The $D_{03}(2380)$ dibaryon resonance excitation in the $pd\to pd\pi\pi$ reaction.

The recent ANKE@COSY data on the differential cross section of reaction pd \to pd\pi\pipd→pdππ demonstrate a peak at invariant mass of the final d\pi\pidππ system 2.38~GeV2.38GeV, that corresponds to the isoscalar J^P = 3^+JP=3+ dibaryon D_{03}D03, and the enhancement in the distribution over the invariant mass of two final pions. The two-resonance model involving the tt-channel \sigmaσ-meson exchange between the proton and deuteron in the subprocess pd\to pD_{03}pd→pD03 and the sequential decays D_{03}\to D_{12}+\piD03→D12+π and D_{12}\to d +\piD12→d+π was applied to describe the shapes of these distributions with the lowest orbital angular momenta in the corresponding vertices. A possible role of higher orbital momenta in those vertices is studied here.