of the neutral component ν 4 and charged component ℓ − 4 .The couplings h i and h ′ j are responsible for the new interactions between leptoquark-VLL and VLL-real scalar sector.

TABLE II .
Benchmark points taken for the collider study and the production cross-section of µ + µ − b b / E T at 3 TeV muon collider.
On the other hand, studies prompted by SUSY or VLL searches in the 2ℓ + 2b + / E T [124-128] or in the 2ℓ + / E T [129-131] channels can, in principle, constrain our model parameters.Although we did not carry out a detailed scan considering these experimental measurements, we have checked that the four benchmark points are not ruled out by any existing analysis in CHECKMATE

TABLE III .
Number of Events after cuts (L = 3000 fb −1 ) SM-background Preselection p T (µ) cut p T (j) cut The cut-flow for signal and backgrounds for 2µ + 2b + / E T channel at the proposed 3