Neutrino Catalyzed Diphoton Excess

In this paper we explain the 750 GeV diphoton resonance observed at the run-2 LHC as a scalar singlet $S$, that plays a key rule in generating tiny but nonzero Majorana neutrino masses. The model contains four electroweak singlets: two leptoquarks, a singly charged scalar and a neutral scalar $S$. Majorana neutrino masses might be generated at the two-loop level as $S$ get nonzero vacuum expectation value. $S$ can be produced at the LHC through the gluon fusion and decays into diphoton at the one-loop level with charged scalars running in the loop. The model fits perfectly with a wide width of the resonance. Constraints on the model are investigated, which shows a negligible mixing between the resonance and the standard model Higgs boson.


I. INTRODUCTION
The standard model (SM) of particle physics fits perfectly with almost all the experimental observations in the elementary particle physics. But there are still hints of new physics beyond the SM. The discovery of the neutrino oscillations has confirmed that neutrinos are massive and lepton flavors are mixed [1], which provided the first evidence for physics beyond the SM. An attractive approach towards understanding the origin of small neutrino masses is using the dimension-five Weinberg operator [2] where L is the left-handed lepton doublet, H is the SM Higgs. The operator, which might come from integrating out some new superheavy particles, gives Majorana masses to active neutrinos after the spontaneous breaking of the electroweak symmetry. A simple way to realize the Weinberg operator is through the tree-level seesaw mechanisms [3][4][5]. But the canonical seesaw scales are usually too high to be accessible by colliders. Many TeV-scale seesaw mechanisms were proposed motivated by the testability, some of which give rise to the Weinberg operator at the loop level.
Recently both the ATLAS [6] and CMS [7] collaborations have observed a new resonance at an invariant mass of 750 GeV in the diphoton channel at the run-2 LHC with center-ofmass energy √ s = 13 TeV. The local significance is 3.6σ and 2.6σ for ATLAS and CMS respectively. The best fit width of the resonance from the ATLAS is about 45 GeV and the corresponding cross section is about 10 ∼ 3 fb, while the CMS result favors the narrow width, which has σ(pp → γγ) ≈ 2.6 ∼ 7.7 fb with Γ ≈ 0.1 GeV. If confirmed, it would be another hint of new physics beyond the SM. According to Landau-Yang theorem [8,9], this resonance can only be spin-0 or spin-2 bosonic state. The heavy quarks and/or gluon fusion production of the resonance are favored, because the run-1 LHC [10,11] at √ s = 8 TeV did not see significant excess at the 750 GeV. It is intriguing to investigate the physics behind this excess as done in a bunch of papers . Especially it would be more interesting if a new physics can explain both the diphoton excess and other unsolved problems of the SM, such as neutrino masses and dark matter.
In this paper, we explain both the diphoton excess and the active neutrino masses in a concrete model. The one singly charged scalar Θ transforming as (1, 1, 1) and a neutral scalar S transforming as (1, 1, 0). New interactions can be written as where L is the left-handed lepton doublet, q L is the left-handed quark doublet, E R and d R are right-handed charged leptons and down-type quarks respectively. The new scalar potential takes the form where dots denotes terms that are irrelevant to our study. Notice that interactions in Eqs.
(2) and (3)  For the case S being a complex scalar, there will be a massless goldstone boson, which is severely constrained by the big bang nucleosynthesis [72] and observations of Bullet Cluster galaxies [73]. To avoid this problem, one might add the soft U (1) L breaking mass term i.e. µ 2 R (S 2 +h.c.) to the potential without introducing any other trouble. Alternatively, if S itself is a real scalar singlet, there will be no massless goldstone boson. Actually, this model can be embedded into a theory with local U (1) B+L gauge symmetry 1 , where anomalies might be cancelled by introducing colorless vector-like fermions [54]. For the systematic studies of local U (1) B × U (1) L gauge symmetries, we refer the reader to Refs. [55][56][57] for detail. After S getting non-zero VEV, the mass eigenvalues of scalars can be written as Given the Yukawa interactions in Eq. (2), neutrino masses can be generated at the twoloop level. The relevant feynman diagram is given in Fig. 1. Neutrino mass elements can 1 We only point out this possibility, but not focus on this scenario in the rest of the paper. be written in terms of loop functions and Yukawa couplings where m e k and m d l are mass eigenvalues of the charged leptons and down-type quarks respectively, I kl is the loop function, which can be written as We refer the reader to Refs. [52,53] for the calculation of this integral in detail. Apparently neutrino masses, generated through Eq. (5), are suppressed by the charged lepton and down-type quark masses as well as the loop factor. All seesaw particles can be at the electroweak scale and the model is detectable at the LHC. A systematic study the neutrino phenomenology and collider signatures induced by this model, which are interesting but beyond the reach of this paper, will be given in a longer paper. Here we only estimate the size of parameters in Eq. (5) constrained by the active neutrino masses. The integral I kl was calculated analytically in Ref. [74], which has If confirmed, the excess would be a solid evidence of new physics beyond the SM. In this section, we explain this resonance as the scalar S, that plays the key rule in generating active neutrino masses at the two-loop level. Furthermore, S might also be the particle breaking the local U (1) B+L gauge symmetry spontaneously though the Higgs mechanism [49]. In this way the diphoton resonance might be a hint of new symmetries beyond the SM. The signal of the resonance at the LHC is where √ s is the centre-of-mass energy, M is the mass of S, C gg and C qq are dimensionless partonic integrals, BR(S → XX) and Γ S tot are the branching ratio and total decay rate of S. Considering C gg C qq and BR(S → qq) is loop suppressed in our model, gluon fusion turns out to be the dominant production channel at the LHC.
The decay rate of S can be written as where the factor 1/2 in the Eq. (9) comes from Tr[λ a λ b ], with λ a (a = 1 · · · 8) the generators of SU (3) c ; τ X ≡ 4M 2 X /M 2 S . The loop function can be written as [58] A(x) = x − x 2 f (x) (11) where f (x) ≡ arcsin 2 ( 1/x) by assuming 2M X > M S . We refer the reader to Ref. [58] for the expression of f (x) when 2M X < M S . There are other decay channels of S, such as invisible decay, which is relevant to fitting the total width and will be discussed later, and four fermions cascade decays, which are suppressed by the phase space.
Two interesting scenarios will be discussed: scenario (i) S is a real singlet and there is no extra gauge symmetry; scenario (ii) S is a complex singlet that triggers the spontaneous breaking of the local U (1) B+L gauge symmetry. We mainly focus on the scenario (i) and will briefly comment on the scenario (ii). We further assume Φ, Ω and Θ have degenerate masses, M X , and the same couplings, g X , with the S just for simplification.
For scenario (i), one has by setting α s ≈ 0.0934 and α ≈ 1/126.8. It is the typical character of this scenario.
Given this typical input, we plot in the Γ S tot − Br(S → γγ) plane the region that has σ(gg → S → γγ) ∈ (5, 10) fb. The vertical dashed line is the best fit width from the ATLAS. For the dot-dashed and dashed horizontal lines, one has Br(S → γγ) = 7 × 10 −4 and 1.0 × 10 −3 , which separately correspond to σ(gg → γγ) = 5 fb and σ(gg → γγ) = 10 fb for Γ S tot = 45 GeV. We plot in the left panel of Fig. 3 contours of the Γ(S → γγ) in the g X −v S plane by assuming M X ≈ 400 GeV, where the solid, dotted and dashed lines correspond to Γ(S → γγ) = 0.10 GeV, 0.05 GeV and 0.02 GeV respectively. It is clear that one needs O(1) quartic coupling g X and a large VEV v S to enhance the decay rate. Large quartic couplings is helpful in keeping the vacuum stable up to the Planck scale, but might probably leads to a non-perturbative theory. One might need extra electroweak multiplets to enhance the diphoton rate for the case of small g X . Apparently a wide width, Γ S , can not be explained if there is only γγ and gg decay channels, which means there should be other decay channels of S. Actually, if 2M X < M S , S might decay into di-scalars, whose decay rate can be written This rate can be very large for the light X, and be suppressed when 2M X ≈ M S . We show in the right panel of Fig. 3, contours of the decay rate in the M X − g X plane by setting v S = 2.5 TeV. So the wide width of S can be explained without introducing new ingredients, but this scenario needs to be tuned and is thus less attractive. Alternatively If S can decay into the hidden valley, a wide Γ S can naturally be explained as was studied in Ref. [14].
Finally we comment on the prediction of the scenario (ii). In this case one needs extra fermions to cancel the global SU (2) L anomaly [59], axial-vector anomaly [60][61][62]  S can naturally decay into dark sector in this scenario, which is helpful in deriving the best fit width. For the systematic study of symmetries behind the 750 GeV diphoton resonance, we refer the reader to Ref. [49] for detail.

IV. CONSTRAINTS AND PREDICTIONS
The run-1 LHC has searched for the pair production of leptoquarks [66], which showed that the first and second generation scalar leptoquarks with the mass less than 1010(850) GeV are excluded for BR(X → lq) = 1.0(0.5). For our case, leptoquarks couple to all three generation fermions, such that branching ratios of leptoquarks decaying into the first and second generation fermions can be suppressed. We show in the right-panel of TΩc Ω + C 2B TΦc Φ + h.c. Then X might decay intoX andB. In this way, the current collider constraint will be invalid. A systematic investigation of collider signatures of leptoquarks at the LHC is beyond the reach of this paper and we leave it to a future study.
Finally we check gauge couplings unification in this model, which is an important motivation of extending the SM. β-functions of gauge couplings can be written as where the SM gauge couplings are normalized based on SU (5) i.e., g = 3/5g 1 . Using the couplings, α i ≡ g 2 i /4π, given as (α 1 , α 2 , α 3 ) = (0.01681, 0.03354, 0.1176) at the Z-pole, one might simulate the running behaviors of gauge couplings, which shows that g 1 crosses with g 2 at µ ≈ 2.5 × 10 11 GeV, and crosses with g 3 at µ ≈ 6.5 × 10 13 GeV. So there is no gauge couplings unification in this model, but one may approximately get the unification immediately by extending the model with a quadruplet scalar with weak hyper charge 1/2, which might play important rules in generating Majorana neutrino masses via the modified type-III seesaw mechanism [71]. We leave the study of this part to a longer paper.

V. CONCLUSION
A new resonance at invariant mass of 750 GeV was observed by the run-2 LHC in the diphoton channel. If confirmed it will be a manifestation of new physics beyond the SM.
In this paper we investigated the possible explanation of this diphoton excess based on a TeV-scale neutrino mass model, that extends the standard model with four scalar singlets, two leptoquarks Ω and Φ, one singly charged scalar Θ and one neutral scalar S. Majorana neutrino masses are generated at the two-loop level. The diphoton excess is explained as the neutral scalar S, which is produced at the LHC through the gluon fusion and decays