750 GeV Resonance in the Dark Left-Right Model

We explain the $750$ GeV diphoton resonance in the context of the dark left-right symmetric model. A global symmetry in this model, stabilizes the dark matter and ensures that the scalar couples dominantly to gluons and photons. The branching fraction of the scalar to diphoton is large as a consequence of the symmetries of the theory. The benchmark values assumed to fit the diphoton signal also give the correct relic density of dark matter and muon $(g-2)$. A specific prediction of this model is that the dark matter has a mass of 200 GeV.


Introduction
A new diphoton excess has been reported by the ATLAS [1] and CMS collaborations [2] in their analysis of √ s = 13 TeV pp collision. The cross-section of σ(pp → γγ) for the 13 TeV run has been given as the excess of the cross-section in γγ channel can be estimated as (6 ± 3) fb (CMS [2]) and (10 ± 3) fb (ATLAS [1]). The excess has taken a wide attention in the community and a wide range of models has been proposed to explain this excess. Since the two photon decay can occur from a spin-0 or spin-2 particle resonance, the models considered of elementary scalars , composite pseudo-Nambu-Goldstone bosons [42][43][44][45][46][47][48][49][50][51], Kaluza-Klein graviton [52,53] or cascade decays of heavier particles [54,55]. The effect of 750 GeV resonance on vacuum stability is studied in [56][57][58]. Previously, the resonant production of (pseudo-)scalars coupled to two photons and gluons in the mass region from 30 GeV to 2 TeV at the LHC has been studied in [59] 1 . The resonance must be produced from gg or qq vertices and decay to γγ via exotic fermions, gauge bosons or scalars in the loop. It would be of interest to examine the possibility of a 750 GeV resonance in an existing well motivated particle physics model. A well studied generalization of the Standard Model (SM) is the left-right model with the gauge group SU (2) L × SU (2) R × U (1) and the same fermions content as the SM. In the left-right model, the right handed neutrino would have been a good candidate as a Dark Matter (DM) if it could be made stable against decays via W ± R . To ensure the stability of the dark matter, an extra global symmetry S is imposed in the so called dark left-right gauge model (DLRM) [63,64]. The spontaneous breaking of SU (2) R × S is achieved in such a way as to leave the combination L ≡ S − T 3R unbroken. The fermion sector is extended by adding two quarks. The generalized lepton number is L = 1 for the SM leptons and L = 0 for all other SM particles. To achieve this pattern of symmetry breaking and give masses to the fermions, one adds two doublets to the usual higgs sector of the left-right model. In this model the right-handed gauge boson W ± R has L = 1 and this prevent the decay of the right-handed neutrino (n R ) via W ± R and makes the lightest right-handed neutrino a candidate for dark matter [63][64][65]. It has also been shown that the charged scalars of the triplet higgs of the DLRM model can give an adequate contributions to the muon (g − 2).
In this paper, we explain the 750 GeV diphoton excess [1,2] in the DLRM model. The neutral component (φ 0 R ) of the right-handed higgs doublet Φ R is interpreted as the resonance. It can couple to gluons via the exotic quarks (x) and to photons via the same quark, W ± R and right-handed charged scalars (∆ ± R , ∆ ±± R ). Interestingly, in this model φ 0 R (750 GeV) dominantly decays into gluons and photons pairs and this explain the large value of Γ(φ 0 R → gg)Γ(φ 0 R → γγ)/Γ tot needed to explain the diphoton signal [1,2]. The cross-section σ(pp → γγ) depends upon the x Yukawa coupling with φ 0 R , the charged higgs masses m ∆ ± R , m ∆ ±± R , and the quartic couplings There is a negative contribution to the φ 0 R → γγ amplitude from the W ± R loop, but this is small due to the large W ± R mass. We scan the parameter space of these couplings and masses, which give the cross-section σ(pp → φ 0 R → γγ) = 3-13 fb. We compute the muon (g − 2) where the ∆ ± R and ∆ ±± R contributes in the loop. We find that by taking the masses of the charged scalars m ∆ ± R m ∆ ±± R = 530 GeV and their Yukawas with µ of the order of unity we get the required ∆a µ of ∼ 3 × 10 −9 . We identify the second generation n R as the dark matter. With these parameters fixed we find that the correct relic density is obtained by taking the dark matter mass 200 GeV.
The paper is organized as follows: in Sec. 2 we described the dark left-right model. In Sec. 3 we explain the observed diphoton signal in this model. The dark matter aspects and the constraints from muon (g − 2) are discussed in Sec. 4 and finally we conclude in Sec. 5.

Dark Left-Right Model
We consider the dark left-right gauge model (DLRM) [63,64] with gauge a group SU (3) C × SU (2) R × SU (2) L × U (1) of the usual left-right model. In DLRM, there is an extra U (1) global symmetry S to ensure that the spontaneous breaking of SU (2) R × S leaves the global symmetry L = S − T 3R unbroken. Here L is identified as generalized lepton number, with L = 1 for the SM leptons, and L = 0 for all other SM particles. In this model W ± R also carries a lepton number, which ensures the stability of dark matter. In addition to the SM fermions (shown in Table 1), model contains new neutral lepton (n R ) and exotic quark (x R ). The model also have a new SU (2) L,R singlet quark (x L ). The exotic quark (x L , x R ), n R carry the generalized lepton number L = 1. This ensures that the Yukawa terms can be written without breaking the global symmetry S. The scalar sector of DLRM consists of a bi-doublet (Φ), two triplets (∆ L , ∆ R ) and two doublets (Φ L , Φ R ) such as, The quantum numbers of scalars under the DLRM gauge group and S are listed in Table 2. As a result of global symmetry S, not all of the Yukawa terms are allowed. The allowed Yukawa terms are: whereas S forbids the Yukawa terms like: ψ L Φψ R , Q L ΦQ R and x L d R . So the masses of charged leptons and up-quark come from the vacuum expectation value (vev) v 2 = φ 0 2 , mass of the down-quark comes from v 3 = φ 0 L , mass of the exotic quark comes from v 4 = φ 0 R , mass of neutrino comes from v 5 = ∆ 0 L , and mass of n R comes from v 6 = ∆ 0 R . The flavor-changing neutral currents will be absent at the tree level as a result of considered model structure. The scalar potential with terms allowed by S is of the form, The higgs potential leaves the combination L = S − T 3R unbroken giving rise to solution v 1 = φ 0 1 = 0. We will focus on the SU (2) R higgs structure of DLRM and consider the most general higgs potential containing Φ R and ∆ R [64], After the electroweak symmetry breaking, the mass matrix of the CP-even neutral scalars contains off-diagonal terms and give as, If we assume a small mixing between φ 0 R and ∆ 0 R by taking f 1 = f 2 and µ λ 1 v 4 , then the lowest mass eigenstate is, which we identify as 750 GeV resonance observed at LHC. We will now discuss the relevant interactions of H 1 = φ 0 R , which are responsible for various decay modes.
There exists exotic quark (x) in the model, the loop induced process of which can produce φ 0 R through gluon fusion. The φ 0 R can subsequently decay to photons (as shown in Fig. 1) giving rise to the observed diphoton signal. The relevant Yukawa interaction is The resonance φ 0 R can also decay through W ± R , ∆ ± R and ∆ ±± R , by the following interactions, Figure 1: Feynman diagrams for the production and decay of φ 0 R .

Diphoton Signal
The diphoton signal cross-section, at the LHC for the proton center-of-mass energy √ s, is given by, where c gg represents the parton integral, zs .
For √ s = 13 TeV and m H1 = 750 GeV, one can get c gg to be ∼ 2137 [18]. Now, within the 1σ error of CMS and ATLAS data the cross section σ ∈ [3,13] fb. In our analysis we use this range and calculate the allowed parameter space, consistent with this cross section measurement, allowed in our model. In this analysis we fix the mass of φ 0 R , i.e., m H1 at 750 GeV.
We compute the decay width Γ(φ 0 R → gg) with gluons, which has contribution from the new quark x, as shown in Fig. 1a. We also compute the Γ(φ 0 R → γγ) decay width; the relevant diagrams are shown in Fig. 1b.
, since φ 0 R does not have couplings with any SM fermions, W ± and Z. It couples to scalars ∆ ±/±± R , but we assume the masses of these scalars in the range such that the decay of φ 0 R to these scalars are kinematically forbidden. The contribution will come from x, W ± R , ∆ ± R and ∆ ±± R , see Fig. 1.
In this context we would like to mention the experimental constraints on the masses of W ± R , ∆ ± R and ∆ ±± R . In DLRM M Z R and M W ± R are related as [63], where zero Z − Z R mixing is assumed. Z R decays into SM fermions; Z R → + − have been reported by CMS (ATLAS) collaboration, which put M Z R > 2.6 TeV (2.9 TeV) [66]. After using Eq. 8, these bounds translate for W ± R giving M W R >1.5 TeV (1.7 TeV). The W ± R diagram contributes with a negative sign, but by taking M W R = 1.8 TeV we find that W ± R diagram has a smaller amplitude in compare to other diagrams of Fig. 1.
The doubly charged scalar (∆ ±± R ) dominantly decays into same sign dileptons and is constrained by CMS (ATLAS) collaboration, which exclude m ∆ ±± below 445 GeV (409 GeV) and 457 GeV (398 GeV) for e ± e ± and µ ± µ ± channels respectively [67,68]. The mass of singly charged scalar below 600 GeV (assuming 100% branching ratio in the τ ν τ channel) is ruled out at 95% confidence level [69,70]. But in DLRM model ∆ ± R not only couples with τ ± , but also with e ± and µ ± , so this bound is relaxed. In Fig. 2  = 460 GeV we found the σ(pp → γγ) ∼ 4.2 fb which lies in the range of observed diphoton cross section; also for these set of parameters the decay width to gg is 1.9 × 10 −3 GeV and to γγ is 1.2 × 10 −3 GeV. Note that the 750 GeV scalar φ 0 R , in this model, can also decay, via loop, to Zγ and ZZ, but these decays are smaller than the diphoton decay by the factors ∼ 1/3 and 1/9 respectively and we have included these in our analysis. At this point it is worth-mentioning that this model can not reproduce the broad decay width mildly favoured by ATLAS data. In our subsequent calculation for dark matter relic density and muon (g − 2), we take m ∆ ± R = m ∆ ±± R = 530 GeV, which is consistent with the diphoton signal.

Dark Matter Relic Density
As an consequence of global symmetry S, the Yukawa term ψ L Φψ R is forbidden in DLRM, which basically connects ν L with n R . This implies that ν L and n R are not Dirac mass partner and the lightest n R (out of three possible generation) can be identified as a viable dark matter candidate. We identify the second generation n R (n µ R ) as dark matter (we will call it χ), because then it can be related to the discrepancy of muon (g−2). This idea is explored in detail in [65]. The mass of dark matter generates through the Yukawa term Ψ R Ψ R ∆ R . We assume that m ∆ ± R is lighter in comparison to W ± R , Z R gauge boson masses. Therefore, the dominant annihilation of dark matter is given by a t-channel χχ → µ + µ − through ∆ ± R . After using the partial-wave expansion, the thermally averaged annihilation cross-section can be written as where m f is the mass of the final state fermions and y χ is the Yukawa type coupling between χ, µ − and ∆ + R . Here the ratio of charged scalar mass with dark matter χ is defined as, w = m 2 ∆ + R /m 2 χ . It is clear from Fig. 2, the allowed mass range of ∆ ± R from diphoton excess lies between ∼ 400 GeV to 540 GeV. We take this bound into account and take m ∆ ± R = 530 GeV, y χ = 1.25 and compute the relic density. As shown in Fig. 3 that the correct relic density is obtained for a dark matter mass 200 GeV. As a result of dominant coupling of dark matter with ∆ ± R , DM annihilates into leptons, evading the stringent bounds from its direct detection search [75,76].

Muon (g − 2)
There exists a 3.6σ discrepancy between SM prediction and experimental value of muon (g − 2) [77,78]. In DLRM [63], there exist additional gauge bosons and charged triplet scalars which give contributions to the muon magnetic moment. As we mentioned before, there exist stringent bounds on the masses of SU (2) R gauge bosons (W ± R , Z R ) from LHC, so the contributions of heavy gauge bosons to muon (g − 2) will be small in comparison to the charged scalars. The relevant interactions term of muon (g − 2) are ψ R ψ R ∆ R and ψ L ψ L ∆ L . But ψ L ψ L ∆ L gives the mass to the neutrino and so have a small Yukawa coupling, whereas ψ R ψ R ∆ R does not have any restriction like this. So, we take into account only the contribution from ∆ ± R , ∆ ±± R loops, as shown in µ µ Figure 4: Dominant Feynman diagrams of doubly (a,b) and singly (c) charged triplet scalar loops contributing to muon (g − 2).

Summary and Conclusions
We explain the 750 GeV diphoton resonance observed by ATLAS and CMS in the context of the existing dark left-right model. A global symmetry in DLRM ensures the stability of dark matter. The same global symmetry also ensures that the scalar particle identified as 750 GeV resonance can dominantly couple to the standard model gluons and photons. This explain the large branching of γγ and gg decay widths which is necessary to explain the diphoton cross-section. After fixing the parameters of the model to explain the diphoton crosssection, we compute the relic density of dark matter and muon (g −2) in this model and we show that a common explanation for all three is possible in DLRM. This explanation predicts a dark matter mass of 200 GeV. It would be interesting to see if future observations of dark matter and LHC will corroborate or rule out this model.