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Soft hadronic collisions with multiple production of (anti)quarks accompanied with soft photon radiation are described in terms of higher Fock states of the colliding hadrons, which contain a photon component as well. The Fock state distribution functions are shaped with the Quark-Gluon String Model. Photon radiation by quarks is described within the color-dipole phenomenology. The results of calculations are in a good accord with available data in a wide range of transverse momenta of the photons.

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