At the LHC, ALPs can be produced resonantly in the process pp → a, or they can be produced in exotic decays of the Z- or Higgs boson. The relevant processes would be Z → γa, h → Za or h → aa. Once produced, the ALP can then either be long lived and escape the detector as missing energy, or it can decay inside the detector. Long-lived or invisibly decaying ALPs at the LHC have been explored recently in (Mimasu,2014 and Brivio,2017). Projections for missing energy signatures, such as pp → aW(γ), pp → ajj(γ), pp → ha and pp → tta with stable ALPs or invisible ALP decays have been considered in Brivio (2017). For short-lived ALPs, ATLAS and CMS can reconstruct its decay products. The only decay mode for light ALPs is into two photons. For ALP masses larger than twice the electron mass, the decay into two electrons opens up. Similarly, for masses larger than twice the muon or tau mass, ALP decays into two muons or taus are possible. ALP masses larger than three times the pion mass are required for hadronic decays into two jets to be kinematically allowed. All these decay modes can be searched for at the LHC. The left panel of Figure 1 shows a summary of current constraints in the plane ALP mass vs ALP-photon coupling. The coloured regions show the different experimental constraints mentioned above. Collider constraints, in particular, exist for large ALP-photon couplings. The blue area shows bounds from LEP looking for e+e- → Z → γa → 3γ. Decays of on shell Zbosons at the LHC have been discussed Bauer(2017), Mimasu (2014), Jaeckel (2015) and Brivio (2017) and are shown in orange. The purple region is excluded by Tevatron searches for pp → 3γ.
Figure 1. Constraints on the ALP mass and ALP-photon coupling derived from various experiments. Right: Enlarged display of the constraints from collider searches: LEP (light blue and blue), CDF (purple), LHC from associated production and Z decays (orange), LHC from photon fusion (light orange), and from heavy-ion collisions at the LHC (green). Plot taken from Bauer (2018).
Exotic decays of Z- or Higgs bosons can be powerful channels to search for axion-like particles. The light green region in Figure 2 shows the expected LHC reach in the channel h → Za → Zγγ with 300 fb-1 integrated luminosity. We see the complementarity to previously excluded regions in parameter space. This is the case because ALPs in the light green region are short-lived enough to decay inside the detector. Projections for h → aa and Z → γa are similar.
Figure 2. Constraints on the ALP mass and ALP-photon coupling along with the parameter regions that can be probed in the decay h → Za → Zγγ in LHC Run-2 with 300 fb-1 of integrated luminosity (light green region). Plot taken from Bauer (2017).
These projected bounds for exotic Higgs decays include an intrinsic assumption on the ALPHiggs coupling. Studies on resonant production, pp → a → γγ, avoid these assumptions since the ALP coupling to gluons and to photons is related in many explicit models. Figure 3 shows current and expected bounds in this process. See Mariotti (2017) for more details on this process.
Figure 3: Shaded regions show constraints from existing collider searches at LEP Adriani (1992) and the CMS (2015, 2017), Sirunyan (2017), and from the bound derived in Mariotti (2017). Lines: projected LHC sensitivities at 8 and 14 TeV. Plot taken from Marriotti (2017).
Ultra-peripheral heavy ion collisions at the LHC present a unique environment to search for ALPs that couple to electromagnetism, owing to a large Z^4 (Z=82 for lead) enhancement to the cross section, and low backgrounds . In fact, the strongest limits on ALPs in the mass range 10 GeV < ma < 100 GeV can be obtained by recasting an ATLAS analysis  using the 480 microbarn-1 Pb-Pb data set.
Ultra-peripheral collisions are characterized by an impact parameter that is much larger than the radius of the ion, and very little breakup of the ions (leading to extremely low activity in the detector). ALPs can be produced via photon-photon fusion, where the initial photon flux is high owing to the strong electric field of the ions; decay back into photons provides a `bump-hunt’ channel with low background – see Fig. 1. Dominant backgrounds in this channel are standard model light-by-light scattering , and electrons faking photons; both backgrounds become negligible for mγγ >=20GeV.
A recent ATLAS measurement of light-by-light scattering  provides an m_gammagamma spectrum in the region 6-30 GeV that can be used to derive a limit on parameter Lambda in the ALP Lagrangian.
The results of this recasting were presented in , following the treatment proposed in . They are shown here in Fig. 2, along with projected sensitivities for 1 nb-1 and 10 nb-1 of lead-lead collision data. The limit is set up to 100 GeV, under the assumption that ATLAS sees no events in bins greater than m_gammagamma >30 GeV.
It is an interesting aspect of ALP physics that lead-lead collisions at the LHC can provide more competitive limits than proton-proton collisions, which usually dominate searches for beyond-the-standard model physics.
Figures: Taken directly from 
ALP production via photon-photon fusion in ultra-peripheral lead-lead collisions, with subsequent decay into two photons.
Caption: 95% exclusion limits on the parameter Lambda in eq. (1), as a function of ALP mass. Figure taken from Ref., and using ATLAS results on light-by-light scattering . Exclusion limits are also shown from other LHC searches (ATLAS 2 and 3 photon), LEP 2 (OPAL 2 and 3 photon) and beam dump experiments (for details see Ref. ). Projections assuming 1 nb-1 and 10 nb-1 luminosity of Pb-Pb collisions are are shown in green.
A) ALP's LHC searches.
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B) ALPs searches with heavy-ion collisions
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 Simon Knapen (LBL, Berkeley & UC, Berkeley), Tongyan Lin (UC, San Diego & LBL, Berkeley & UC, Berkeley), Hou Keong Lou (LBL, Berkeley & UC, Berkeley), Tom Melia (Tokyo U., IPMU & LBL, Berkeley& UC, Berkeley). Sep 20, 2017. 4 pp. arXiv:1709.07110 Conference proceedings