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The recent ANKE@COSY data on the differential cross section ofreaction    pd \to pd\pi\pi    p  d  →  p  d  π  πdemonstrate a peak at invariant mass of the final   d\pi\pi    d  π  πsystem    2.38~GeV    2.38   G  e  V,that corresponds to the isoscalar    J^P = 3^+J  P   =   3  +dibaryon    D_{03}    D  03,and the enhancement in the distribution over the invariant mass of twofinal pions. The two-resonance model involving the   t   t    -channel   \sigma   σ    -mesonexchange between the proton and deuteron in the subprocess   pd\to pD_{03}    p  d  →  p   D  03and the sequential decays    D_{03}\to D_{12}+\piD  03   →   D  12   +  πand    D_{12}\to d +\piD  12   →  d  +  πwas applied to describe the shapes of these distributions with thelowest orbital angular momenta in the corresponding vertices. A possiblerole of higher orbital momenta in those vertices is studied here.

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