Heavy photophobic ALP at the LHC

We study the photophobic ALP model in high-mass regions under LHC Run-II. Since the ALP is predominantly coupled with electroweak gauge bosons such as $ZZ$, $WW$, and $Z\gamma$, and less with di-photon, the model may be probed via multi-boson final-state processes. We find that on-shell ALP productions with $Z\gamma$ final states currently provide the best sensitivities for $m_{a}>40~{\rm GeV}$.


Introduction
Pseudo-scalar bosons are one of the most attractive candidates for new particles.They often appear in models with extended scalar sectors.In particular, an axionlike particle (ALP) has been widely studied.Its mass is assumed to be generated by explicit violations of global symmetries, and couplings with gauge bosons in the Standard Model (SM) are characterized by remnant shift symmetries.
In this paper, we study heavy photophobic ALPs in light of the LHC Run-II results.In the previous work [1], on-shell productions of ALPs have been investigated by using LHC data at the center-of-mass energy √ s = 8 TeV with an integrated luminosity L dt ≃ 20 fb −1 .The sensitivities are degraded in the high-mass regions because the production cross section and/or luminosity was not large enough.In another work [15], non-resonant signals of off-shell ALPs were explored for ALP masses up to 100 GeV.Above this mass range, on-shell productions become relevant.Hence, we revisit LHC searches for on-shell ALP productions especially in high-mass regions by employing the latest LHC Run-II data.Since the ALP is coupled mainly with the electroweak gauge bosons (ZZ, W W , and Zγ), we investigate multi-boson final-state processes, pp → W W W , pp → Zγ → ν νγ, and pp → Zγ → ℓ + ℓ − γ.
This paper is organized as follows.In Sec. 2, we briefly introduce the photophobic ALP model.In Sec. 3, we explain how to reinterpret the LHC data for constraints on the ALP coupling, and show numerical results in Sec. 4. We conclude in Sec. 5. Lastly, although the original photophobic ALP model does not include a direct ALPgluon coupling, we analyze the case when the coupling is introduced in Appendix A.

Model
The photophobic ALP is assumed to be coupled to the SU(2) L and U(1) Y gauge bosons.The other direct couplings with SM particles are suppressed.The ALP Lagrangian is shown as [28] where f a is the ALP decay constant, and where we assume that m a ≲ f a is satisfied, see Refs.[26,27] for our conventions.After electroweak symmetry breaking, the interactions are generally expressed as 2) The coupling constants are related to c W W and c BB as ) where c W = cos θ W , s W = sin θ W , c 2W = cos 2θ W , and s 2W = sin 2θ W with the Weinberg angle θ W .In the photophobic model, the ALP coupling to di-photon is absent at the tree level, i.e., s 2 W c W W + c 2 W c BB = 0 is satisfied, yielding g aγγ = 0.Then, g aZγ , g aZZ are denoted in terms of g aW W as (2.7) In the model, there are no direct ALP couplings with SM particles other than ZZ, W W , and Zγ.In particular, no direct ALP-gluon coupling g aGG or ALP-fermion couplings g af f are introduced.In UV models (see e.g., Ref. [1]), g aγγ = g aGG = g af f = 0 is realized at a high scale.If the ALP is massless, as a result of the shift symmetry, g aγγ and g aGG are not generated via renormalization group evolution, but g af f is generated at the one-loop level (see Ref. [29,30]).On the other hand, non-zero ALP mass generates g aγγ and g aGG at the one-and two-loop levels, respectively [6], since the symmetry is softly broken.Nonetheless, such loop-induced g aγγ and g aGG are considered to be less effective for LHC searches.#2

Decay of ALP
The ALP decays into a pair of SM gauge bosons.The partial decay widths for a → V i V j (V i,j = γ, Z, W ± ) are obtained as [1,6,31] with λ(x, y) = (1 − x − y) 2 − 4xy.Here m V is the gauge-boson mass (m γ = 0).Note that δ ij = 0 for a → Zγ and a → W + W − .The ALP coupling to di-photon g eff aγγ is induced by loop corrections with g aW W in Eq. (2.6) as [6] where α ≡ e 2 /(4π) with the QED coupling e = gs W .The loop function B 2 is defined as where f (τ ) is given by #2 Although the original setup of the photophobic ALP model predicts g aGG = 0, its presence may affect the collider signatures significantly.We investigate LHC signatures when g aGG is turned on at tree level in Appendix A.
with τ W = 4m 2 W /m 2 a .On the other hand, it is sufficient for us to evaluate the decay widths for a → Zγ, ZZ, W + W − at the tree level, i.e., g eff aV i V j = g aV i V j .When the ALP is lighter than the Z boson, the ALP decays into either a pair of SM fermions, a → f f , or the fermions with a photon, a → Z * γ → f f γ, by exchanging an off-shell Z boson.Since the ALP does not couple with SM fermions directly, the former proceeds via radiative corrections.On the other hand, even though the latter is a three-body decay, it proceeds at the tree level, and thus, its decay width can be comparable to the former.
For m a ≪ m Z , the partial decay width of a → Z * γ → f f γ is obtained as where N f c = 1 (3) is the color factor for leptons (quarks), and g Z = g/c W is the Zboson coupling constant.The vector and axial form-factors of Z boson are defined as g The formula valid for any m a is provided in Ref. [26].
The ALP decays into a pair of leptons and heavy quarks, a → f f , via gaugeboson loops.The partial decay widths are obtained as [6,29] The effective coupling induced by radiative corrections is given by where Q f and I f 3 are the electric charge and the weak isospin of the fermion f , and Here, we keep the terms enhanced by ln (Λ 2 /m 2 f ) or ln (Λ 2 /m 2 V ) (V = Z, W ). We take the cutoff scale Λ to be 4πf a in this paper.Subleading terms are given in Refs.[6,29,31], though they are irrelevant here (cf., Ref. [32]).
On the other hand, the inclusive rate for the ALP decaying into light hadrons is shown as (cf., Ref. [6]) where m a ≫ Λ QCD is assumed.The effective coupling with gluons is given by Note that the above expression is not valid for m a ≲ 3 GeV, where the perturbative QCD is not applicable, and various hadronic decay channels appear (cf., Refs.[6,33]).We show the branching ratios of the photophobic ALP decay in Fig. 1.We set g aW W = 0.1 TeV −1 and the cutoff scale Λ = 4πf a = 4π × 10 TeV.For m a ≲ m Z , the decay is dominated by loop-induced decays into a pair of fermions, and by the tree-level decays into a pair of gauge bosons for m a > m Z .In particular, a → W W and/or Zγ becomes dominant for m a ≳ 100 GeV.Note that the neutrino channels are extremely suppressed.Also, a → Zh and a → hh vanish in our setup.

LHC signatures
Light ALPs are constrained by cosmology and precision/collider experiments.If the ALP mass is smaller than ∼ 1 GeV, the model is severely limited by cosmological measurements [1], while heavier ALPs are constrained by flavor and collider experiments.In particular, heavy meson decays are sensitive to g aW W for m a ≲ 4.8 GeV.The current status is summarized in Ref. [26].For 4.8 GeV ≲ m a ≲ m Z , LEP results have provided the leading constraints via searches for Z-boson invisible decays and Z → γa → γjj.The detailed analysis can be found in Ref. [1].
In this paper, we focus on heavy ALPs.For m a ≳ m Z the LHC measurements are sensitive to ALP contributions and have provided constraints on g aW W .In the previous work [1], on-shell ALP productions have been studied extensively with the LHC results at √ s = 8 TeV and L dt ≃ 20 fb −1 .The sensitivities are degraded rapidly as the ALP mass is increased because the production cross section/luminosity is not large enough.In the following, we reinterpret the latest LHC results obtained at √ s = 13 TeV.In particular, we analyze pp → W W W , pp → Zγ → ν νγ, and pp → Zγ → ℓ + ℓ − γ, via on-shell ALP production.#3  To generate the event samples, we employ MadGraph5_aMC@NLO 3.5.2[37] interfaced with PYTHIA 8.3 [38] for parton showering and hadronization.The ALP model is implemented by using a UFO model file generated with FeynRules 2.3 [39].Detector simulations are performed by DELPHES 3.5.0[40].

Statistical method
The signals are investigated by comparing the number of ALP signal events (n sig ) with the number of observed events (n obs ) and the expected number of background events (n bkg ).For pp → W W W and pp → Zγ → ν νγ, we evaluate the upper limits by using a modified frequentist approach, which is also called the CL s method [41,42].#4 The events are assumed to follow Poisson distributions, and the p-value and CL s are defined as The upper limit on the number of signal events at the 95% level, n sig up , is determined by solving CL s = 0.05.Then, the upper bound on g aW W is obtained from where L I is an integrated luminosity, A is the acceptance, and ϵ accounts for the efficiency.The production cross section σ is a function of m a and g aW W .For a given ALP mass, σ scales as g 2 aW W when the process is dominated by on-shell ALP productions.In practice, signal categories are defined by imposing cuts on the events, and an upper limit is obtained in each signal category.Among the categories, the most stringent constraint is adopted as the result.
There are two comments in order.First, although the CL s method does not always provide a real confidence interval, it is useful especially to accommodate the case where an experimental result appears to contain fewer events than the expected number of background events due to a fluctuation, which is likely to lead #3 There are briefly two approaches to studying ALP contributions at the LHC: searches for new resonances in event distributions and for event number excesses after kinematical cuts.For the former, among the ALP decay channels, a → Zγ provides a sensitive probe and will be studied in this paper.See Refs.[34,35] for a → ZZ, W W .For the latter approach, we analyze pp → W W W and pp → Zγ → ν νγ proceeding via a → W W and Zγ respectively.Although other processes such as pp → W W Z, W ZZ, and ZZZ (see Ref. [36]) may contribute, their limits on the ALP models are expected to be weaker than those obtained in this paper.

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to too strong exclusions.Such a situation occurs in some of the signal categories for pp → W W W and pp → Zγ → ν νγ.Next, Eq. (3.1) does not take account of systematic uncertainties.In the literature, they are not provided explicitly for each signal category.Besides, although there are potential correlations among the categories, such information is not shown, and we therefore omit them for simplicity.As explained below, the validity of the above method is checked by deriving limits on new physics models that are explored in Refs.[43,44] and comparing the results with those in the literature.

CMS W
The analysis is based on a data sample from the CMS collaboration at √ s = 13 TeV with L I = 35.9fb −1 [43].#5 The signal process is pp → W ± a → W ± W ± W ∓ (Fig. 2).In the event generation, we do not restrict the ALP and W boson to being produced on-shell, and their off-shell contributions are also taken into account.Owing to decay channels of the W bosons, two classes of signal events are considered in the experimental analysis: final states with two same-sign (SS) leptons and those with at least two jets and three leptons (3ℓ).
The event reconstruction and event selection criteria are based on Ref. [43].For the detector simulations, we modify the default DELPHES card for CMS as follows.Electron and muon candidates which satisfy p T > 10 GeV and |η| < 2.4 are selected.We discard the electron candidates with 1.4 < |η| < 1.6 and assume 95% and 85% efficiencies for those with |η| < 1.4 and 1.6 < |η| < 2.4, respectively.Jet clustering is performed in the anti-k T algorithm [46] with distance parameter R = 0.4, and jets with p T > 20 GeV and |η| < 5 within ∆R < 0.4 are selected.The efficiency to select b-quark jets is set to 80%.For other variables, we use the default values.
The kinematical cuts are summarized in Tables 1 and 2 for SS and 3ℓ events, respectively.The SS events are classified into six signal categories by the invariant mass of two jets m jj closest in ∆R ('m jj -in' and 'm jj -out') and the flavors of SS #5 In this paper, we do not use the results based on the LHC Run-II data samples with L I = 137 fb −1 (CMS) [36] and 139 fb −1 (ATLAS) [45], because they utilize multivariate techniques and it is not straightforward to implement them into our analysis.Table 1: Kinematical cuts for the SS final states based on Ref. [43], which contains two same-sign leptons and at least two jets.Table 2: Kinematical cuts for the 3ℓ final events based on Ref. [43], which contains exactly three leptons.
leptons ('e ± e ± ', 'e ± µ ± ', and 'µ ± µ ± ').Events with 65 GeV < m jj < 95 GeV are categorized in m jj -in, and the others in m jj -out.On the other hand, the 3ℓ events are classified into three categories by the flavors of final-state leptons: zero, one, or two same-flavor opposite-sign (SFOS) lepton pairs.#6 The ALP model has been analyzed by the CMS collaboration in the limited mass region, 200 GeV < m a < 600 GeV [43].We utilize their result for the validation of our analysis.There are two main differences between our approach and the experimental analysis.Although the production cross section is evaluated at the next-to-leading order in Ref. [43], our analysis is performed at the leading order.Furthermore, we employed the CL s method as explained above.We found that our upper bound on #6 The 3ℓ production processes can affect the SS category if one of the charged leptons is not detected, though the contribution is minor.
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s 5 S G p W a T p Z J 6 s F x t u B R X w p m 8 5 K m C 6 P H S G e X z Z T W S b 5 Y S n b H M M 1 j Z r p H H c d 0 o 5 p R y a d j e W a f Z y h e s U r r d T q
H w j X 8 g v 8 m 9 s r W 5 U I + y l g 3 e r 7 + X e 3 u z b m 5 t / z 3 U 1 8 S 5 h / 9 g 1 s W c J N X g Q 9 S q w d y 9 S w l 2 w v r 9 9 Table 3: Kinematical cuts for the Z(→ ν ν)γjj events based on Ref. [44].
g aW W is weaker by ∼ 40% compared to those in Fig. 3 in Ref. [43].#7 Therefore, the CL s method is found to provide a conservative limit on g aW W .

ATLAS Z(→ ν ν)γjj search
The analysis is based on a data sample from the ATLAS collaboration at √ s = 13 TeV with L I = 139 fb −1 [44].The signal process is pp → ajj → Z(→ ν ν)γjj (cf., Fig. 3).In the event production, off-shell contributions of a and Z are taken into account.We reinterpret the experimental results using the signal categories aimed at vector-boson fusion (VBF) productions of a Higgs boson decaying into a photon γ and massless invisible dark photon γ D .
The event reconstruction and event selection criteria are based on Ref. [44].We modify the default DELPHES card for ATLAS so that jet clustering is performed in the anti-k T algorithm with distance parameter R = 0.4.For other variables, we use the default values.The kinematical cuts are summarized in Table 3, where the photon centrality C γ is defined as We also evaluated the upper bounds without using the CL s method by employing the mean value of Poisson distributions for the upper bound following Ref.[1].The results become stronger by ∼ 50% than those in Ref. [43].In addition, higher-order effects can affect the results.Those effects as well as the analysis method could cause the discrepancy from the CMS result.4: Kinematical cuts for the Z(→ ℓ + ℓ − )γjj events, which are based on Ref. [51] but the cut for m Zγ (see the text).
The centrality for a third leading jet C 3 can be obtained by replacing η(γ) with η(j 3 ).The transverse mass constructed from the photon and E miss T is defined as The events are classified into ten 'categories' by the invariant mass of the leading two jets m jj (m jj < 1 TeV and m jj ≥ 1 TeV) and m T (0-90, 90-130, 130-200, 200-350, and > 350 GeV).
For the validation, we evaluated VBF productions of the Higgs boson decaying into γ + γ D .The signal events were produced at the next-to-leading order in Ref. [44] by using POWHEG v2 [47][48][49][50], where the diagrams exchanging a weak boson at the schannel are discarded.For comparison, we generated the events at the leading order using MadGraph5_aMC@NLO 3.5.2while excluding the s-channel diagrams.#8 We found that our results are consistent with those of Auxiliary table 3 in HEPData #9 , but larger by 20-40% than those in Table 9 in Ref. [44].
The analysis is based on a data sample from the ATLAS collaboration at √ s = 13 TeV with L I = 140 fb −1 [51].In contrast to the previous processes, the experimental analysis is aimed at searching for new resonances in the Zγ final state.We recast the experimental results specified for CP-even spin-0 productions, where the upper bound on the production cross section times a branching ratio of the resonance decaying into Zγ is provided.The result is given in the mass range from 220 GeV to 3400 GeV.The signal process is pp → ajj → Z(→ ℓ + ℓ − )γjj (cf., Fig. 3).Since it is the resonance signature that is of interest, the ALPs are assumed to be produced on-shell, and off-shell contributions are discarded.#8 We checked that the results are almost unchanged even if the s-channel diagrams are included.#9 https://www.hepdata.net/record/ins1915357 The event reconstruction and selection criteria are based on Ref. [51].We use the default DELPHES card for ATLAS.The kinematical cuts are summarized in Table 4. Here, we put a looser cut on the Zγ invariant mass m Zγ (100 GeV < m Zγ < 4000 GeV) than that in Ref. [51] (200 GeV < m Zγ < 3500 GeV).This is because we evaluated A × ϵ for CP-even spin-0 resonances by ourselves and found that the result was inconsistent with the experimental one (cf., Fig. 1 in Ref. [51]).Among the kinematical cuts, we noticed that the results are sensitive to the choice of m Zγ .It may be affected by reconstruction resolutions, and instead of refining the smearing function implemented in DELPHES, we simply loosen the cut for m Zγ such that the experimental result is reproduced.#10 Then, the upper limit on the number of signal events is obtained as where σ(pp → X → Zγ) up is the observed upper limit on the production cross section times branching ratio of the spin-0 resonance in Ref. [51].On the other hand, the number of signal events is obtained for the ALP as Since the cross section is from on-shell productions of ALPs, it is proportional to g 2 aW W , and we obtain an upper limit on g aW W from n sig < n sig up .

Results
In Fig. 4, we show the observed 95% upper limit on g aW W as a function of ALP mass m a .Here, Λ = 4πf a = 4π ×10 TeV is chosen to evaluate the branching ratios of loopinduced ALP decays.The bounds are obtained by reinterpreting the multi-boson searches for pp → W W W (blue), pp → Zγ → ν νγ (red), and pp → Zγ → ℓ + ℓ − γ (green).They are compared with the other constraints; the gray regions surrounded by dashed lines are excluded by LEP constraints and flavor limits.#11 We also show the previous LHC constraint [1] by the gray region surrounded by a solid line.
It is found that the best limit is obtained by pp → Zγ → ℓ + ℓ − γ (green) for 220 GeV < m a < 3400 GeV, for which the ATLAS result for new resonance searches [51] is used.The scattering proceeds via on-shell ALP production associated with two jets, pp → ajj → Z(→ ℓ + ℓ − )γjj (See Fig. 3).Here, the Z boson as well as the ALP is produced on-shell.For m a < 220 GeV, the limit is given by pp → ν νγjj (red).#12 If the mass is larger than ∼ 100 GeV, the signal events are dominated by pp → ajj → Z(→ ν ν)γjj, where both the ALP and Z boson are on-shell.On the other hand, in the smaller mass regions either a or Z would be off-shell.We found that the ALP is favored to be onshell for m a ≳ 30 GeV, i.e., the process is pp → ajj, a → Z * γ → ν νγ.Nonetheless, there are non-negligible contributions from the off-shell ALP productions, which are taken into account in our analysis.It is noted that the loop-induced ALP decays, especially a → b b, are taken into account in evaluating the signal events because they dominate the ALP total decay width for m a ≲ m Z (see Fig. 1).It is found that the LHC results supersede the LEP constraint for m a > 40 GeV.For lighter ALPs, the upper limit on g aW W is degraded because the branching ratio of a → Z * γ → ν νγ is suppressed.For m a ≲ 30 GeV the signal events are dominated by the off-shell ALP productions, and the constraint on g aW W eventually becomes insensitive to the ALP #12 Here, we generate the ALP events including the s-channel diagrams (cf., the left panel of Fig. 3).The results are insensitive to the contribution due to the kinematical cuts.Also, the production cross section for pp → a(→ ν ν)γjj is suppressed by BR(a → ν ν) ≃ 0. mass.In the plot, the result for pp → ν νγjj is shown only in the region m a > 10 GeV because the on-shell ALP productions are of interest in this paper.
Although the ALP decay is dominated by a → W W for m a ≳ 2m W , we find that the measurement of pp → W W W (blue) provides a weaker limit on the model.The signal events are dominated by on-shell productions of ALPs followed by decay into a pair of on-shell W bosons (pp → aW, a → W W ) for m a ≳ 2m W .The off-shell ALP contributions are relevant for lighter ALPs.The constraint on g aW W eventually becomes insensitive to the ALP mass, and the result is shown only for m a > 100 GeV.
As mentioned above, the ALP is favored to be on-shell even below the Z-boson mass scale for pp → ν νγjj.In contrast, for pp → W W W the on-shell ALP production pp → aW, a → W W * does not dominate the signal events for m a ≲ 2m W .This is probably because the branching ratio of a → W W * is suppressed due to a → Zγ proceeding at tree level in the latter case.In the former case (pp → ν νγjj), since the ALP total width is dominated by the loop-induced decay a → b b, the three-body decay a → Z * γ → ν νγ can contribute sizably even for m a ≲ m Z .
Let us compare our results with previous works.In Ref. [1], the collider constraints on on-shell ALP productions have been studied with the LEP and LHC results.In particular, the Z-boson decays were investigated for the former, and the latter was based on the data at √ s = 8 TeV and L dt ≃ 20 fb −1 .In comparison, we find that our result provides the best limit for m a > 40 GeV.Besides, even pp → W W W gives a stronger bound than what is given in the literature for m a > 200 GeV.In Ref. [15], off-shell ALP production has been studied for LHC data at √ s = 13 TeV.We found that our results are more severe than what is given in the literature for m a > 20 GeV, where the off-shell productions are dominant, and the constraint for m a < 20 GeV is comparable with the previous one.

Conclusion
In this paper, we have studied the photophobic ALP model in high-mass regions using the LHC Run-II results.Since the ALP-photon coupling is suppressed, the model can avoid tight constraints from searches for di-photon final states.The ALPs are predominantly coupled with electroweak gauge bosons, and we investigated the multi-boson final-state signatures at the LHC.We reinterpreted the LHC analyses of pp → W W W , pp → Zγ → ν νγ, and pp → Zγ → ℓ + ℓ − γ.We found that the on-shell ALP productions via pp → Zγ → ν νγ shows the best sensitivity in the mass range, 40 < m a < 220 GeV.For the mass region 220 < m a < 3400 GeV, the ALP resonance search via pp → Zγ → ℓ + ℓ − γ provides the most severe constrains.] Figure 6: Observed 95% upper limits on g aW W for g aGG = 0.1 TeV −1 (blue) and 1 TeV −1 (orange) as a function of m a obtained by the multi-boson searches for pp → Zγ → ℓ + ℓ − γ (left) and pp → Zγ → ν νγ (right).
where C F = 4/3.Here, we keep the terms enhanced by ln (Λ 2 /m 2 f ) or ln (Λ 2 /m 2 V ) (V = Z, W ). Subleading terms are given in Refs.[6,29,31], though they are irrelevant here.For m a ≳ 3 GeV, the hadronic decay rates are calculated perturbatively [6,29,31,32].#13 As for the hadronic decay rate, it is sufficient to evaluate Eq. (2.15) with the tree-level ALP-gluon coupling, i.e., g eff aGG = g aGG .In Fig. 5, we show the branching ratio of a → Zγ as a function of g aW W /g aGG .We find that the ratio decreases due to the hadronic contributions for g aW W ≲ g aGG .For m a ≲ 2m W , the ratio increases for larger g aW W /g aGG .On the other hand, the ratio is close to 0.2 at g aW W /g aGG ∼ 10 for m a > 2m W , where the total width is dominated by a → W W , and a → Zγ provides the next-to-largest contribution (see Fig. 1).
In Fig. 6, we show the observed 95% upper limit on g aW W as a function of ALP mass m a for g aGG = 0.1 TeV −1 (blue) and 1 TeV −1 (orange).The bounds are obtained by reinterpreting the experimental results for pp → Zγ → ℓ + ℓ − γ (left) and pp → Zγ → ν νγ (right).In the left panel, the constraints are provided for m a > 220 GeV.We find that the results are insensitive to g aGG for m a ≲ 2 TeV.This is because the cross section is given by the on-shell ALP production, gg → a → Zγ, Z → ℓ + ℓ − , and is proportional to σ(gg → a) × Br(a → Zγ) × Br(Z → ℓ + ℓ − ).Note that σ(gg → a) is proportional to g 2 aGG .If g aW W is small enough, since Br(a → Zγ) is scaled by (g aW W /g aGG ) 2 (see Fig. 5), the cross section becomes insensitive to g aGG .For larger m a the constraints lie above g aW W ≳ 0.1 TeV −1 , and Br(a → Zγ) is not scaled by (g aW W /g aGG ) 2 for g aGG = 0.1 TeV −1 .The constraint line terminates at m a ≃ 3 TeV #13 Meson productions should be considered for lighter cases [6,33].
for g aGG = 0.1 TeV −1 .As the ALP mass is increased, the production cross section decreases, and a larger branching ratio is required to saturate the upper bound on the number of signal events.However, since Br(a → Zγ) cannot be too large, LHC searches do not have a sensitivity above the ALP mass scale.
In the right panel, the pp → Zγ → ν νγ constraints are shown for m a > 100 GeV.Here, the on-shell ALP production gg → a → Zγ, Z → ν ν dominates the signal events.Since the constraint is weaker than g aW W = 0.1 TeV −1 , the branching ratio of a → Zγ is not scaled by (g aW W /g aGG ) 2 for g aGG = 0.1 TeV −1 .For heavier ALPs, since the production cross section decreases, the constraint line terminates at m a ≃ 800 GeV (2700 GeV) for g aGG = 0.1 TeV −1 (1 TeV −1 ).
In summary, although g aGG = 0.1 TeV −1 and 1 TeV −1 are likely to be too large to be generated by renormalization group evolution because the contribution arises at the two-loop level in the presence of g aW W (see the discussion in Sec. 2), the ALPgluon coupling can affect the LHC signatures significantly if it is introduced.It is found that if g aGG is sizable the LHC measurements can provide better sensitivities than the original photophobic ALP model.

)
with p T > 25/20/20 GeV and charge sum = ±1e Additional leptons No additional rejection lepton Jets At most one jet with p T > 30 GeV, |η| < 5 b-tagged jets No b-tagged jets tau-tagged jets No tau-tagged jets p T (ℓℓℓ) -> 60 GeV > 60 GeV ∆ϕ(p T (ℓℓℓ), p miss T |mee − m Z | > 15 GeV -m SFOS -|m SFOS − m Z | > 20 GeV |m SFOS − m Z | > 20 GeV and m SFOS > 20 GeV and m SFOS > 20 GeV m ℓℓℓ |m ℓℓℓ − m Z | > 10 GeV x b c c Z w 2 b R 5 M F P v O P e f c e + 6 M L c 8 W g S T k c G o 6 d i 5 + / s L M x c S l y 1 e u z s 7 N X 8 s H b s N n P M d c 2 / X 3 L B p w W z g 8 J 4 W 0 + Z 7 n c 1 q 3

Figure 4 :
Figure 4: Observed 95% upper limits on g aW W as a function of ALP mass obtained by the multi-boson searches for pp → W W W (blue), pp → Zγ → ν νγ and pp → Zγ → ℓ + ℓ − γ (green) at the LHC with √ s = 13 TeV.Here, the intermediate ALP, Z, and W bosons can be off-shell (see text for details).The gray regions surrounded by dashed lines are excluded by LEP constraints and flavor limits.The gray region surrounded by a solid line indicates the previous LHC constraint [1].
m a = 150 GeV m a = 200 GeV m a = 300 GeV m a = 400 GeV m a = 500 GeV