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We calculate the cross section of J/psi plus prompt-photon inclusiveproduction in gamma gamma collisions at next-to-leading order within thefactorization formalism of nonrelativistic quantum chromodynamics (NRQCD)focusing on direct photoproduction. Apart from direct J/psi production, we alsoinclude the feed-down from directly-produced chi_{cJ} and psi' mesons. Wediscuss the analytical calculation, in particular the treatment of the varioustypes of singularities and the NRQCD operator renormalization, in some detail.We present theoretical predictions for the future e^+e^- linear collider TESLA,taking into account both brems- and beamstrahlung.Comment: 31 pages, 9 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:math>plus prompt-photon associated production in two-photon collisions at next-to-leading order

J/ψplus prompt-photon associated production in two-photon collisions at next-to-leading order