  The theoretical description of photon production at particle colliders
combines direct photon radiation and fragmentation processes, which can not be
separated from each other for definitions of photon isolation used in
experimental measurements. The theoretical description of these processes must
account for collinear parton-photon configurations, retaining the dependence on
the photon momentum fraction, and includes the parton-to-photon fragmentation
functions. We extend the antenna subtraction method to include photon
fragmentation processes up to next-to-next-to-leading order (NNLO) in QCD.
Collinear photon radiation is handled using newly introduced fragmentation
antenna functions and associated phase space mappings. We derive the integrated
forms of the fragmentation antenna functions and describe their interplay with
the mass factorisation of the photon fragmentation functions. The construction
principles of antenna subtraction terms up to NNLO for identified photons are
outlined, thereby enabling the application of the method to different photon
production processes at colliders.
