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Low scale string models naturally have axion-like pseudoscalars which couple directly to gluons and photons (but not $W$s) at tree level.
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S. Chatrchyan et al
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F. Marchesano, G. Shiu and A. M. Uranga, “F-term Axion Monodromy Inflation,” JHEP 1409
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CMS Collaboration, “Search for new physics in high mass diphoton events in proton-proton collisions at s = 13 \sqrt{s}=13 TeV”, CMS-PAS-EXO-15-004
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ATLAS Collaboration, “Search for new phenomena in the dilepton final state using proton-proton collisions at sqrt(s) = 13 TeV with the ATLAS detector” ATLAS-CONF-2015-070
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