How resonance-continuum interference changes 750 GeV diphoton excess: signal enhancement and peak shift

A hypothetical new scalar resonance, a candidate explanation for the recently observed 750 GeV diphoton excess at the LHC 13 TeV, necessarily interferes with the continuum background gg → γγ. The interference has two considerable effects: (1) enhancing or suppressing diphoton signal rate due to the imaginary-part interference and (2) distorting resonance shape due to the real-part interference. We study them based on the best-fit analysis of two benchmark models: two Higgs doublets with ∼50 GeV width (exhibiting the imaginary-part interference effect) and a singlet scalar with 5 GeV width (exhibiting the real-part one), both extended with vector-like fermions. We find that the resonance contribution can be enhanced by a factor of 2 (1.6) for 3 (6) fb signal rate, or the 68% CL allowed mass region is shifted by O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document} (1) GeV. If the best-fit excess rate decreases in the future data, the interference effects will become more significant.


Introduction
Recently, mild excesses in diphoton invariant mass distribution have been observed in both ATLAS [1] and CMS [2] experiments at Large Hadron Collider (LHC) 13 TeV running. The local significances of the excesses are 3.6σ and 2.6σ, respectively, preferring a new resonance at around 750 GeV decaying to diphotons [1][2][3]. Although LHC 8 TeV data did not reveal significant excess at the same mass range, they are not currently inconsistent with the 13 TeV excess; see e.g. [3]. The tantalizing hint of a new resonance triggered various theoretical proposals  that are allegedly said to fit the 750 GeV excess rate ∼ O(1) fb. Also, both a narrow and a somewhat broad resonance with Γ ∼ O(10) GeV were found to fit the data similarly well [1,3].
The effects can be especially sizable if the resonance width is at least comparable to experimental resolutions or bin sizes, Γ 5 GeV. For the 125 GeV SM Higgs boson, for example, even though it is narrow, the resulting peak-shift is ∼ 70 MeV [89,91] and will be comparable to the pole-mass measurement uncertainty soon (currently ∼ 490 MeV [95]). For a 750 GeV gg-fused scalar resonance with O(1) fb diphoton rate, the resonance-continuum interference is generally large: the resonance-squared S ∼ O(1) fb and the gg → γγ continuum background B ∼ 0.2 fb/40 GeV naively generate 2 √ SB/S ∼ (30 − 90)% relative interference effect. The interference is particularly large in the diphoton channel because the scalar resonance contribution is two-loop while the interfering continuum background is only one-loop as shown in figure 1, so that the above naive estimation of the relative interference is generally loop-factor enhanced [93,94].
The two main interference effects arise according to the relative phase between the resonance and the continuum processes. The real-part interference (with the relative phase φ ∼ 0, π, as will be defined and discussed) induces either peak-dip or dip-peak pattern added to a resonance peak, distorting the resonance shape from a pure resonance peak. On the other hand, the imaginary-part interference (with φ ∼ π/2, 3π/2) simply rescales the resonance peak, hence enhancing or suppressing the resonance peak. The non-zero phase is generated when some particles running in loops are lighter than 375 GeV.
In this paper, we investigate each interference effect on the current 750 GeV excess data by considering two benchmark models. Each model exhibits each interference effect. We first describe our method of calculating resonance shapes including interferences in section 2.1 and the diphoton datasets and best-fit analysis method in section 2.2. The two benchmark models are introduced and our main results are discussed in section 3 and section 4. Then we conclude and discuss prospects in section 5.

Diphoton rate and resonance shape
We consider a scalar resonance in the gg → γγ. It interferes with the one-loop continuum backgrounds shown in figure 1. The total differential cross section including the interference is written as where L gg (x) = 1 x dy (x/y)f g/p (y)f g/p (x/y) is the gg parton luminosity andσ cont,sig are the parton-level cross sections. We use CT10NNLO PDF set [96]. The signal cross-section σ sig , the deviation from the SM background, consists of the resonance-squared and the resonance-continuum interference [93], where s φ = sin φ and c φ = cos φ, and we factor out Breit-Wigner (BW) parts. We definê σ res,int and the relative phase φ in terms of phase-space integrated squared amplitudes where θ * is the scattering angle in the c.m. frame, and the summation is over helicity and color indices. We introduce a ratio R, defined by which measures the relative size of interference. The shape of the invariant mass distribution is determined by the relative phase φ. In figure 2, we present the m γγ distribution for various φ's with M = 750 GeV, Γ/M = 0.05 and R = 0.06 at the 13 TeV LHC. The left panel corresponds to the cases for purely real φ or purely imaginary φ. We find that φ = 0 (φ = 180 • ) yields a dip-peak (peak-dip) structure. If φ = 90 • , an enhanced peak structure appears. φ = 270 • generates a reduced JHEP05(2016)009 BW-type peak (when 2Γ < RM ) or a dip (when 2Γ > RM ). In the right panel, more general cases with both real-part and imaginary-part interferences are considered. The φ = 45 • (φ = 135 • ) case, which can be considered as the deviated one from φ = 90 • toward φ = 0 (φ = 180 • ), yields a shifted peak into higher (lower) mass, accompanying a mild dip. On the other hand, the φ = 315 • (φ = 225 • ) case shifts the dip into lower (higher) mass, with a mild peak.
Finite bin sizes in real experiments, however, limit the measurement of the full m γγ distribution. The crucial factor is the total width of the resonance particle. For a narrow resonance, the real part interference, the term proportional to c φ in eq. (2.2), is washed out after the integration over m γγ . Since the invariant mass distribution is highly accumulated near the resonance peak, we can consider parameters R, φ and parton luminosity as constant values. Then the total signal rate with the interference effect, defined as σ mNWA , is obtained as [93] σ mNWA = σ NWA · C = M π Γ L gg M 2 /s σ res (M 2 ) · C, for a narrow resonance, (2.6) where C = (1 + 2Γ RM s φ ) quantifies the strength of the imaginary-part interference. Note that the terms inside the square bracket corresponds to the usual total rate in the narrow width approximation (NWA), production cross section times branching ratio. The subscript mNWA represents modified NWA. It is useful to expressσ sig (ŝ) in terms of σ mNWA which is measured in experiments: This is our resonance shape function for a narrow resonance. For a broad resonance, with Γ 50 GeV, we now need to take into account the m γγ dependence of R, φ and parton luminosity; they are not constant in m γγ anymore. We redefine the total rate σ mNWA for a broad resonance by the integrated differential rate around the resonance mass M : , for a broad resonance, (2.8) where σ sig is given in eq. (2.1). We set ∆ = 100 GeV for our broad resonance example. We also use the following ratio to quantify the strength of the imaginary-part interference for a broad resonance. This K intf factor is approximately equal to the C factor for a narrow resonance in eq. (2.6). The resonance shape function is parameterized not only by usual mass M , width Γ and the total rate σ mNWA but also by the relative interference phase φ. R is not a completely independent parameter as shall be discussed. The purely real-part (imaginarypart) interference corresponds to φ = 0, 180 • (φ = ±90 • ). The real-part interference induces peak-dip or dip-peak structure in addition to a BW peak while the imaginarypart interference either enhances or reduces the BW peak or convert the peak to a BW JHEP05(2016)009 dip [93]. Thus, the purely real-part interference can most significantly change the resonance shape from a BW peak while the purely imaginary-part interference can most significantly enhance the signal rate (or peak height). These two effects are our main topics. We will study two benchmark models for each of them.
It is hard to carry out a model-independent best-fit analysis including interference effects based on eq. (2.2) and eq. (2.7). The interference depends not only on M , Γ, σ mNWA , which are usually chosen in model-independent analysis without interference effects, but also on φ and R. In particular, R is correlated with σ mNWA , which is hard to obtain the analytic relation. In this regard we use two benchmark models to numerically discuss the interference effects. For the (purely) real-part interference, we consider a singlet model which introduces a CP-odd SM singlet scalar with a minimal set of vector-like quarks and vector-like leptons: see section 3. For the (purely) imaginary-part interference, Type II 2HDM with vector-like leptons is to be studied: section 4.
We also comment on our implementation of higher-order corrections. We first compare our LO total rate without interferences to the result obtained by HIGLU fortran package [97], which includes next-to-next-to-leading-order QCD and next-to-leading-order EW contributions, to obtain the correction factor. Then we multiply the same correction factor to the resonance-square termσ res and the interference termσ int . Although this assumption approximately accounts for higher-order corrections to the total rate, it implies that R =σ res /σ int does not receive appreciable higher-order corrections. It is reasonable to expect a substantial cancelation of higher order correction betweenσ res andσ int . We relegate any existing correction of R to the theoretical uncertainty due to lacking of higher order calculation for interference term. In any case, both the real-part and the imaginary-part interferences approximately grow with 1/R. Thus, any corrections to R would directly affect what we discuss in this paper.

Dataset and method
In order to quantitatively study interference effects on the 750 GeV diphoton excess data, we perform a Poissonian likelihood analysis to find the best fit. The dataset is from the latest LHC 8 and 13 TeV diphoton resonance search at around m γγ = 750 GeV of both ATLAS and CMS experiments. We read in the predicted backgrounds and observed data from the reported plots in refs. [1,2,98,99]. The total uncertainty in each bin is assumed to be 2 (1.5) × statistical uncertainty for LHC 13 (8) TeV data.
The fit ranges considered in this paper are We choose ATLAS 8 data bins closest to 630 and 830 GeV. The range is somewhat broad so that we can consider a broad resonance as well. CMS 13 dataset is divided into CMS EBEB 13 and CMS EBEE 13 categories depending on which parts of detectors identify photons. We consider them as independent datasets. Fiducial signal efficiencies are taken from the experimental references and ref. [3].

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We carry out a χ 2 -fit to all the data bins within the range, and take the total change of χ 2 compared to the SM-fit (background-only), ∆χ 2 = χ 2 − χ 2 SM , as a measure of how well the model fits the data. Our SM-fit (background-only) results are: 3 Singlet Model: real-part interference

Singlet Model
Consider a CP-odd SM-singlet scalar Φ = A which couples to vector-like quarks Q ≡ Q 7/6 = (3, 2, 7/6) and vector-like where s Q,L are real Yukawa couplings, M Φ,Q,L mass eigenvalues, N Q,L number of fermions, and q Q,L electric charges. We choose Q 7/6 and L 3/2 from the minimal matter list [100]the list of new particles that can eventually decay to SM particles -since they have the largest electric charges. We consider A, but H shall also exhibit similar effects.
In the quark sector, we introduce a single vector-like Q with fixed parameters We still have enough lepton sector free parameters that we can use to fit the data and to illustrate interference effects.
In the lepton sector, we consider The sign of the Yukawa s L determines the sign of the relative phase: s L → −s L approximately changes the relative phase φ → π + φ. It is an approximate relation because Q also contributes to the Φ → γγ part although it is subdominant to the L contribution. We will compare the results with positive and negative s L (as well as with the results without any interference accounted for) to see how the best-fit changes with interference effects. Although we only need N ≥ 2 to make BR(Φ → γγ) 90%, we also want to make Φ broad enough by having large enough N , as will be discussed below.

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Another important parameter is the width. In the above model, the width is typically too small ( 1 GeV) to make interference effects apparent in current experiments; Φ mainly decays to loop-induced gg and γγ where loop functions A Φ=A 1/2 are defined as in ref. [101], and other signals such as Zγ, ZZ, W W are currently well below their LHC 8 sensitivities. If such a narrow resonance falls within a single experimental bin, the real-part interference (although itself is independent on the width) is cancelled out. In addition, the imaginary-part interference is small since it is directly proportional to the width as (C − 1) ∝ Γ. Thus, to illustrate the impacts of interference effects, we assume a bigger constant width which is easily accomplished by adding extra hidden decay modes of Φ, not constrained at all [102]. We cannot assume an arbitrarily large new decay width because diphoton signal will then be relatively suppressed. If the N L is smaller, the total width decreases and the interference effects will be less significant. Meanwhile, for M L ≤ M Φ /2, the decays into vector-like leptons dominate and the diphoton signal becomes too suppressed. Although such light leptons can change the phase φ and introduce different interference effects, we cannot fit the diphoton excess data well and do not discuss this possibility further. An important feature of the singlet scalar model is which induces almost purely real-part interference. This is the case in which resonance shape is maximally distorted from pure BW shape (and the peak location is maximally shifted), for the given total rate. The small but non-zero phase is generated from the SM quark loops in gg → γγ background box diagrams.

Results -Singlet Model
In figure 3 we show an example of the SM-singlet scalar resonance shapes for s L > 0 (blue-solid) and s L < 0 (red-dashed) with full interference effects. For comparison, we also show the resonance shape without interference (green-dotted). All three cases have the same NWA rates and the width Γ Φ . But s L > 0 (s L < 0) induces a small dip-peak (peak-dip) interference pattern added to the BW peak, so that a long tail toward a high (low) invariant mass region appears and the peak shifts toward the same direction. As a result, the best-fit results change, even with the same NWA rates, masses and widths. We Almost real part intf singlet A Figure 3. Example diphoton resonance shapes with s L > 0 (dip-peak interference, blue-solid ), s L < 0 (peak-dip interference, red-dashed ), and no interference (green-dotted ) for the same mass M Φ = 750 GeV and the NWA rate σ NWA 4 fb. The relative phase φ 8.3 • (188.3 • ) for s L > 0(< 0) induces almost purely real-part interference, and the resulting peak shifts and long tails affect bestfit analysis. The small imaginary-part interference also makes true observable mNWA rates σ mNWA and peak heights slightly different. We set |s L | 1.5 and Γ Φ =5 GeV.
quantify such interference effects in this subsection. The small but non-zero imaginary-part interference, eq. (3.7), actually makes σ mNWA (true observable rate defined in eq. (2.6)) and the peak heights slightly different among the three shapes. Figure 4 shows the 68% and 95% CL allowed regions from individual ATLAS 13 (left) and CMS EBEB 13 (right) datasets, for a singlet scalar Φ = A model with s L > 0 (upper) and s L < 0 (lower). For comparison, we also show the results without any interferences accounted for (dashed). These datasets are the ones that most strongly prefer the existence of a 750 GeV resonance. And the interference effect does not change the preference of a new resonance contribution; the data fit still better with a new resonance even with interference effects. Comparing the upper panels for s L > 0 with the lower panels for s L < 0, we find that the 68% CL best-fit mass parameter is shifted by about 1-4 GeV while a much bigger shift O(1) GeV is expected for the 95% CL region. The shift is also bigger for weaker couplings s L because the signal is smaller and R is relatively bigger. For s L > 0 producing a dip-peak interference, the resonance peak location shifts toward a higher mass region (see figure 3); consequently, a somewhat smaller mass parameter can fit the data most well. Meanwhile, the best-fit coupling strength is not significantly changed with both signs of interference effects.
In figure 5, we investigate the interference effects in the whole dataset including LHC 13 and LHC 8 dataset that do not strongly prefer the existence of a new resonance. The 68% C.L. allowed regions again shift due to the interference by about 1-4 GeV and a bigger shift is expected for the 95% CL region or for weaker couplings s L . The preference of an additional resonance still exists.
There is a noticeable tendency that interference effects become stronger with a weaker s L , as can be deduced from a wider best-fit mass shift with smaller s L in figure 4 and  . This is a general result of interference; the real-part interference approximately grows with 1/R ∼ A cont /A res amplitude ratio, which measures the background-resonance interference contribution compared to the resonance-squared contribution. If future data prefer a weaker signal, the interference effects will be larger and more important.
Finally, we briefly compare various best-fit results. Compared to the ATLAS 13 result in figure 4, the CMS EBEB 13 prefers a resonance with a slightly higher mass and weaker coupling. But the preferences of a new resonance around 750 GeV from both data are consistent with each other. Including LHC 8 datasets in figure 5 significantly prefers a weaker coupling and actually worsens the best-fit (total |∆χ 2 min | in the right panel decreased from the left panel). This may imply that the LHC 8 datasets do not strongly favor the resonance contribution.

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Note that the top quark Yukawa couplings of H 0 and A 0 are inversely proportional to t β in the alignment limit. The observed diphoton excess rate of O(1) fb is too large to be explained in the original 2HDM with the perturbativity of Yukawa coupling [4,86]. The alignment limit is efficient to enhance Br(H 0 → γγ) by forbidding H 0 → W W, ZZ decays. If t β is small like ∼ 1, the heavy Higgs bosons dominantly decay to the top pair, and the diphoton branching ratio is still very small such as Br(φ → γγ) = 7.8 (8.7) × 10 −6 for φ = H(A). The diphoton signal rate is just σ(pp → H/A → γγ) 0.01 fb. If t β is large, we may enhance the diphoton branching ratio by reducing Br(H/A → tt), but the gluon fusion production cross section is also suppressed. In order to achieve the needed O(1) fb diphoton signal, we extend the model with extra VLLs, to be called the VLL-2HDM.
We now introduce VLLs, L L , E R , D R , L R , E L , D L , of which the quantum numbers are summarized in table 1. Note that the electric charges of E ( ) and D ( ) are −1 and −2, respectively. All of the VLLs in table 1 are imbedded in one family. In the following analysis we introduce 3 VLL families. The Lagrangian of the VLLs in Type II 2HDM is In this work we neglect the mixing between VLLs and the SM leptons although its phenomenological impact is interesting [105,106].

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The mass matrix in the basis of (E, E ) is We have similar form of M D by changing Y ( ) We consider the case where heavier mass eigenvalues are much larger than the lighter ones, for exam- 1. Then, the contributions from the heavier mass eigenstates E 2 and D 2 are suppressed. For simplicity, we assume the two light mass eigenvalues are degenerated in mass, (M E 1 = M D 1 = M ). We do not consider the mass M below M Φ /2 since the new decay channels of H/A → EĒ/DD suppress the diphoton branching ratio quickly. We also assume that Y E = Y E and Y D = Y D for simplicity.
The Yukawa terms for the VLLs in the mass eigenstate basis become where where τ f = M 2 Φ /(4m 2 f ), the relative Yukawa couplings normalized by the SM values arê y h t,b,τ = 1,ŷ H,A t = ∓1/t β andŷ H,A b,τ = t β for Type II in the aligned 2HDM, and the loop functions A H/A 1,1/2 (τ ) are referred to ref. [101]. The VLL contributions A Φ γγ,VLL in eq. (4.5) are given as We vary M from 375 GeV to 600 GeV and y E,D from −4π to 4π. The final comment is on the constraint from the Higgs precision data. As shown eq. (4.5), the VLL loop also contributes to h → γγ, which is already very limited by the 8 TeV LHC data. If two Yukawa couplings y D and y E are tuned as

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new contribution to the Higgs precision data vanishes. If t β = 1, the cancellation of the VLL contributions to h → γγ equally happens to the A → γγ decay. Since the A diphoton signal is usually larger than the H signal if there is no cancellation, we choose t β = 0.7 in the analysis. This small t β and thus enhanced top quark Yukawa couplings of H and A shall bring about the excesses in the tt resonance searches. At the 8 TeV LHC, we find that the C factor for gg → H(A) → tt is −0.53 (−0.76), which yields about σ · Br −430 fb. This is under the LHC8 upper bound of 550 fb [107]. Other exclusion limits from Zγ [108], bb [109], τ + τ − [110], and jj [111] channels at the 8 TeV LHC are also satisfied in the parameter space under consideration.

Results -VLL-2HDM model
We first discuss the total widths of H and A, both of which are dominated by the tt decay channel. Using the running top quark mass m t (µ = 750 GeV) = 147 GeV [112], we have Γ H(A) = 46(58) GeV. Since the degenerate H and A do not interfere, we regard them as independent resonances and superpose those resonance distributions. We perform a minimum χ 2 analysis (see section 2.2) and find the best-fit signal rates to the LHC 13+8 datasets σ(pp → Φ → γγ) = 6.5 ± 2.5 fb (68%CL) 6.5 +4.5 −3.5 fb (95%CL) , (4.8) which are in agreement with ref. [3]. In our scenario of VLL-2HDM the relative interference phase is close to ±90 • , corresponding to the imaginary interference. The interference between the H resonance and the continuum background, for example, yields φ ∈ Depending on the sign of Yukawa coupling y E , the whole complex phase is changed by π. It maximally enhances the signal rate for φ ≈ 90 • (constructive interference) and maximally suppress the signal rate for φ ≈ −90 • (destructive interference). Figure 6 shows our results in the parameter space (y E , M ) for the VLL-2HDM. In the upper panels, the contours of the K intf (green solid lines) defined in eq. (2.9) and the modified NWA rate (red dashed lines) are presented. Considering the observed excess of diphoton signal, σ mNWA for K intf is obtained only for the excess region over the continuum background. For comparison, the 68% C.L. allowed parameter space is also presented. It is of great interest that quite large interference effects, i.e., large (K intf − 1), appear around the measured total signal rate, as shown in figures 6(a) and (b). For y E > 0, K intf > 1 and thus constructive interference occurs: the interference enhances the signal by factor of 2 for the 3 fb total rate. Within the allowed region at 68% C.L., the interference effect ranges from 40% to 80% when y E > 0. For y E < 0, K intf < 1 so that destructive interference occurs: in order to explain the signal rate, we need quite large magnitude of y E and thus very limited parameter space is allowed. Figures 6(c) and (d) show the 1σ allowed region (red colored) and 2σ allowed region (yellow colored) with interference in the parameter space (y E , M ). In order to present the interference effect, the 1σ allowed region without interference (hatched) is also given. For both positive y E and negative y E cases, the interference affect the underlying physics quite significantly. With positive y E and M = 400 GeV, for example, y E required for the signal rate 6.5 fb is reduced from ∼ 7.5 to ∼ 5.5 by including the interference effects. Equivalently, the required number of VLL family is also reduced from 4 to 3.  Table 2. Numerical values for φ, K intf , and σ mNWA for H, A and the total in the VLL-2HDM. The benchmark parameter points are chosen to yield total signal rates of 1, 3, 6 fb.

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In table 2, we present the numerical values for φ, K intf , and σ mNWA for five benchmark parameter points. In order to see the individual interference effects, we show φ and K intf separately for H and A. For both H and A, the relative interference phase is about ±90 • : almost purely imaginary interference occurs. K H intf and K A intf show that the interference effects are larger for A than for H. This is because the A contribution is small due to the significant cancelations among VLL loops. The resulting small R (resonance to continuum ratio) yields large interference as can be seen in eq. (2.2). One crucial result is that the interference effects become larger with decreasing signal rate. For 1 fb signal rate, for example, the enhancement factor due to the interference can be as large as a factor of three. If the current signal rate is fluctuated up and the future precision measurements lead to lower signal rate, the interference effects become crucial.
Finally we make some comments on the interference effects in a higher order production process, the quark-gluon initiated one. Although the resonance signal rate S is smaller than that in the gluon fusion production, the tree-level continuum background gq → γγq has large rate B. The interference rate ∼ 2 √ SB can be non-negligible. Since this is a 2 → 3 process, our formalism based on the m γγ distribution for a 2 → 2 process in eqs. (2.1) and (2.2) do not apply. Full analytic study of the interference effects in a 2 → 3 process is beyond the scope of this paper. Nevertheless estimating the interference signal rate in the gq process is required to validate our main results in figures 4, 5, and 6: if σ int (qg → γγj) is compatible with σ int (gg → γγ), the preferred regions by the 750 GeV diphoton excess shall be changed. By using MCFM [113] for the SM continuum background rate B and the HIGLU for the pure resonance rate S, we perform a rough estimation for the interference effect, 2 √ SB. Since the gq process is a reducible one, a hard jet with p j T > 30 GeV is vetoed. We find that σ int (qg → γγj) in the bin of m γγ ∈ [700, 800] GeV is about 10% of the corresponding σ int (gg → γγ). Our main results are not affected significantly.

Conclusions and discussions
We have investigated the impacts of the resonance-continuum interference in the gg → γγ process on the recently observed 750 GeV diphoton excess. The two most important interference effects -signal enhancement from the purely imaginary-part interference and shape distortion from the purely real-part interference -have been studied in two benchmark models.

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First, a CP-odd singlet scalar with Γ = 5 GeV (extended with vector-like fermions) was considered to represent the purely real-part interference case. The model predicts that the 68%(95%) CL allowed mass range shifts by 1-4 (any O(1)) GeV as a result of the interference. The shift is expected to be larger with a weaker coupling parameter space, which will be more preferred if the excess rate decreases in the future. Second, the heavy Higgs bosons in the two-Higgs-doublet-model with Γ ∼ 50 GeV (extended with vector-like leptons) was considered to represent the purely imaginary-part interference case. In this case, the diphoton resonance signal is found to be enhanced or suppressed by a factor of 2(1.6) for 3(6) fb signal rate. Again, the effect is bigger for a weaker coupling parameter space.
Although our results are obtained with benchmark models, any scalar resonance in the gg → γγ process with similar widths and total rates would exhibit similar sizes of interference effects. In addition, the relative phase φ between the resonance and the continuum will determine the type of interference effects. For the given diphoton rate and the phase φ, the total width is the most important parameter. If the width is much smaller than the current resolution ∼ O(1) GeV, the real-part interference will cancel out and the imaginary-part interference will be small in proportion to the width. If a resonance is very broad, a careful study of resonance shape including its m γγ -dependence should be carried out, based on our formalism and method presented in this paper.
The future precision shape measurements and interpretations taking into account the resonance-continuum interference can provide important information and consistency check of a new resonance. One cannot only test a BW resonance hypothesis but also measure φ and various other parameters that come into the interference effects. Remarkably, if any noticeable deviations from a BW shape can be fit well with the real-part interference, this would be another convincing evidence of a new resonance.