Pure leptonic proposal to $W^{+}W^{-}$ excess and neutrino mass generation

We investigate the TeV models for neutrino mass generation as candidate models to explain the recent 2$\sigma$ excess of leptonic $W^{+}W^{-}$ pair production at LHC. Several models with singly charged exotic states that may explain the excess require light masses completely excluded by LEP experiments. One possible model with new lepton doublets can fit the observation and evade all direct search bounds but with tuned Yukawa structure to satisfy lepton universality. The new exotic leptons $L^{\pm}$ decay into $L^{\pm}\to \ell^{\pm} \phi$ where $\phi$ is a light singlet scalar of $\cal O$(MeV) that decays into neutrinos. Drell-Yan production of $L^{+}L^{-}\to \ell^{+}\ell^{-}+\cancel{E}_{T}$ fits the excess and $L^{\pm}L^{0}\to \ell^{\pm}+\cancel{E}_{T}$ is completely buried in SM background.

Very recently, both ATLAS and CMS found 2σ excess in W + W − pair measurements [2] while the ZZ measurements are more consistent with the SM predictions. The latest analysis on pure leptonic W + W − based on 8 TeV LHC data from ATLAS and CMS are listed in Eq. 1 as σ AT LAS@8T eV W + W − = 71.4 ± 1.2(stat.) ± 4.5(syst.) ± 2.1(lumi.)pb σ CM S@8T eV W + W − = 69.9 ± 2.8(stat.) ± 5.6(syst.) ± 3.1(lumi.)pb . (1) The SM prediction [3] is At Tevatron experiments, both CDF and D ✁ 0 also found central values significantly larger than the SM predictions but the error bars were also large [4]. On the other hand, combined analysis of LEP II experiments [5] put stringent bounds on pure leptonic W pair below √ s ≤ 206 GeV with R W + W − = 0.995 ± 0.008 which is the ratio of measured production cross section for W + W − pair and the SM prediction. There are attempts to explain the excess through new resummation calculation [6] but the excess has also generated several proposals based on supersymmetric models, in particular, light top squark in "natural SUSY" scenario [7]. The colored scalar production rate at 8 TeV LHC is of O(10 pb). With similar leptonic decay branching as Br(W − → ℓ −ν ), signal identical visible final states can well fake the leptonic W . Degeneracy condition in spectrum as is also imposed to avoid the visible b-jet. On the other hand, the excess of leptonic W + W − may also imply the extension in leptonic sector, in particular, TeV "see-saw" scenarios (also known as "inverse see-saw" sometimes) for neutrino mass generation and, in this paper, we investigate the possibility of this pure leptonic approach.

Discovery of a 125 GeV Standard Model (SM)-like Higgs boson at the CERN Large Hadron
Collider has dramatically improved our knowledge on mass generation for elementary particles in SM [8]. However, clear evidence for physics beyond SM lies in experimental confirmation of sub-eV neutrino masses based on distance/energy dependence measurements in various neutrino oscillation experiments [9]. Being complete neutral under unbroken gauge symmetry SU(3) C × U(1) EM , neutrino can be Majorana fermion. Moreover, Majorana nature of neutrino also ensures the uniqueness of hyper-charge assignment predicted by gauge anomaly free conditions [10]. The total mass of neutrino states and upper bound on neutrino charge 1 are given in [12] .
The most elegant proposal of neutrino mass generation is the "see-saw" mechanism [13,14] where the tiny but non-zero neutrino mass arises as a consequence of ultra-high scale (O(Λ GU T )) physics and the mechanism can be naturally embedded into grand unification framework [14]. In addition, "see-saw" mechanism can naturally account for the observed baryon asymmetry of the universe from WMAP seven year results [15] through "leptogenesis" [16] where ρ B is the baryon number density and s is the entropy density of the universe.
On the other hand, the "see-saw" mechanism is unlikely to be direct tested experimentally in near future. Heavy singlet fermion with strong Yukawa coupling to the Higgs boson leads to huge correction to the Higgs boson mass as δm 2 h ≃ m ν M 3 R /(2πv) 2 log(q/M R ) [17]. Supersymmetry is then inevitable to stabilize the Higgs boson mass while low energy supersymmetry suffers severe direct search bounds at LHC. Thermal leptogenesis also requires lower "see-saw" scale of O(10 9 GeV) with smaller Dirac neutrino Yukawa couplings and large hierarchies in the right-handed neutrino masses [18]. Therefore, there are alternative proposals to generate neutrino masses within TeV. Taking an effective field theory approach, neutrino mass in these models can be categorized into higher dimensional operator (φ n /Λ n+1 )ℓℓhh with n = 0. For cut-off Λ within TeV, φ is typically KeV-MeV known as inverse "see-saw" [1,19]. Since the models mostly involve exotic physics only in leptonic sector, many of them have very distinguished predictions at hadron colliders with controlled background.
If the new exotic states only decay into leptonic final states as we discussed, one will only need O(10 × (1/3) 2 pb) to fake leptonic W + W − final states. However, pure leptonic decaying scalar is typically excluded up to the LEP √ s ≤ 206 GeV 2 while Drell-Yan production rate of scalar pair with mass greater than 103 GeV is much smaller than 1 pb and cannot account for the excess. Therefore, we focus on inverse "see-saw" (also known as TeV "see-saw" ) scenarios with Fermionic extension 3 .
Original inverse "see-saw" model only involves SM singlet fermions N which decay into dilepton plus E T as N → ℓ + ℓ − ν. N is produced at LHC as pp → ℓN which contribute to triplelepton final states. In addition, the production is through light neutrino mixing which is also tiny.
In TeV Type-III "see-saw" [21], a singly charged fermion from the SU(2) L triplet Σ ± can decay into ℓ + E as However, first of all, Σ + does not always contribute to leptonic final states with only 80% × 3/9 + 20% × 20% ≃ 30% to ℓ + + E T final states which is similar to W decay. It then requires much larger production rate while Drell-Yan production at 8 TeV LHC for this non-colored fermion above the LEP bounds is not sufficient to account for the excess which has to be of O(10 pb) in total. Secondly, Σ ± Σ 0 production which is larger than Σ + Σ − pair production simultaneously predicts multi-lepton final states which suffers much severe experimental constraints. Therefore, a viable solution is to introduce new doublet fermion which is introduced in [1].
In [1], a pair of vector-like SU(2) L doublet fermions L and L c , a SM singlet N are introduced.
where l is the SU(2) lepton doublet in SM, h is the SM-like Higgs.
φ is a singlet scalar with mass of O(MeV) that decays into neutrino thus completely invisible in the detectors.
Light neutrino mass arises as the dimensional-seven operator, When M N + m h > M, L → Nh decay is kinematically forbidden. In the SU(2) limit, L 0 and L − are nearly degenerate and L − → L 0 π − decay partial width is extremely small. However, as long as y is not highly suppressed, decay will dominate. The new neutral fermion L 0 is completely invisible. The singly charged exotic lepton decay into SM charged lepton plus E T which is identical to leptonic W decay experimentally.
The exotic fermions pair of L ± and L 0 can be produced at LHC through gauge interaction where the di-lepton mode can be mis-identified as leptonic W + W − while the single-lepton mode is also subject to test at direct search for W ′ . Figure 1 shows the production rate for L + L − as well as the L ± L 0 at 8 TeV LHC. As argued Lepton universality is well tested at W + W − pair measurements and the excess has been observed in all lepton final states e + e − , µ + µ − as well as e ± µ ∓ . Therefore, it also put stringent constraints on L ± decay. There are in principle three generations of L ± and their decays are determined by the y ij . The exotic lepton L ± decay into electron or muon through the Yukawa type of interactions y ij L c i l j φ. The structure of Yukawa couplings y ij and the mass spectrum of L i may in principle affect the neutrino mass spectrum as in Eq.8. However, this model contains much more freedoms than original "see-saw" mechanism [13] and therefore, y ij and L-mass matrix M are less constrained. To keep the lepton universality, the simplest approach is that the lightest L states dominated decay into τ ± φ and the excess arises from τ ± → µ ± νν or τ → e ± νν which makes about 17% of τ decay each. The leptons from τ decay are typically softer than leptons directly from W ± decay. But, with larger mass, τ -boost from L-decay is more significant than τ s from W -decay. In addition, leptons from left-handed polarized τ are also moving in the τ -boosted direction. With all these factors taken into account, the lepton cut survival probability is expected to be higher than leptons from τ decaying from W s but less than the direct leptons from W decay. Therefore, it would require much larger production rate at the beginning.
Therefore, even though with challenge, it is still possible to achieve the universality. To illustrate the feature, in this paper, we discuss an oversimplified scenario with lepton universality for L-decay with decoupled L 2 and L 3 . The Yukawa couplings y ij are taken to be The structure may suffer from constraints from lepton flavor violation tests and neutrino mass generation. First of all, the Large mixing between different generation leptons may lead to large flavor violation mediated by φ and the model may be severely constrained by bounds on µ → eγ or µ → eγ or so. But , with the contribution proportional to y 4 , this bound can be evaded by making y ij smaller and this is irrelevant to collider phenomenology as long as the L decay is not in meta-stable or long-lived range. Secondly, as we argued, Eq.8 connects y ij with neutrino mass matrix. However, even taken y ij as universal, there are as many degrees of freedom as Type-I "see- saw" mechanism and one should be able to accommodate viable neutrino mass matrix just as in Type-I "see-saw" mechanism. If the Yukawa couplings y ij have universal structure. If L 2 and L 3 are of 250-300 GeV, the production rate of L 2 ,L 3 pairs are only few percent of L + 1 L − 1 . W ′ search around this mass range is much less constrained due to background [12]. With L 2 , L 3 decoupled, we neglect the notation i of L i in the following discussion and focus on the lightest L i production.
We plot the normalized lepton p T distribution from L ± → ℓ ± φ decay of L + L − pair in Fig. 2 in comparison with leptons in W + W − production. In addition, lepton p T distribution in L ± L 0 production is very similar to its in L + L − . For comparison of W ′ search, we also plot the lepton GeV. L ± is slightly heavier than W ± which results in harder lepton in its decay in comparison with W decay. The E T in L ± decay is also larger.
Therefore, the lepton final states from L + L − would have higher cuts survival probability. We compare the cut survival probability in L + L − with W + W − and listed them in Table I by [22]. We use the ratio between survival probabilities of two channels, ǫ W + W − /ǫ L + L − , to estimate the required production rate for L + L − . In principle, L ± i → ℓ ± j φ decay strongly depends on Yukawa couplings y ij which play important role in determining neutrino mass spectrum.
One can study implications on L ± decays for different neutrino scenario, inverted hierarchy or normal hierarchy, etc, by studying correlation between Yukawa couplings y ij and Y lm and neutrino masses. These couplings are also strongly constrained by lepton flavor violation at the same time.
To only illustrate the W + W − excess feature, we do not make any further assumption on neutrino masses except the estimated mass scale. Naively, the leading order production rate of σ L + L − can be estimate from where K QCD is the perturbative QCD K-factor for this Drell-Yan processes which is about 1. L ± L 0 → ℓ ± + E T mode encounters direct search of W ′ at the LHC as single lepton plus missing transverse energy. However, single W production with W ± → ℓ ± ν at 8 TeV LHC is about 5 nb with error bar 100 pb while L ± L 0 is only of O(pb) production rate. Lepton p T distribution in Fig. 2 also shows significant difference between L ± decay from heavy W ′ . The latter one has a Jaccobian peak of M W ′ /2. The leptons from O(100 GeV) L ± state are more like leptons from W decay so L ± L 0 is completely buried in tails of SM W background [12].
Only left-handed SM lepton participates in L − decay L − → τ − φ. On the other hand, the SM W − decay W − → τ −ν , τ − is also left-handed polarized. Hence, τ -polarization cannot be used to distinguish the two channels.

Conclusion
We study the TeV "see-saw" scenarios for neutrino mass generation to explain the recent 2σ excess of leptonic W + W − pair production at LHC and find a model [1] with one singlet neutrino plus additional vector-like lepton doublets can fit the observation and evade all direct search bounds. But the lepton universality test put stringent constraints over the Yukawa structure.