Axion-Like Particles at the ILC Giga-Z
11January 5, 2021
Axion-Like Particles at the ILC Giga-Z
Noah Steinberg, James D. Wells
Leinweber Center for Theoretical PhysicsPhysics Department, University of MichiganAnn Arbor, MI 48109-1040 USAAbstract:
Axion-Like Particles (ALPs) are a generic, calculable, and well motivated exten-sion of the Standard Model with far reaching phenomenology. ALPs that couple only tohypercharge represent one subset of such models, coupling the ALP to both photons and the Z boson. We examine the current constraints on this class of models with an ALP mass inthe 100 MeV to 100 GeV range, paying particular attention to the region between 100 MeVto 10 GeV, a portion of parameter space which is ill constrained by current experiments.We show that the more than 10 Z bosons produced in the Giga-Z mode of the future ILCexperiment, combined with the highly granular nature of its detectors, will allow for ALPscoupled to hypercharge to be discovered with couplings down to nearly 10 − GeV − over arange of masses from 0.4 to 50 GeV. a r X i v : . [ h e p - ph ] J a n
1. INTRODUCTION
One of the simplest BSM scenarios comes from augmenting the Standard Model withnew singlet (pseudo)scalar particles. Such models have rich phenomenology despite theirsimplicity, and can influence the structure of the Electroweak phase transition [1], providenatural dark matter candidates [2, 3], and can be naturally accommodated in well motivatedUV models [4]. One class of new light scalars is the Axion-Like Particle (ALP) [5, 6].An ALP is defined as a relatively light pseudo-scalar that couples to two gauge bosonsand possibly SM fermions. Via the PQ mechanism [7] or other tunings, these particlesare particularly well motivated as solutions to the Dark Matter and Strong CP problems,but can appear generically as pseudo Nambu-Goldstone bosons of spontaneously brokenapproximate symmetries or descend from phenomenogical string theory models. Regardlessof their origin, ALPs are an extremely general extension of the SM and serve as a test casefor investigating BSM physics. In addition, as the LHC and other experiments search fornew physics in the form of heavy ( M (cid:29) M W ) particles, ALPs serve as an orthogonal butcomplementary search direction for theorists and experimentalists, as they are generally lowmass but very weakly coupled. Fortunately, we will show that the next generation of leptoncolliders like the ILC will provide clean signatures to weakly coupled ALP physics at the O (10 − GeV) level for a range of interesting masses near and below the weak scale.Many dedicated search strategies have been developed to study their production andinfluence on cosmology and particle physics, depending on the exact nature of the ALP inquestion [8]. In more detail, these searches depend on which gauge bosons the ALPs coupleto, e.g. U (1) Y , SU (2) L , or SU (3) C , and whether the the ALP couples to the SM fermions.In an effective field theory approach each of these couplings should be allowed, but each canbe taken to be independent (modulo RG effects [9, 10]), allowing one to examine each portalone at a time. In this paper we take up one ALP model where our Axion-Like Particle, a ,couples only to hypercharge through a dimension 5 interaction, L = L SM + 12 ∂ µ a∂ µ a − m a a − g aBB aB µν ˜ B µν (representative theory) . (1)Here, m a is the tree level mass of the ALP which couples to hypercharge via the dimensionfulcoupling g aBB , and ˜ B µν = 1 / ε µναβ B αβ is the dual hypercharge field strength tensor. Ofcourse many other effective Lagrangians involving couplings to additional gauge bosons andfermions would be equally valid to write down, but the resulting phenomenology is eitherqualitatively similar or produces orthogonal observables which would not affect subsequentdiscussion. Note, that several other authors study ALPs below the weak scale which couplepurely to F ˜ F rather than to B ˜ B . In the former case, the ALP couples only to photonsand cannot couple to the Z . We choose to study the latter, aB ˜ B operator, because in agauge invariant, UV completion of any model including an ALP there are likely to be O (1)connections between operators coupling the ALP to each of the electroweak gauge bosons.Thus we would like to put ALP-photon couplings on equal footing with ALP- Z/W couplings.This, as we shall see below, opens up further experimental discovery channels.
2. ALPS IN RARE Z DECAYS
Much of the parameter space of this particular model, shown in Fig. 1, is highly con-strained by terrestrial experiments [11], as well as cosmology and astrophysics [12, 13]. Lightshining through wall (LSW) experiments and helioscopes constrain ALP masses up to sev-eral eV, and down to g aBB = 10 − GeV − , while cosmology and astrophysical constraintscover larger masses in the eV to GeV range and couplings down to 10 − GeV − and lower.Complimentary constraints can be obtained with colliders and beam dump experiments,which can probe masses in the MeV to TeV range. ALPs produced at beam dumps pen-etrate shielding and then decay to pairs of photons which are detected by a downstreamdetector. These rely on relatively smaller ALP couplings than colliders as the ALP has totravel a macroscopic distance to make it through the shielding and reach the downstreamdetector. Future experiments like FASER and DarkQuest will probe ALP-photon couplingsaround 10 − − − GeV − in 10 MeV - several 100 MeV range [19, 20]. Collider searchestarget ALP production in association with a photon, with the ALP either leaving the de-tector leading to MET, or decaying in the detector volume leading to displaced vertices orother identifying signatures. Belle II (not shown in Fig. 1) for example searches for ALPsin e + e − → aγ → γ , and has found constraints of g aγγ < − GeV − in the mass range of0.2 GeV to 10 GeV [21].Interesting constraints also come from light by light scattering at the LHC in PbPbcollisions. Here, the γγ scattering cross sections are enhanced by a factor of Z [18], where Zis the number of protons in the nucleus. The presence of an ALP which couples to photons Figure 1: Current constraints on ALP model with hypercharge coupling. Figure adapted from[14–18]. would enhance the light by light scattering ( γγ → γγ ) cross section. Measurements of thiscross section at CMS and ATLAS place constraints on Axion-Like Particles coupling tophotons from 5 to 100 GeV down to a few × − GeV [15, 16, 18], competitive with LEPand other LHC searches over this mass range.We would like to mention the analysis by Bauer et al. in [22] where the authors considerthe ALP discovery prospects of the FCC-ee, HL-LHC, CLIC, and other future experimentsin the context of a similar ALP model in the MeV to TeV mass range. Their analysisconcludes that these experiments will probe ALP-photon couplings down to 10 − TeV − forcertain ranges of masses. We caution that a detector level analysis with realistic cuts and athorough background analysis will most likely weaken the claimed sensitivities.After electroweak symmetry breaking the ALP develops a coupling to both the Z bosonand to the photon, opening up the decay of an on-shell Z into an ALP and a photon withwidth Γ Z → a + γ = g aBB s W c W ( m Z − m a ) πm Z . (2) Figure 2: Proper decay length as a function of g aBB for several different ALP masses. As long as the ALP has a mass less than m Z , it will then decay to two photons with abranching ratio of nearly 1. It can of course decay to other standard model particles atloop level but these will be heavily suppressed. This leads to the decay chain Z → γ or”tri-photon” signature.Whether the ALP will promptly decay or lead to a displaced vertex depends on theALP mass and hypercharge coupling, with the decay length given by l = cτ = γ a / Γ a → γγ ,where γ a = E a /m a is the boost factor of the ALP. While dedicated searches for displacedvertices and or MET lead to interesting constraints [23, 24], this note will focus on masses andcouplings which lead only to prompt decays. This is shown in Fig. 2 for m a = 0 . , . , . , m a ≥ . Z → γ is an interesting final state to search for as it is absent at tree level in the SM, butloop induced with a tiny branching ratio of ≈ − [25]. This rare decay has been searchedfor by LEP, the Tevatron, and the LHC in an effective field theory context searching forSM and anomalous Zγ couplings [17, 26, 27], with no excess over the SM background beingfound, establishing an upper limit of B ( Z → γ ) < . × − . Translating this into the( m a , g aBB ) plane leads to the constraint g aBB < − . GeV − , for masses large enough wherethe two photons from the ALP decay can be independently resolved. The exact value of theALP mass, m a , which leads to well separated decay photons depends on the details of theexperimental analysis and detector and cannot straightforwardly be pinpointed, though itshould lie at least above 10 GeV. Below O (10 GeV) lies a subtle region of parameter spacein collider searches which is the subject of this paper.In dedicated ALP searches at experiments like the LHC and LEP, analyses are limitedby their ability to reconstruct collimated pairs of photons [28]. Low mass ALPs producedfrom on-shell Z decays, subsequently decay into pairs of photons with a ∆ R separationwhich peaks at 4 m a /m Z . Here ∆ R = (cid:112) ∆ φ + ∆ η is the angular distance measure betweenparticles. ALPs with masses between 1 and 10 GeV tend to decay to collimated photon pairswhich will overlap in a detector and thus not be correctly reconstructed as two individualphotons. See [29] for a discussion on reconstructing overlapping photons at the LHC. Atthe LHC and in the LEP experiment, photons must be separated from charged particlesand other photons by a ∆ R > .
2, though this requirement depends on the details of eachdetector as well as the algorithms responsible for reconstructing photons. This should betaken as a rule of thumb. If a photon does not meet these requirements it is not reconstructedand rejected as a photon candidate. Above m a = 10 GeV, the photons are well separatedenough to be efficiently reconstructed. Low mass ALPs ( m a < Z → γ in the e + e − → γγ ( γ )measurement into limits on the ALP model. In different ALP mass regions, m a < m π , m π < m a <
10 GeV, and m a >
10 GeV, either searches for two or three photons were usedbased on whether the photons from the ALP decay would be well separated or not. Thiswas used to set leading bounds on ALP masses and couplings between 100 MeV and 90GeV, with the weakest bounds being in the intermediate mass regime of 1 GeV to 10 GeV.Though jet substructure techniques can be used to disentangle collimate pairs of photonsfrom single photons [30], an experiment that can resolve individual photons via a granulardetector in this ALP mass regime is crucial to enhance discovery prospects and increase oursensitivity to new physics with the same decay topology.The International Linear Collider (ILC) represents exactly this opportunity to search forthis rare decay in the sought after intermediate mass regime. Recent advances in photonidentification algorithms, combined with the highly granular ILC detectors can allow forphoton identification with much more relaxed photon separation requirements, meaningphotons can be much closer to other charged particles and other photons. In the next sectionwe will investigate to what extent the ILC can improve on past searches for Z → aγ → γ .
3. ILC AND PHOTON RECONSTRUCTION
The ILC is a next generation, high luminosity, linear e + e − collider designed for high pre-cision SM and BSM physics measurements [31–33]. The collider, though nominally designedto operate at 250 GeV center of mass energy, can be adjusted to run at a variety of center ofmass energies, including operating at the Z pole. Operating the ILC at √ s = m Z is dubbedthe Giga-Z mode of the ILC, as the ILC will produce on the order of 10 or greater Z bosons,orders of magnitude more than the LEP physics program. This will result in drastic im-provements in precision Z measurements, and measurements of sin θ eff . Production of thismany Z bosons will also allow for the search for rare decay modes, one of which is Z → γ .We first begin with a discussion of photon reconstruction at the ILC. Photon identificationcan be done via the GARLIC photon reconstruction algorithm [34] which was developed bythe International Large Detector (ILD) group. GARLIC (GAmma Reconstruction at aLInear Collider experiment) is designed to achieve highly efficient identification of photonswithin hadronic showers, which mostly come from high energy neutral pion decays. Becausethe photons from these pions will be highly collimated, this same technique can be used toidentify collimated photons from low mass ALP decays. To begin, we examine in Fig. 3 theangle between photons from π decays as a function of the π energy and the ECAL radiusat the ILD (nominal ECAL radius is 1843mm). The photon reconstruction performance isa function of the Moli`ere radius, which is the transverse radius at which a single photondeposits 90% of its energy. The smaller the Moli`ere radius, the more separated each singlephoton will be. At E π = 20 GeV, the Moli`ere radius is roughly half the distance betweenthe pair of photons. At a pion energy of 20 GeV, GARLIC reconstructs 2 photons correctly Figure 3: Angle between photons from π decays as a function of π energy. Also depicted withdashed lines are the angle subtended by half a Moli`ere radius at different ECAL radii. Figure from[34]. about 85% of the time.We would like to adopt this performance to reconstruct photons from low-mass ALPdecays. To do so we first need to understand what is the minimum ∆ R between photonpairs that we can expect to reconstruct. If we take the results from the 20 GeV pion seriously,the photons from this decay have a peak separation of ∆ R = 4 × m π /E π = . π that have photons separated by greater than2, 1, 0.5 Moli`ere radii in the ECAL. At the nominal ECAL radius, almost 100% of pionswith E = 15 GeV have photons separated by 2 Moli`ere radii. This means that if we formcones around each photon of ∆ R = 4 × m π / (15 GeV) = .
035 [35], then roughly 10% of theenergy inside each cone will be from the other photon. Thus we can use this as our photonseparation criteria.We choose to make photons with an isolation cone of ∆ R = 0 . P T iso = 0 . Figure 4: Fraction of π that have photons separated by greater than 2, 1, 0.5 Moli`ere radius inthe ECAL. Figure from [34]. photon. The effect of this cut will have on our efficiency to identity photons can be seenfrom Fig. 5 below. For masses below 0.5 GeV, the ∆ R between photons can be significantlysmaller than 0.035, making photon pair reconstruction challenging. At m a = 0.5 GeV, thepeak of the distribution is near ∆ R = 0 .
04 which allows for sufficient separation for bothphotons in the pair. We simulated 50,000 e + e − → aγ → γγγ events at √ s = m Z , for m a = 0 . , , , , m a = 0 . m a = 1 GeV and above the average number of photonsreconstructed is 2.7 due to the much larger ∆ R between photon pairs.
4. SIGNAL VS. BACKGROUND
Searches for Z → γ have been made difficult because of the relatively large SM back-ground e + e − → γ , which has a cross section at √ s = m Z of approximately 4.1 pb (computedat leading order using MadGraph aMC@NLO [36]).0 Figure 5: ∆ R between photons from the ALP decay for a range of ALP masses between 0.1 and6.0 GeV. The peak of the distribution shifts towards higher ∆ R for larger masses, following theform ∆ R peak = 4 m a /m Z . The tree level e + e − → Z → γ cross section in the ALP extension we are consideringdepends on the mass of the scalar, m a , and the coupling of the ALP to the hyperchargegauge bosons. We want to investigate the sensitivity to light scalars in this channel. Wesimulated 100,000 signal events over a range of masses from 0.4 GeV to 50 GeV using oursignal model with MadGraph v2.6.7 aMC@NLO [36], showered with Pythia 8.2 [37]. Weuse the generic ILC Delphes card [38] provided by the ILCSoft developers which simulatesthe response of a generic ILC detector. We modify the detector cards in accordance withsection 3. To isolate our signal over the Standard Model background e + e − background weneed only make a small number of simple cuts. The first is of course that we have three nonoverlapping, efficiently reconstructable photons. The effect of this cut and its limitations aredescribed in section 3. The second cut utilizes kinematic information from the two body,on-shell Z decay. Being a two body decay, the energy of the recoiling photon is a fixedfunction of m a , E γ recoil ( m a ) = ( M Z − m a ) / M Z . Thus, when searching for an ALP of mass m a , one can require that one photon out of the three have an energy near E γ recoil ( m a ). Wechoose to search for photons within 5 GeV of this energy. These cuts are summarized below.1. 3 non-overlapping (∆ R > . E γ > Figure 6: Reconstruction recoil photon energy distribution from Z → aγ signal events. For eachvalue of m a photons are required to have an energy within 5 GeV of E γ recoil ( m a ). Each reconstructeddistribution is peaked near the true value of E γ recoil ( m a ). | E γ − E γ recoil ( m a ) | < m a , E γ recoil is approximately m Z /
2. As can be seen in Fig. 6, the recoil photonenergy cut is especially import for m a above 30 GeV where the recoil energy starts todecrease significantly from m Z /
2. Below in Fig. 7 we plot the signal and background yieldas a function of m a with g aBB = 1 TeV − . With just the above cuts, the ILC Giga-Z wouldobserve O (10 events) over the entire range of masses between 0.4 GeV and 50 GeV withonly 100 f b − of integrated luminosity. We can easily examine the sensitivity of the ILC tothe above model as the coupling g aBB decreases. For a given coupling, g , producing a signalyield, N , we can find the signal yield, N (cid:48) , with coupling g (cid:48) simply by using N (cid:48) = N ( g (cid:48) g ) . Toproduce an upper limit on g aBB at a 95% confidence level, we can look for when the signalyield, as a function of m a and g aBB , exceeds two times the uncertainty on the background.Essentially, if the background yield in the signal region for m a = m GeV is B events, thenwe can exclude all couplings for an ALP with mass m GeV that produce more than 2 × √ B signal events. Doing this for a range of masses gives us the exclusionary power of the ILCGiga-Z program at 95% confidence.After obtaining the signal and background yields in our mass range of interest, we compute2 Figure 7: Signal and background yields for a range of ALP masses for fixed g aBB = 1 TeV − . Yieldsare normalized to an integrated luminosity of 100 fb − . Almost 10 signal events are expected forthis value of g aBB , well above the Standard Model background. the upper limit on g aBB , shown in Fig. 8, according to the procedure described above. Weinclude 1 σ and 2 σ error bars which take into account the statistical uncertainties on the signalyield. Obviously in a real analysis systematic experimental and theoretical uncertaintieswould have to be taken into account, but we do not expect this to modify our bounds asignificant amount. We find that at masses between 0.4 and 50 GeV, the ILC can placestringent upper limits on g aBB which improve on LEP’s by over an order of magnitude. Tocompare against current bounds we plot in Fig. 10 the ILC Giga-Z exclusion region alongwith current constraints, both as a function of g aBB (TeV − ) and as a function of g − aBB (TeV),which is indicative of the scale of new physics which produces the operator O = aB ˜ B . Wewould like to stress that this simple analysis, based only on the granularity of the future ILCdetectors and the kinematics expected from the Z → aγ decay, is able to probe much moredeeply new regions of parameter space in this model. A more sophisticated experimentalanalysis would involve a bump-hunt search on the invariant mass of the two photon systemfrom the ALP decay. Additional information which could be used to make these bounds3 Figure 8: Upper limit on g aBB over the range of masses 0.4 to 50 GeV. 1 σ and 2 σ error bars areshown in yellow and green. even stronger could be obtained from the angular separation between the photons from theALP decay. For m a <
20 GeV, the distribution of ∆ R of these two photons is peakedat low values (see Fig. 5), while the background distribution falls quickly in this region.Utilizing the excellent angular separation abilities of the ILC detectors, one could requirethat this two photon system be below a particular angular separation, further reducing thebackground. Finally, for very small masses ( < .
5. CONCLUSION
Axion-Like Particles (ALPs) represent an exciting and generic, calculable SM extension,with a parameter space that is being investigated through many different fronts. We haveshown that even small ( O (10 − TeV − )) ALP couplings to hypercharge generate a significant4 Figure 9: ILC Giga-Z exclusion region against past experiments exclusion regions. We plot thelimit here as a function of g aBB (TeV − ) The ILC will significantly improve limits from over thewhole range of masses from 0.4 to 50 GeV. number of signal events at an experiment like the ILC over a range of masses from 0.4 GeVto 50 GeV. The exceptional photon reconstruction abilities of the future ILC detector(s) willallow for efficient identification of 3 photon events even at very small photon separations.This represents an exciting opportunity for the ILC to probe new light, weakly coupledphysics which interacts with the Z and to make a discovery.
6. ACKNOWLEDGEMENTS
We thank Advanced Research Computing at the University of Michigan, Ann Arbor fortheir computational resources. This work was supported by the DOE under grant DE-SC0007859. N. Steinberg is supported by a fellowship from the Leinweber Center for Theo-5
Figure 10: ILC Giga-Z exclusion region against past experiments exclusion regions. We plot thelimit here as a function of g − aBB (TeV) The ILC will significantly improve limits over the wholerange of masses from 0.4 to 50 GeV. retical Physics. [1] M. Carena, Z. Liu, and Y. Wang, “Electroweak phase transition with spontaneousZ -breaking,” JHEP (2020) 107, arXiv:1911.10206 [hep-ph] .[2] L. D. Duffy and K. van Bibber, “Axions as Dark Matter Particles,” New J. Phys. (2009)105008, arXiv:0904.3346 [hep-ph] .[3] GAMBIT
Collaboration, P. Athron et al. , “Status of the scalar singlet dark matter model,”
Eur. Phys. J. C no. 8, (2017) 568, arXiv:1705.07931 [hep-ph] .[4] P. Svrcek and E. Witten, “Axions In String Theory,” JHEP (2006) 051, arXiv:hep-th/0605206 .[5] A. Ringwald, “Axions and Axion-Like Particles,” in , pp. 223–230. 2014. arXiv:1407.0546[hep-ph] . [6] J. Beacham et al. , “Physics Beyond Colliders at CERN: Beyond the Standard ModelWorking Group Report,” J. Phys. G no. 1, (2020) 010501, arXiv:1901.09966 [hep-ex] .[7] S. Weinberg, “A new light boson?” Phys. Rev. Lett. (Jan, 1978) 223–226. https://link.aps.org/doi/10.1103/PhysRevLett.40.223 .[8] J. E. Kim, “Light Pseudoscalars, Particle Physics and Cosmology,” Phys. Rept. (1987)1–177.[9] M. Bauer, M. Neubert, S. Renner, M. Schnubel, and A. Thamm, “The Low-Energy EffectiveTheory of Axions and ALPs,” arXiv:2012.12272 [hep-ph] .[10] M. Chala, G. Guedes, M. Ramos, and J. Santiago, “Running in the ALPs,” arXiv:2012.09017 [hep-ph] .[11] P. W. Graham, I. G. Irastorza, S. K. Lamoreaux, A. Lindner, and K. A. van Bibber,“Experimental Searches for the Axion and Axion-Like Particles,”
Ann. Rev. Nucl. Part. Sci. (2015) 485–514, arXiv:1602.00039 [hep-ex] .[12] A. J. Powell, The cosmology and astrophysics of axion-like particles . PhD thesis, Oxford U.,2016.[13] M. Millea, L. Knox, and B. Fields, “New Bounds for Axions and Axion-Like Particles withkeV-GeV Masses,”
Phys. Rev. D no. 2, (2015) 023010, arXiv:1501.04097[astro-ph.CO] .[14] J. Jaeckel and M. Spannowsky, “Probing MeV to 90 GeV axion-like particles with LEP andLHC,” Phys. Lett. B (2016) 482–487, arXiv:1509.00476 [hep-ph] .[15]
CMS
Collaboration, A. M. Sirunyan et al. , “Evidence for light-by-light scattering andsearches for axion-like particles in ultraperipheral PbPb collisions at √ s NN = 5.02 TeV,” Phys. Lett. B (2019) 134826, arXiv:1810.04602 [hep-ex] .[16]
ATLAS
Collaboration, G. Aad et al. , “Measurement of light-by-light scattering and searchfor axion-like particles with 2.2 nb − of Pb+Pb data with the ATLAS detector,” arXiv:2008.05355 [hep-ex] .[17] ATLAS
Collaboration, G. Aad et al. , “Search for new phenomena in events with at leastthree photons collected in pp collisions at √ s = 8 TeV with the ATLAS detector,” Eur.Phys. J. C no. 4, (2016) 210, arXiv:1509.05051 [hep-ex] .[18] S. Knapen, T. Lin, H. K. Lou, and T. Melia, “Searching for Axionlike Particles withUltraperipheral Heavy-Ion Collisions,” Phys. Rev. Lett. no. 17, (2017) 171801, arXiv:1607.06083 [hep-ph] .[19] J. L. Feng, I. Galon, F. Kling, and S. Trojanowski, “Axionlike particles at FASER: The LHCas a photon beam dump,” Phys. Rev. D no. 5, (2018) 055021, arXiv:1806.02348[hep-ph] .[20] E. Kowalczyk and N. Blinov, “Searching for Axion-like Particles at DarkQuest,”.[21] Belle-II
Collaboration, F. Abudin´en et al. , “Search for Axion-Like Particles produced in e + e − collisions at Belle II,” Phys. Rev. Lett. no. 16, (2020) 161806, arXiv:2007.13071[hep-ex] .[22] M. Bauer, M. Heiles, M. Neubert, and A. Thamm, “Axion-Like Particles at FutureColliders,”
Eur. Phys. J. C no. 1, (2019) 74, arXiv:1808.10323 [hep-ph] .[23] Y. Gershtein, S. Knapen, and D. Redigolo, “Probing naturally light singlets with a displacedvertex trigger,” arXiv:2012.07864 [hep-ph] .[24] L. Darm´e, F. Giacchino, E. Nardi, and M. Raggi, “Invisible decays of axion-like particles:constraints and prospects,” arXiv:2012.07894 [hep-ph] .[25] E. Glover and A. Morgan, “Z boson decay into photons,” Phys. C - Particles and Fields (1993) 175–180.[26] L3 Collaboration, M. Acciarri et al. , “Search for anomalous Z – > gamma gamma gammaevents at LEP,” Phys. Lett. B (1995) 609–616.[27]
CDF
Collaboration, T. A. Aaltonen et al. , “First Search for Exotic Z Boson Decays intoPhotons and Neutral Pions in Hadron Collisions,”
Phys. Rev. Lett. (2014) 111803, arXiv:1311.3282 [hep-ex] .[28] K. Mimasu and V. Sanz, “ALPs at Colliders,”
JHEP (2015) 173, arXiv:1409.4792[hep-ph] .[29] B. Sheff, N. Steinberg, and J. D. Wells, “Higgs boson decays into narrow di-photon jets andtheir search strategies at the Large Hadron Collider,” arXiv:2008.10568 [hep-ph] .[30] S. D. Ellis, T. S. Roy, and J. Scholtz, “Phenomenology of Photon-Jets,” Phys. Rev. D no. 1, (2013) 014015, arXiv:1210.3657 [hep-ph] .[31] P. Bambade et al. , “The International Linear Collider: A Global Project,” arXiv:1903.01629 [hep-ex] .[32] J. Erler, S. Heinemeyer, W. Hollik, G. Weiglein, and P. Zerwas, “Physics impact of GigaZ,” arXiv:hep-ph/0005024 . [33] “The International Linear Collider Technical Design Report - Volume 2: Physics,” arXiv:1306.6352 [hep-ph] .[34] D. Jeans, J. Brient, and M. Reinhard, “GARLIC: GAmma Reconstruction at a LInearCollider experiment,” JINST (2012) P06003, arXiv:1203.0774 [physics.ins-det] .[35] ATLAS
Collaboration, M. Aaboud et al. , “A search for pairs of highly collimatedphoton-jets in pp collisions at √ s = 13 TeV with the ATLAS detector,” Phys. Rev. D no. 1, (2019) 012008, arXiv:1808.10515 [hep-ex] .[36] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H. S. Shao,T. Stelzer, P. Torrielli, and M. Zaro, “The automated computation of tree-level andnext-to-leading order differential cross sections, and their matching to parton showersimulations,” JHEP (2014) 079, arXiv:1405.0301 [hep-ph] .[37] T. Sj¨ostrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel,C. O. Rasmussen, and P. Z. Skands, “An introduction to PYTHIA 8.2” Comput. Phys.Commun. (2015) 159–177, arXiv:1410.3012 [hep-ph] .[38] A. F. ˙Zarnecki, “Generic ilc detector model for delphes,” August, 2020. https://github.com/iLCSoft/ILCDelpheshttps://github.com/iLCSoft/ILCDelphes