Diffractive mechanisms in $pp \to pp \pi^{0}$ reaction at high energies

We present a study of exclusive production of $\pi^{0}$ meson in proton-proton collisions at high energies. Both diffractive bremsstrahlung (Drell-Hiida-Deck type model), photon-photon, photon-omega and photon-odderon exchange mechanisms are included in the calculation. The $\pi^{0}$-bremsstrahlung contribution dominates at large (forward, backward) pion rapidities and contributes at small $\pi^0 p$ invariant mass and could be therefore misinterpreted as the Roper resonance $N^{*}(1440)$. Large cross sections of the order of mb are predicted. We predict strong dependence of the slope in $t$ (squared four-momentum transfer between ingoing and outgoing proton) on the mass of the supplementary excited $\pi^{0} p$ system. At high energy and midrapidity, the photon-photon contribution dominates over the diffractive components, however, the corresponding cross section is rather small. The photon-odderon and odderon-photon contributions are included in addition and first estimates (upper limits) of their contributions are presented. We suggest a search for the odderon contribution at midrapidity and at $p_{\perp,\pi^{0}} \sim$ 0.5 GeV. Our predictions are ready for verification at LHC. The bremsstrahlung mechanisms discussed here contribute also to the $pp \to p(n \pi^{+})$ reaction. Both channels give a sizable contribution to the low-mass single diffractive cross section and must be included in extrapolating the measured experimental single diffractive cross section.