LHC Future Prospects of the 750 GeV Resonance

A quantitative discussion on the future prospects of the 750 GeV resonance at the LHC experiment is given using a simple effective field theory analysis. The relative size of two effective operators relevant to diphoton decays can be probed by ratios of diboson signals in a robust way. We obtain the future sensitivities of $Z\gamma $, $ZZ$ and $WW$ resonance searches at the high luminosity LHC, rescaling from the current sensitivities at $\sqrt{s}=13$ TeV. Then, we show that a large fraction of parameter space in the effective field theory will be covered with 300 fb$^{-1}$ and almost the whole parameter space will be tested with 3000 fb$^{-1}$. This discussion is independent of production processes, other decay modes and total decay width.


I. INTRODUCTION
Recently, the LHC experiment reported an event excess in diphoton invariant mass distribution near 750 GeV [1][2][3][4]. This event excess triggered significant theoretical interest and hundreds of papers have appeared. One of the plausible candidates to explain this excess is a heavy pion associated with new strong dynamics [5,6] (see also Refs. [7][8][9][10][11][12][13][14][15][16]). This model naturally explains the relatively large cross section of the diphoton signal, and the heavy pion φ couples with the standard model gauge bosons due to the chiral anomaly as φB µνB µν and φW µνW µν . Moreover, it is worth noting that such a model predicts other resonances at the TeV scale, e.g., a color-octet pion as discussed in Ref. [17]. Although such new resonance search is model dependent discussion, if we focus on the 750 GeV resonance, a model independent discussion becomes possible. Actually, there are various models that can be described by a similar effective Lagrangian. See Ref. [18] and references therein. The effective Lagrangian tells us that we can expect a Zγ or ZZ resonance at 750 GeV in addition to the diphoton signal because of electroweak gauge invariance [19]. Also, if some part of diphoton signal is contributed by the SU (2) L gauge boson, we can expect a W W signal. Thus it is interesting to discuss the future prospects of diphoton and other modes, e.g., at the LHC [20][21][22][23] and the ILC [24]. In particular, the results of the resonance searches for diboson modes of the LHC 13 TeV run were reported recently [25][26][27][28][29]. Then it is possible to discuss the future prospects of the diboson modes quantitatively.
In this paper, we discuss the future prospects of the 750 GeV resonance by using an effective field theory analysis. We take the effective Lagrangian for the 750 GeV resonance and calculate the ratios of the signal strengths for diboson modes 1 . These ratios are free from QCD corrections and it could tell us some information about the 1 A recent trigger level analysis of dijet resonance search gives an upper bound of ∼ 3 pb on 750 GeV resonance if we take 40 % UV theory behind the 750 GeV resonance. For example, in the case of the heavy pion models, the charge of the "new quarks" can be extracted from the ratio of signal strengths. This information will be useful for the discrimination of the various models. Here we discuss the high luminosity LHC with √ s = 13 TeV for simplicity. However results we obtain in this paper can be applied to those at √ s = 14 TeV because parton luminosities (gg,qq) at 750 GeV are changed by only up to 25% [31].

II. ANALYSIS
For concreteness, we assume that the 750 GeV diphoton resonance is explained by a CP odd scalar boson φ. The effective interaction of φ with electroweak gauge bosons is where k L and k Y are determined by the UV theory. As we mentioned in the introduction, this is an effective theory of various models. If we consider a CP-even scalar, the effective interactions are changed to φB µν B µν and φW µν W µν and the following discussion is same in the limit of m φ m Z,W assuming no mixing with the Higgs boson. By using the above effective interaction, the partial widths of φ decaying into a pair of electroweak gauge acceptance [30]. Although we do not discuss dijet search, this could be important in some models.
where s W = sin θ W and t W = tan θ W with the Weinberg angle θ W . Although there are four possible observables of σ · Br in the electroweak gauge boson final states against two parameters, a robust measurement is possible only for a relative size of the two parameters k Y /k L (see Refs. [15,19] for related works). Therefore, we parametrize the coefficients as [15] k Y = k cos θ, k L = k sin θ.
By taking ratios of the signal strengths, we obtain functions depending on only θ and θ W , We, therefore, study diboson (ZZ, Zγ, W W ) final states with respect to θ and σ · Br γγ . The discussion is independent of other decay modes, total decay width, and production processes (therefore independent of QCD uncertainties associated with the productions from quarks and gluons). In order to see the above statement more explicitly, it is shown in Fig. 1 that the LHC bounds on diboson resonances at 750 GeV are given by the angle θ and are insensitive to k if we take a fixed value of σ ·Br γγ . For the LHC future prospects, based on the current bounds of 3.2 fb −1 , we obtain future sensitivities in Table I, using Gaussian probability distribution. We assume a narrow width of the resonance here. In a case of large width the bounds and sensitivities become weaker by up to 50% because backgrounds in the wider mass range will be relevant (c.f., a difference between narrow width approximation (NWA) and large width approximation (LWA) in Ref. [27]). For the estimation of the

FIG. 1. Current exclusion limits at
√ s = 13 TeV in kY -kL plane. For a fixed diphoton rate, σ · Brγγ = 5 fb, shaded regions are excluded by Zγ (blue) [25], ZZ (magenta) [26], and W W (red) [27] resonance searches. Bounds at √ s = 8 TeV are not considered because translation to 13 TeV depends on the production process.   [28] is not included and a search in 4 final state is not reported yet. For Zγ mode, we adopted ATLAS result [25] and CMS reported a similar result [29]. In Fig. 2, we show current bound, expected cross section, and future prospects for each diboson resonance search in (σ · Br γγ )-θ plane. At angle of θ 3π/4, the cross sections are enhanced because of cancellation in the diphoton channel as in Eqs. (7,8,9). This is also seen in Fig. 1. On the other hand, there are angles where each diboson channel is cancelled. Eqs. (7,8,9) tell that the signals vanish at The angles θ and θ+π in the present effective Lagrangian are physically equivalent, and we can see the cancellation angles are rather close to each other due to the small Weinberg angle. Thus we need large luminosity to cover the region near θ 0, π.
The combined plots are presented in Fig. 3. We also include the 2σ allowed range of diphoton rate assuming 3. Future prospects for 750 GeV resonance in Zγ , ZZ, and W W final states with 300 fb −1 (left) and 3000 fb −1 (right). The shaded regions with magenta, red, and blue lines can be probed in Zγ , ZZ, and W W channels at 95% CL, respectively. The upper and lower shaded regions (cyan) are out of 2σ allowed region of CMS and ATLAS diphoton searches assuming narrow width [18], and the central gray shaded region is excluded by ATLAS diboson resonance searches as in Fig. 2. The dashed lines in the right panel correspond to future sensitivities with 3000 fb −1 if a factor of 3 improvement is achieved in each channel.
narrow width [18], 2.5 σ · Br γγ 8.5 fb (ATLAS, 3.2 fb −1 ), 0.6 σ · Br γγ 9 fb (CMS, 3.3 fb −1 ). (11) While most of the parameter space will be covered, a region around the Zγ cancellation angle of θ 0.09π cannot be reached with L = 300 fb −1 as shown in Fig. 3 left. Part of the region can be covered by the W W channel with the higher luminosity of 3000 fb −1 as shown in Fig. 3 right. However, a small region near θ 0.06π still remains uncovered. This window can be almost closed if a factor of 3 improvement in sensitivities can be achieved, especially in the ZZ or W W channels. Such improvement could occur by (i) multivariate analysis, (ii) including searches in 4 and qq final states, (iii) combining ATLAS and CMS data, and (iv) improvement of Z-and W -taggers.
Finally, we apply the results to specific models. If we take the simplest heavy pion model with SU (2) L singlet "new quarks" (see e.g., Ref. [6]), φ does not have φW µνW µν and then θ = 0. In this case, Fig. 3 shows Zγ resonance searches will be important for the future.
Other interesting examples are GUT motivated models. In a GUT motivated heavy pion model [5], φ is a SM singlet in an adjoint multiplet of SU (5) GU T . The GUT relation predicts θ = arctan 9/5 0.34π, and Fig. 3 shows W W and Zγ resonance searches will be important with 300 fb −1 and ZZ resonance search will be relevant if σ · Br γγ 4 fb. If φ is a singlet of SU (5) GU T , the GUT relation predicts θ = arctan 3/5 0.17π [15], and Fig. 3 shows W W resonance search will be important with 300 fb −1 and also ZZ resonance search will be relevant with 3000 fb −1 . The ratio of the signal strength is important information for the discrimination of the various models.

III. CONCLUSION
In this paper, we discussed the LHC future prospects of the 750 GeV diphoton resonance. As pointed out in Refs. [15,19], the ratio of the signal strengths between different final states can be discussed by using the coefficient of the effective interactions. Our analysis is based on √ s = 13 TeV, but the results can be applied to those at √ s = 14 TeV. We found, at the high luminosity LHC, a large fraction of the parameter space in the effective theory will be covered with 300 fb −1 and almost the whole parameter space will be tested with 3000 fb −1 . In particular, in the case with only φB µνB µν (θ = 0) as in the simplest heavy pion model, Zγ resonance searches will have good sensitivity. Also, in the GUT motivated case (θ = arctan 9/5 0.34π), W W and Zγ resonance searches will have good sensitivity and also ZZ resonance search will be relevant with 300 fb −1 .