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Vector exchanges in production of light meson pairs and elementary atoms

The production of pseudoscalar and scalar mesons pairs and bound states (positronium or pionium atoms) in high energy $γγ$ collisions at high energies provided by photon or vector meson exchanges are considered. The vector exchanges lead to nondecreasing with energy cross section of binary process $γ+γ\to h_a+h_b$ with $h_a, h_b$ states in the fragmentation regions of initial particles. The production of light mesons pairs $ππ, ηη, η'η', σσ$ as well as a pairs of positronium $Ps$ and pionium $A_π$ atoms in peripheral kinematics are discussed. Unlike the photon exchange the vector meson exchange needs a reggeization, leading to fall with energy. Nevertheless due to peripheral kinematics out of very forward production angles the vector meson exchanges dominated. The proposed approach allows to express the matrix elements of the considered processes through impact factors, which can be calculated in perturbation models like Chiral Perturbation Theory (ChPT) or Nambu-Jona-Lasinio (NJL) model or determined from $γγ$ sub-processes or vector mesons radiative decay widths. We obtain the cross sections for pionium atom production in collisions of high energy pions and electrons with protons. The possibility to measure these processes in experiment are discussed.