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A resonance without resonance: scrutinizing the diphoton excess at 750 GeV

Motivated by the recent diphoton excesses reported by both ATLAS and CMS collaborations, we suggest that a new heavy spinless particle is produced in gluon fusion at the LHC and decays to a couple of lighter pseudoscalars which then decay to photons. The new resonances could arise from a new strongly interacting sector and couple to Standard Model gauge bosons only via the corresponding Wess-Zumino-Witten anomaly. We present a detailed recast of the newest 13 TeV data from ATLAS and CMS together with the 8 TeV data to scan the consistency of the parameter space for those resonances.


Introduction
After analyzing the first 13 TeV data, the ATLAS and CMS collaborations have reported an excess with respect to the background predictions in the diphoton channel search [1,2]. ATLAS has found the most significant deviation for a mass of about 750 GeV, corresponding to a local significance of 3.64 σ using 3.3 fb −1 accumulated data, whereas CMS has a significance of 2.6 σ for a mass about the same as ATLAS using 2.7 fb −1 data.
A simple explanation of such an excess could be through a resonance of a spin-0 or spin-2 particle with mass ∼ 750 GeV that decays to photons , while spin-1 is excluded by the Yang-Landau theorem [41,42]. However, resonant production via the s-channel might be in tension with bounds imposed by run-I data [43][44][45]. This tension was quantified in e.g. [46]. Though a direct production of a resonance at 750 GeV and subsequent decay to two photons is not excluded, we propose an alternative scenario to explain the excess via a non-resonant process. We demonstrate our idea within the framework of strong dynamics around the TeV scale. The basis of the theoretical model are outlined in [47] (some of these ideas have also been mentioned in [3]) with the addition of two composite singlet scalar (or pseudoscalar) particles which couple to Standard Model (SM) gauge bosons via the Wess-Zumino-Witten anomaly [48,49], and to each other via a trilinear coupling. Here, we assume that the lighter 750 GeV pseudoscalar has no effective coupling to gluons and thus cannot be directly produced. Therefore, the lighter pseudoscalar has to be produced in the decay of the heavy one which can be produced via gluon fusion. In contrast to e.g. [3] we do not try to embed this into a complete model, but concentrate on the minimal simplified model that resembles a "composite sector toy model" including two resonances to describe the LHC results from the 8 and 13 TeV data sets.
The parameter space of the model then consists of the masses of the two (pseudo)scalar states, their decay constants, and their three operator coefficients to the field strengths of the three gauge groups of the SM. In this work we search for solutions that explain the excess, and to determine the best fit to the data by means of a numerical analysis.
This work is structured as follows. In Section 2 we present a general description of our model assumptions, whereas in Section 3 we describe the numerical procedure used to fit the data and show the results, and finally in Section 4 the conclusions are outlined.

Model assumptions
In this section, we describe in detail the assumptions for our simplified model setup to explain the ATLAS and CMS data. We discuss the most important phenomenological aspects of the simplified model below. Detailed in-formation about the underlying assumptions on strongly interacting sectors for such a setup can be found e.g. in Ref. [3,47]. In our simplified model, we consider the SM particle spectrum extended by possible weak scale singlet spin 0 resonances. We assume that these new resonances (and possibly also the SM-like Higgs boson) are composite objects. However, the details of the electroweak symmetry breaking will not affect our numerical analysis and its results and thus we do not discuss it any further. We assume a hidden strongly interacting (confining) gauge group G N . Two pseudoscalar resonances σ and η emerge as the Nambu Goldstone bosons of the broken gauge group G N . 1 The kinetic terms of the weak singlet pseudoscalars are given by Here, m η and m σ are the mass terms of the real pseudoscalar fields η and σ. We assume the following parity violating trilinear σ-η-η interaction term, 2 where λ is a real parameter of mass dimension one. In a more general framework, all interaction terms up to mass dimension 4 consistent with our model should be included. However, since the diphoton excess can be explained with the trilinear interaction term only, we will omit these terms in the remainder of the letter. Note that such a term is the simplest assumption one can make about such a trilinear coupling. This kind of coupling arises e.g. in the form of a scalar-pseudoscalar-pseudoscalar coupling, Φηη, in certain types of Little Higgs models [50,51]. These are variants of composite models, endowed with a certain symmetry structure. Similar mechanisms can generate such couplings also in plain composite models. Introducing explicit CP violation into symmetry-breaking terms of the non-linear sector will correspondingly generate couplings of the type Eq. (2).
Alternatively, such couplings could arise with a different Lorentz structure using chiral perturbation theory for composite models as [52,53] Here, U is the Goldstone boson non-linear field matrix, and M is a mass matrix for the underlying, condensing new fermions. Though this leads to a different Lorentz 1 There are possibly more resonances, but they do not play a role for the moment as no further signals have been observed yet. 2 We assume that parity is explicitly violated via a nonzero θ term in the gauge group G N . In principle, the heavier resonance σ could also be scalar, without the need for CP violation in this interaction. However, then it needs to be a glueball in the confining theory which is difficult to justify why it should be so much heavier then the η [47]. structure, for the signal rate arguments used in this paper, it does not change the conclusions.
The new resonances only couple to the SM gauge bosons via the Wess-Zumino-Witten (WZW) anomaly [48,49], with φ = η or σ. Here, κ η i , κ σ i and F η , F σ denote arbitrary real coefficients and pseudoscalar decay constants, respectively. G µν , W µν and B µν are the color, weak isospin and abelian hypercharge field strength, and g 3 , g 2 and g Y denote the corresponding dimensionless SM gauge couplings. The prefactors κ η i and κ σ i can be explicitly calculated in a complete model, i.e. if the particle content (fermions in the composite sector and their exact quantum numbers) in the triangle loop is known [3,47]. However, in this work we do not consider a particular model and assume that the coefficients κ η i and κ σ i are free parameters of our effective Lagrangian. In the following, we will assume that the coefficients are independent and determine their values in a numerical analysis without referring to a specific model. A possible realization of the phenomenological model discussed here will be presented below at the end of the section.
In this paper, we assume that the 750 GeV resonance is not directly produced via s channel, as this has already been studied in the literature, and there is this tension with constraints from Run 1 data. In order to accomplish indirect production, we set the corresponding anomaly coefficient to zero, κ η g = 0. So its production must occur via the heavy resonance σ assuming that σ has anomaly induced couplings to the gluons. Thus, we consider a hierarchical scenario in order to evade the 8 TeV limits. We focus on resonant production of the heavy singlet pseudoscalar σ via gluon fusion with subsequent on-shell decay into a pair of ηs. The light pseudoscalar η is allowed to decay into all electroweak SM gauge bosons via the WZW mechanism (but at least photons and Z, which is inevitable). Thus, we expect the following signature where X denotes the rest of the event. Both experiments, ATLAS and CMS do not veto on X. We have listed the selection cuts from ATLAS and CMS in Table 1. Hence, this signature can explain the diphoton excess. The anomaly coefficients for the weak and hypercharge group have been partially set to zero as they are phenomenologically not relevant for the numerical analysis (in the case of the heavy resonance), or are not allowed in order not to give a too small branching fraction into photons (for the light res- onance). Note that there is a certain redundancy of parameters in the simplified model, as changes to the decay constant can within a certain range of parameters always be emulated by changes in the anomaly coefficient. 3 Our choice of anomaly coefficients resembles the following composite model which was discussed in Ref. [3]. Here, two vector-like fermions Q 1 and Q 2 are introduced. Both vector-like fermions are in the fundamental representation of the strong gauge group G N with a dynamical scale Λ.
Here, we identify G N with an asymptotically free SU(N) gauge theory. The charge assignments of Q 1 and Q 2 under SU (N )×SU(3) C ×SU(2) L ×U(1) Y are (N, 1, 2, a) and (N,3, 1, b), respectively. N denotes the fundamental representation of the SU (N ). Now, we assume that m 1 < Λ < m 2 . At low energies, we have the following condensate where η is a triplet under SU(2) L . The only allowed anomaly induced coupling of η is given by the following term Since the (pseudo)scalar η b cannot couple to gluons, it cannot be produced directly. However, heavy resonances with Q 1 pairs can be produced which then decay into the lighter pseudoscalar via Eq. (2). The latter can then decay to two photons. Using more than two underlying fundamental fermions of the confining gauge group SU (N ) with appropriate quantum numbers, more general scenarios can be constructed.

Numerical results
In the following, we first briefly discuss the numerical tools and then describe our numerical framework. Finally, we will discuss our results.

Numerical tools
We have implemented the model discussed in Section 2 with the program FeynRules 2.3.13 [54] and created a

Scan procedure
In order to find values of parameters that provide a good description of data we performed a scan in λ, κ σ g and the mass of heavier resonance, m σ , in the ranges displayed in Table 2. We simulated pair production of η states via resonant s-channel σ exchange. 4 All decay modes of η were included in the simulation. For each point the number of events passing experimental selections in our simulation is compared to the number of events reported by the LHC collaborations, see Table 3. The expected number of background events is extracted from the respective publication. Because the experiments did not clearly define signal regions, we performed a fit in the invariant mass window 700 < m γγ < 800 GeV. For the CMS search we split the events into the barrel (EBEB) and end-cap (EBEE) regions, following the collaboration's procedure. Finally, the 8 TeV searches are used solely as a consistency check in order to see if the parameter points were not excluded during the previous run. Clearly, the pseudoscalar sector is parametrized by several a priori free parameters, as can be seen in Table 2.
For simplicity, in the current analysis we set some of them to zero, therefore our heavy pseudoscalar couples only to gluons through the anomaly while the light one only to B.
The light pseudoscalar will still have other decay modes to ZZ and Zγ. Once the κ η W coupling is allowed, additional decay modes to W W pairs will be open. We show the decay pattern of η in Figure 1. This will provide a distinctive feature at colliders: the diphoton pairs will be often accompanied by jets, leptons or missing transverse energy. Depending on the actual mass hierarchy between scalars, the γγ pair can have a significant transverse momentum, which will eventually vanish close to the threshold for the decay σ → ηη. This feature together with an additional activity in the event can serve as a way to probe this type of models soon 5 .
The fit was performed with the χ 2 test statistics. Namely, where Here, n i is the number of observed events, µ i,b is the expected number of background events, µ i,s is the expected number of signal events, σ i,stat and σ i,b are the statistical and systematic uncertainty on the expected number of background events for each signal region, where the index i runs over the i = ATLAS, CMS EBEB, CMS EBEE selections. The systematic errors combine the experimental ones as given by the collaborations and additionally 10% error on the CheckMATE event yield. In any case, 5 We note that according to the CMS speaker's statement during the seminar presenting those results at CERN, no difference between the peak and side-band regions was observed. Given the low number of events and lack of details in the conference note [2] we do not take this remark as conclusive.   the total error is dominated by the statistical errors due to the low number of events. We assume that all errors are uncorrelated. The signal regions are defined as 700 < m γγ < 800 GeV.

Discussion
As explained above, we have performed a scan as a function of the couplings λ, κ σ g and the mass m σ while keeping the other parameters fixed as it is shown in Table 2. This has been done with the ATLAS and CMS searches and in the following we combine the data of both experiments. Figure 2 shows the χ 2 as a function of κ σ g and λ (left panel for ATLAS data alone, middle panel for CMS data alone and right panel for their combination). The contours are plotted for ∆χ 2 = 1, 4, 9 above minimum respectively. It is interesting to notice that the χ 2 follows a hyperbolic shape in the λ, κ σ g plane since as it is expected there is a degeneracy among the two couplings. Namely an increase in the κ σ g coupling enhances the production rate of the σ field via gluon-fusion which is compensated by a decrease of the λ coupling which affects the decay branching fraction of σ decaying to a pair of η's. The black dots represent one of the low χ 2 points: λ = 0.22 TeV, κ σ g = 4.3, m σ = 1.75 TeV. Figure 3 shows the χ 2 as a function of m σ and λ (again, left panel for ATLAS data alone, middle panel for CMS data alone and right panel for their combination). The contours are plotted for ∆χ 2 = 1, 4, 9 above minimum respectively. Finally, Figure 4 shows the χ 2 as a function of κ σ g and m σ , with the black dot defined as above. The preferred values of parameters lie close to the border of 1-σ for each of the experiments. Clearly CMS is more consistent with the no signal hypothesis, while ATLAS prefers higher event yields.
Because we effectively only have one observable it is not surprising that there is a continuum of points with minimum χ 2 value. The combined analysis gives the χ 2 value at the minimum of 1.8. This should be compared to the SM-only hypothesis which yields χ 2 SM = 8.8. Finally, we provide the expected and observed numbers of events for each signal region in Table 3.
be resolved at this point. The degeneracy could be broken by an observation of a peak in the dijet mass spectra from the decay σ → gg. Since in the range of masses m σ studied here the results are consistent with the background-only hypothesis [64,65], one should also take into account an additional constraint from these searches. CMS [64] provides explicit limits for the digluon final state. For our sample point at m σ = 1.75 TeV, the upper limit on the visible dijet cross section is 1.8 pb. Taking into account the efficiency of 60% the truth cross section should be less than ∼ 3 pb. This implies κ σ g 25.
Finally, we comment on the visibility of the diphoton signal at 8 TeV [43][44][45]66]. The cross section, assuming the gluon-gluon production mode [67], would be a factor 15 smaller. On the other hand, the luminosity recorded at 8 TeV was some 6 times larger than at 13 TeV in case of ATLAS. For the sample point from Table 3 the expected event yield would be 4.8 events in the ATLAS search [44], while the observed (expected) 95% CL upper limit is 23.1 (21.9). Similarly, in the CMS case we find the 8 TeV constraints easily fulfilled.

Conclusions
In this work we present a model based on composite states that fits well the diphoton excess observed by the ATLAS and CMS collaborations which points to the existence of a resonance of mass of about 750 GeV.
The mechanism consists in the production of a heavy pseudoscalar via gluon fusion with a mass in a range 1.5-2.5 TeV, which decays to a pair of lighter pseudoscalars with a mass of about 750 GeV that finally decay to photons. While both pseudoscalars couple to the SM gauge bosons via the WZW anomaly, the heavy pseudoscalar couples to the light ones via a dimensionful trilinear coupling which is allowed by the theory.
We find a specific direction in the parameter space of the simplified model that minimizes χ 2 from the combined analysis of the ATLAS and CMS data at the value of 1.8 and the models markedly improves the SM-only value of 8.8. It is also consistent with the 8 TeV searches. Its distinctive feature in the collider experiments compared to the direct s-channel resonance would be a non-trivial p T spectrum of the diphoton pairs and the presence of additional jets, leptons or missing energy, depending on the decays of gauge bosons produced in the opposite decay chain, which makes it easily testable with more data from the upcoming run.