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ATLAS and CMS sometimes refer to converted or unconverted photons, but I could not find the meaning of these two terms. I assume they have something to do with conversion of the photon to electron-poitron pairs. It can't be after the ECAL since it is something like 20+ radiation lengths long...

My guess is that the term `converted' photon refers to a photon that has pair produced before the ECAL (say in the tracker) and that 'unconverted' photons only pair produce in the ECAL. Can someone confirm this guess?

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Your guess is right. The ATLAS "twiki" has some nice event displays with converted photon candidates : https://twiki.cern.ch/twiki/bin/view/AtlasPublic/EventDisplaysFromHiggsSearches

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