Predictions are made for elliptic flow in collisions of polarized deuterons with a heavy nucleus. It is shown that the eccentricity of the initial fireball, evaluated with respect to the deuteron polarization axis perpendicular to the beam direction, has a substantial magnitude for collisions of highest multiplicity. Within the Glauber approach we obtain $sim 7%$ for the deuteron states with spin projection 0, and $sim -3 %$ for spin projection $pm 1$. We propose to measure the elliptic flow coefficient as the second order harmonic coefficient in the azimuthal distribution of produced charged hadrons with respect to the fixed polarization axis. Collective expansion yields a value of the order of $1%$ for this quantity, as compared to zero in the absence of polarization and/or collectivity. Such a vivid rotational symmetry breaking could be measured with the current experimental accuracy of the relativistic heavy-ion experiments. The effect has a fundamental significance for understanding the nature of dynamics in small systems, as its experimental confirmation would prove the presence of the shape-flow transmutation mechanism, typical of hydrodynamic expansion or rescattering in the later stages of the fireball evolution.
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