Studying 750 GeV Di-photon Resonance at Photon-Photon Collider

Motivated by the recent LHC discovery of the di-photon excess at the invariant mass of ~ 750 GeV, we study the prospect of investigating the scalar resonance at a future photon-photon collider. We show that, if the di-photon excess observed at the LHC is due to a new scalar boson coupled to the standard-model gauge bosons, such a scalar boson can be observed and studied at the photon-photon collider with the center-of-mass energy of ~ 1 TeV in large fraction of parameter space.

Recently, both ATLAS and CMS collaborations have reported the results of their analysis of di-photon events. The result of ATLAS, which is based on the 2015 data with the integrated luminosity of 3.2 fb −1 , shows the excess with the local (global) significance of 3.6σ (2.0σ) at the di-photon invariant-mass of M γγ ∼ 750 GeV [1]. In addition, the CMS result, which is based on their 2015 data with the integrated luminosity of 2.6 fb −1 , also indicates an excess at similar M γγ ; the local significance of the excess is claimed to be 2.6σ (while the global significance is smaller than 1.2σ) [2]. These excesses may indicate the existence of a new resonance Φ with its mass of m Φ ∼ 750 GeV. The production cross section and branching ratio into di-photon are suggested to satisfy [3]- [8] σ(pp → Φ → γγ) = σ(pp → Φ)Br(Φ → γγ) ∼ 5 − 10 fb : at √ s pp = 13 TeV, where √ s pp is the center-of-mass energy of pp.
One of the explanations of such an excess is a new scalar boson coupled to standard-model gauge bosons via higher dimensional operators [3]- [99]. The scalar boson may interact as for the case of pseudo-scalar boson ϕ, or as for the case of real scalar boson φ. Here, F (i),a µν is the field strength of the standard-model gauge bosons where i = 1, 2, and 3 correspond to U(1) Y , SU(2) L , and SU(3) C , respectively, and the superscript a denotes the index for the adjoint representations. The summations over the repeated indices are implicit. With these interactions, the scalar boson can be produced at the LHC via the gluon-gluon scattering process, and it can decay into photon pair. Then, the di-photon excess observed at the LHC can be explained by the process of gg → Φ → γγ (where Φ = φ or ϕ, and g is gluon).
If there exists such a new scalar boson, the next task for future collider experiments is to precisely study its properties. The LHC will play very important role in such a program [38], [100]- [104]. Here, we consider another possibility, which is the photon-photon collider. The photon-photon collider can be realized at the facility of the International e + e − Linear Collider (ILC) by converting electron beam to high energy photons. Because the scalar field of our interest decays into di-photon, it can be produced via the photon-photon scattering process. For the case of the scalar fields with the interactions given in Eq. (2) or (3), one of the advantages of the photon-photon collider is that the single production of the scalar boson is possible so that the kinematical reach is close to the total center-of-mass energy of the collider. In the case of our interest where the mass of the scalar boson is about m Φ ∼ 750 GeV, the scalar boson can be produced at the photon-photon collider with √ s ee ∼ 1 TeV (where 1 2 √ s ee is the energy of the initial-state electron beam), which is within the range of the upgrade ILC. In addition, the clean environment of the photon-photon collider may help precisely studying the properties of the scalar boson.
In this letter, we study the prospect for the study of the scalar boson at the photon-photon collider. Assuming the effective Lagrangian given above, we calculate the production cross section of the scalar boson. Because the effective interaction may originate from the loop effects of heavy vector-like particles or from unknown strong dynamics, we do not specify the origin of the effective Lagrangian and treat Λ i as free parameters. We also estimate the cross sections for standard-model backgrounds. We will see that, if the di-photon excess observed at the LHC is due to a scalar boson with its mass of m Φ ∼ 750 GeV and couplings given in Eq.
(2) or (3), such a new scalar boson can be observed and studied at the photon-photon collider in large fraction of the paramter space. In particular, the cross section for the process γγ → Φ → gg is large enough so that such a process can be observed at the photon-photon collider. In addition, some of the processes γγ → Φ → γγ, γZ, ZZ, or W + W − may be also observed. With these observations, information about the parameters Λ i in Eq. (2) or (3) is obtained.
First, we summarize the formulas of the cross sections for the scalar production processes at the LHC and ILC. Hereafter, we concentrate on the case where Γ Φ ≪ m Φ (with Γ Φ being the total decay width of Φ). Then, assuming that the gluon-gluon scattering process is the dominant production process at the LHC, the cross section for the processes pp → Φ → γγ is given by where g(x) is the parton distribution function (PDF) of gluon. We use MSTW2008NLO PDF [106], with which the integral in Eq. (4) is evaluated to be 1.7 × 10 3 for m Φ = 750 GeV and √ s pp = 13 TeV. In addition, Γ(Φ → gg) and Γ(Φ → γγ) are partial decay widths for the gg and γγ final states, respectively. For the monochromatic photon beams, the cross section for the process γγ → Φ → F at √ s γγ ∼ m Φ (with √ s γγ being the center-of-mass energy of γγ) is given bŷ where ξ 2 and ξ ′ 2 are Stokes parameters of the initial-state photons, where ξ 2 = ±1 corresponds to the photons with helicity ±1.
At the photon-photon collider, the initial-state photons are provided as back-scattered photons off the electron beams, and are not monochromatic. For the calculation of the cross section at the photon-photon collider, we use the luminosity function of the back-scattered photons given in [107,108]: where L ee is the luminosity of the electron beam, y and y ′ denote the photon energies normalized by the energy of the electron beam 1 2 √ s ee , and x ≡ 2 √ s ee ω 0 /m 2 e , with m e being the electron mass and ω 0 the averaged energy of the laser photons in a laboratory frame. The function f is given in the following form: where α is the QED fine structure constant, and with r ≡ y/x(1 − y). In Eq. (8), λ e /2 and P l are the mean helicities of initial electrons and laser photons, respectively. In our numerical calculation, we take λ e = 0.85 and P l = −1. In addition, where The function B is given by where y m ≡ x/(x + 1), and ρ is the reduced distance between conversion and collision points. We assume the photon-photon collider with x = 4.8, which maximizes y m without spoiling the photon luminosity [107,108], and take ρ = 1 in our numerical calculation. In addition, the Stokes parameter is given by where Notice that ξ 2 (y) → 1 as y → y m . Using the luminosity function of the back-scattered photons, the cross section at the photon-photon collider is given by We normalize the cross section at the photon-photon collider using L ee . For the calculation of the cross sections, it is important to understand the decay widths of the scalar boson. In the following numerical analysis, we consider the case where the scalar resonance is a pseudo-scalar boson ϕ. (For m Φ ≫ m Z , the following results are almost the same even if we consider the case of real scalar boson.) In such a case, adopting the effective Lagrangian given in Eq. (2), the partial decay widths of ϕ are given by where m ϕ , m Z , and m W are the masses of pseudo-scalar boson ϕ, Z boson, and W ± boson, respectively, and with θ W being the Weinberg angle. (The decay widths of the real scalar boson can be found, for example, in [38].) In our analysis, the total decay width is treated as a free parameter, because there may exist decay modes other than Φ → V V ′ (with V and V ′ denoting standardmodel gauge bosons), like the decay into dark matter pairs [10,53,54,63,72,75,109,111]. Thus, there are four free parameters in our analysis, i.e., Λ 1 , Λ 2 , Λ 3 , and as we discuss in the following. Using Eq. (15), we calculate the total cross section for the scalar-boson production process at the photon-photon collider. Assuming that the Φ production at the LHC is via the gluonfusion process, the cross sections σ(γγ → Φ → F ) and σ(pp → Φ → γγ) are related as where σ gg is a numerical constant. (See Eqs. (4), (5) and (15).) In our numerical calculation, we take σ(pp → Φ → γγ; √ s pp = 13 TeV) = 10 fb. We note here that, although we mostly consider the decay of Φ into gauge-boson pairs, the above equation is applicable to any final state.
We calculate σ gg for the narrow width case (i.e., Γ Φ ≪ m Φ ) as well as for the cases of Γ Φ = 25 and 50 GeV. For the latter cases, the integration in Eq. (15) In Fig. 1, we plot σ gg as a function of √ s ee , taking m Φ = 750 GeV. We can see that σ gg is maximized when √ s ee ∼ 950 GeV. The maximal value of σ gg depends on the width of the scalar boson, and σ gg can be as large as 110 − 170 fb for Γ Φ 50 GeV. We are using the photon luminosity function which has a peak at √ s γγ ≃ 0.79 √ s ee . Thus, in the narrow width case, σ gg takes its maximal value of 170 fb for √ s ee ≃ 945 GeV. With the integrated luminosity of L ee ∼ O(1) ab −1 , the total number of the events at the photon-photon collider is as large as (or larger than) O(10 5 ), which may make the detailed study of the scalar boson Φ possible at the photon-photon collider. (We note that we neglect the interference between the scalar-boson-exchange and standard-model diagrams, and hence our results are not reliable for the parameter region where the signal cross sections become comparable to the background ones.) In order to discuss the collider phenomenology of the scalar boson at the photon-photon collider, we need to understand background processes. Assuming the effective Lagrangian given in Eq.
(2) or (3), we consider the signal processes of where V V ′ = γγ, γZ, ZZ, W + W − , and gg. For these signal events, there exist standardmodel backgrounds. In order to estimate the number of backgrounds for V V ′ = γγ, γZ, ZZ, and W + W − , we calculate the following quantity in the standard-model: where m V V ′ is the invariant mass of the final-state gauge boson pair. Some of the final-state gauge bosons are likely to be emitted to the beam direction. Thus, in order to reduce the number of backgrounds, the phase-space integration is limited to the region of | cos θ CM | < cos θ cut , where θ CM is the angle between initial-state photon and the final-state gauge boson in the center-of-mass frame. Correspondingly, in the calculation of the signal cross section, the phase-space integration should be performed in the region of | cos θ CM | < cos θ cut . Because the final-state particles are emitted spherically in the signal events, the effect of limiting the final-state phase space is taken into account by multiplying the total cross section by cos θ cut . We expect to reduce the standard-model backgrounds by using the kinematical variable m V V ′ (as well as cos θ CM ), and hence the expected numbers of the background events are estimated as where ∆m V V ′ is the width of the bin for the study of the scalar boson production. In the standard model, the processes γγ → γγ, γZ, and ZZ happen at the loop level, and their cross sections can be found in [113,114,115]. On the contrary, the process γγ → W + W − occurs at the tree level. The cross section for this process is evaluated with the use of MadGraph5 [116]. The values of κ V V ′ (with V V ′ = γγ, γZ, ZZ, and W + W − ) are summarized in Table  1.
For the gluon-gluon final state, the dominant background is from the pair-production of light quarks, γγ →qq, because gluon and light-quark jets are indistinguishable. Thus, we calculate where mq q is the invariant mass of the final-stateqq system, and cos θ CM denotes the angle between the initial-state photon and the final-state quark in the center-of-mass frame. (For our numerical calculation, MadGraph5 is used.) Because we expect a high b-tagging efficiency at the ILC detectors, i.e., ǫ b ∼ 70 − 80 % with the mis-identification efficiency of light quarks being O(1) % [117], we assume that thebb contribution can be largely eliminated and hence is sub-dominant. Thus, we do not include its effect into the calculation of κq q . We found that κq q has a sizable dependence on mq q , and hence we calculate this quantity for several values of mq q . The results are shown in Table 2. Importantly, the light-quark pair production cross section is strongly dependent on the poralization of initial-state photons. In particular, the cross section vanishes when the stokes parameters of two initial-state photons satisfy ξ 2 ξ ′ 2 = 1; with our choice of collider parameters, this relation is realized at the end-point of  the spectrum of back-scattered photon, i.e., y = y ′ = y m . Even at the peak of the photon luminosity function, the product ξ 2 ξ ′ 2 is close to 1, and the light-quark pair production cross section is significantly suppressed compared to the case of unpolarized initial-state photons. Now we discuss the signal-to-background ratio for various final states. For this purpose, we specify relevant size of the bin, ∆m V V ′ , for the study of the scalar-boson production. If the width of the scalar boson is narrow enough, ∆m V V ′ is determined by the detector resolution (where we consider the events with no missing momentum). It is expected that, at the ILC detectors, the energy of charged particles and hadronic jets will be measured with excellent accuracies [117]. With the ILC detectors, the jet energy will be measured with the accuracy of 3 % or better for jet energies above 100 GeV. In addition, the energy resolution of the electromagnetic calorimeter of the SiD detector, for example, is expected to be δE/E = 0.17/ √ E ⊕ 1 % for electrons or photons, and hence we expect that the energy of the photons emitted by the decay of Φ will be measured with the uncertainty of ∼ 1 %.
Combining Eq. (24) and Fig. 1, the cross section for the gluon-gluon final state at the photon-photon collider is estimated to be 170 fb in the narrow width case, taking σ(pp → Φ → γγ) = 10 fb and √ s ee = 945 GeV. (The cross section becomes smaller as Γ Φ increases.) On the contrary, using the results given in Table 2, the cross section of theqq background is significantly smaller than the signal cross section even if we take ∆m V V ′ ∼ O(10) GeV.
Integrating out κq q for 0.94 m Φ ≤ mq q ≤ 1.06 m Φ , for example, we found that the background cross section is 23 fb for cos θ cut = 0.9. Thus, it will be possible to observe and study signal events with gluon-gluon final state with the luminosity of L ee ∼ O(0.1 − 1) fb −1 or larger. For the final states containing weak bosons and photon, with Γ Φ being fixed, the cross sections depend on Λ 3 through the following ratio: In the limit of m Φ ≫ m Z , η ≃ ( 1 8 Λ −2 1 + 3 8 Λ −2 2 )Λ 2 3 . Then, the cross sections for the processes γγ → Φ → γγ, γZ, ZZ, and W + W − depend on two parameters, i.e., η and the ratio Λ 1 /Λ 2 (as far as Γ Φ and σ(pp → Φ → γγ) are fixed). In addition, the cross sections for these processes are proportional to η for a given value of Λ 1 /Λ 2 . In Fig. 2, taking η = 1, we plot the cross sections of these processes as functions of Λ 1 /Λ 2 . We can see that σ(γγ → Φ → γZ) becomes suppressed when Λ 1 ≃ Λ 2 ; this is because, in such a case, the Φγ-Z coupling is suppressed (see Eq. (22)). In addition, the cross sections σ(γγ → Φ → γγ) and σ(γγ → Φ → ZZ) are suppressed when Λ 1 ≃ − cot 2 θ W Λ 2 and Λ 1 ≃ − tan 2 θ W Λ 2 , respectively. We note here that the present scenario is constrained by the searches for the resonances which decay into a pair of electroweak gauge bosons performed at the LHC Run-1. In particular, the negative search for the resonance which decays into γZ final state gives the most stringent constraint. According to [6], for example, the parameter region of Γ(Φ → γZ) 2Γ(Φ → γγ) is excluded, where we adopted σ(pp → Φ → γγ) ∼ 10 fb. The regions of Λ 1 /Λ 2 −1 and Λ 1 /Λ 2 6 conflict with such a constraint. (If we adopt a smaller value of σ(pp → Φ → γγ), the constraint becomes weaker.) Because the cross sections for the processes γγ → Φ → γγ, γZ, ZZ, and W + W − are proportional to η with the present parameterization, each mode is expected to be observed at the photon-photon collider if η is large enough. In order to estimate the minimal value of √ s pp = 13 TeV) = 10 fb, cos θ cut = 0.9, and L ee = 1 ab −1 .
η for the observation of each mode, we calculate the following quantity: For the processes γγ → Φ → γZ, ZZ, and W + W − , the uncertainties in the measurement of m V V ′ are expected to be dominated by jet energy resolution, concentrating on the hadronic decay modes of weak bosons. Thus, in the narrow width case, 1 2 ∆m V V ′ is taken to be twice the detector resolution; we adopt ∆m V V ′ = 0.12 m Φ for these final states. For γγ → Φ → γγ, we take ∆m V V ′ = 0.04 m Φ , assuming a good resolution of the electromagnetic calorimeter.
Then, we determine the minimal value of η which realizes The result is shown in Fig. 3. We note that, if the detector resolution (in particular, for hadronic objects) is not good enough, hadronic decay of W ± may be mis-identified as that of Z boson. Then, the standard-model W + W − production process may also contribute to the background of the signal with ZZ final state with the hadronic decays of Z bosons. Such a problem may be avoided by requiring that at least one of the Z bosons decays into e + e − or µ + µ − ; if we impose such a requirement, the minimal value of η for S ZZ / N (BG) ZZ > 5 shown in Fig. 3 should be divided by ∼ 0.36.
We can see that, if η O(10 −2 ), cross sections for several modes with electroweak gauge boson final states may be measured at the photon-photon collider. With measuring the cross sections of two (or more) of such final states, the ratio Λ 1 /Λ 2 can be determined up to two-fold ambiguity. In addition, combined with the information about σ(γγ → Φ → gg) (or about σ(pp → Φ → γγ) at the LHC), the quantity η can be determined. (The determination of η may be challenging only with the LHC experiment unless the cross section for the process pp → Φ → gg is measurable at the LHC.) Thus, we will understand the relative size of Λ i 's, from which we will acquire information about the physics behind the higher-dimensional operators given in Eq.
(2) or (3). We also note that, if a large amount of the event sample of the process σ(γγ → Φ → ZZ) is obtained, CP property of Φ may be obtained from the angular correlation of the decay products of Z bosons.
So far, we have assumed that the di-photon events observed at the LHC is due to the scalar-boson production via the gluon-gluon fusion. Another possibility is the production of the scalar boson due to photon-photon collision. In such a case, the cross section for the scalar-boson production at the LHC is estimated as [104] Then, for the narrow width case, we obtain (The cross section for other final state F can be obtained by multiplying Eq. (31) by Br(Φ → F )/Br(Φ → γγ).) Thus, the cross section for the γγ final state is orders of magnitude larger than that of the background (see Table 1), and hence the process γγ → Φ → γγ will be observed by the photon-photon collider. In addition, the cross sections for the γZ and ZZ final states are typically of the same order of that for the γγ final state unless Λ −1 γZ and Λ −1 ZZ are extremely small. The cross section for the W + W − final state can be also sizable unless Λ 2 ≫ Λ 1 . Thus, in this case, detailed studies of the di-photon resonance production with the electroweak gauge boson final states are expected. The detectability of the process of γγ → Φ → gg depends on Br(Φ → gg); S gg / N (BG) qq becomes larger than 5 at L ee = 1ab −1 when Br(Φ → gg)/Br(Φ → γγ) 2 × 10 −4 .
Finally, we comment on the production of Φ with the e + e − collision. With the interaction given in Eq. (2) or (3), Φ can be produced with the process of e + e − → Φγ and ΦZ. The Φ production is also possible via the vector-boson fusion processes of e + e − → Φe + e − and e + e − → Φν e ν e . We have estimated the cross section for these processes, taking the centerof-mass energy of 1 TeV. For η = 1 and −10 ≤ Λ 1 /Λ 2 ≤ 10, the cross sections for these processes are typically 10 −1 − 10 −2 fb. Thus, the cross sections at the photon-photon collider are a few orders of magnitude larger. The discussion about the detectability of Φ at the e + e − collider requires detailed study of the backgrounds, which we leave for future study.
In summary, we have studied the prospect of investigating a scalar boson Φ at the photonphoton collider, assuming that the recently observed LHC di-photon excess is due to the scalar boson. Assuming also that the scalar-boson production at the LHC is dominated by the gluon-gluon scattering and that σ(pp → Φ → γγ) ∼ 10 fb at √ s pp = 13 TeV, the total cross section for the scalar-boson production at the photon-photon collider with √ s ee ≃ 945 GeV can be as large as ∼ 170 fb (taking m Φ = 750 GeV). We have also seen that various decay modes of the scalar boson may be observed. Thus, if the existence of the new scalar boson is confirmed with the next run of the LHC, the photon-photon collider can play an important role to study the detailed properties of the scalar boson.