Elliptic Flow in Ultrarelativistic Collisions with Polarized Deuterons

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.

Figure 1

A schematic view of the ultrarelativistic $d+A$ collision, where the deuteron is polarized along the axis ${\mathrm{\Phi }}_P$ perpendicular to the beam and has the spin projection $j_3=\pm 1$ [panel (a)] or $j_3=0$ [panel (b)]. During the collision a fireball is formed, whose orientation in the transverse plane reflects the deformation of the deuteron distribution. Via the shape-flow transmutation, the elliptic flow is generated, with the sign as indicated in the figure.

Figure 2

Radial wave functions of the $S$ wave, $U(r)$, and $D$ wave, $V(r)$, components of the deuteron, multiplied by the relative radius $r$, taken from the parametrization provided in Ref. [23] for the Reid93 nucleon-nucleon potential.

Figure 3

Ellipticities of the fireball formed in polarized $d+\mathrm{Au}$ collisions at the energy of $\sqrt{s_{\mathrm{NN}}}=200\mathrm{GeV}$. The lower coordinate axis shows the centrality as defined via the produced entropy $S$. The top coordinate axis shows the corresponding number of the wounded nucleons. The arrows indicate the ellipticities of the modulus squared of the deuteron wave function of Eq. (8).

Figure 4

Same as in Fig. 3 but for the participant-plane ellipticity ${\epsilon }_2$. It is dominated by fluctuations and the relative splitting effect between the $j_3=0$ and $j_3=\pm 1$ cases is small.