Flow in collisions of light nuclei

In this talk we discuss several interesting aspects of collective flow in small systems in reference to planned future experiments. First, we bring in the novel possibility of exploring elliptic flow with heavy nuclei collisions on polarized deuteron targets, accessible in AFTER@LHC program after Long Shutdown 3. Then we pass to the Glauber model predictions for the presently considered ${}^{16}{\rm O}-{}^{16}{\rm O}$ program and RHIC and the LHC. Finally, we turn to our previous proposal concerning specific flow signatures of intrinsic correlations (such as the supposed $\alpha$ clusterization) in the structure of light nuclei in collisions with heavy nuclei. In particular, ${}^{12}{\rm C}$--heavy nucleus ultrarelativistic reactions would provide insight into the ground-state ${}^{12}{\rm C}$ structure, complementary to the traditional nuclear structure features.


Collisions on polarized deuteron targets
The deuteron, being a spin j = 1 nucleus, can be polarized in an external magnetic field B. The admixture of the D-wave in its ground-state wave function leads to an intrinsic deformation of the nucleon matter distribution; it is prolate for j 3 = ±1 and oblate for for j 3 = 0, where j 3 is the projection of spin along the polarization axis B (see Fig. 1). When such a polarized deuteron target is hit with an ultrarelativistic heavy nucleus, the deformation of the formed fireball in the transverse plane reflects, to a large degree, the intrinsic deformation of the deuteron. The following collective evolution produces, via the shape-flow transmutation mechanism, elliptic flow which can be quantified with respect to the (fixed) polarization axis in terms of a one-body quantity, which would be straightforward to measure experimentally [1,2]. The planned fixed target AFTER@LHC experiments, in particular SMOG2@LHCb [3,4,5,6], will be able to study collisions of a 2.76A TeV Pb beam on fixed targets, with a possibility of using in the future polarized hydrogen and deuterium targets [7], which can be installed during the LHC Long Shutdown 3 in the years 2023-2025. We note that the proposed method requires a measurement of a one-body distribution and, with a very high intensity beam, could be simply performed with minimum bias events and without event reconstruction or pile-up corrections. Precise estimates, including hydrodynamic simulations, error estimates, etc., are provided in [2].
An analogous effect is present for collisions on other light targets with j ≥ 1, such as 7 Li, 9 Be, or 10 B. Interestingly, the magnitude of the elliptic flow can be estimated from their known mean square radii and quadrupole moments, and is sizable, even larger that for the case of the deuteron. The estimate for the elliptic flow coefficient evaluated with respect to the polarization axis is [ where k ∼ 0.1 is the hydrodynamic response coefficient, Q 2 is the quadrupole moment, Z is the atomic number, and r 2 is that mean squared charge radius of the light nucleus. The quantity b 2 ∼ 1 fm 2 is the average impact parameter squared in inelastic NN collisions. The formula holds for perfect polarization, sufficiently central collisions, and j ≥ 1.
If the effect of the elliptic flow in polarized heavy-light collisions is indeed confirmed, it would corroborate the scenario of the late-stage generation of collectivity. Other interesting opportunities emerging from such collisions involve studies of hard probes as well as femtoscopic correlations, with appropriate measures defined with respect to the polarization axis.

16 O − 16 O collisions
Proposals to study collisions with 16 O beams at the LHC [8] and at RHIC [9] are presently under serious consideration. In this regard we have carried out an analysis of the initial state in 16 O- 16 O in the Monte Carlo Glauber approach [10]. Similar results in other models were presented earlier in [11,12]. The results can be  summarized with a statement that they are qualitatively similar to the effects find in heavier systems, with a natural scaling towards the smaller number of participants. A typical result is shown in the left panel of Fig. 2, where we plot the normalized symmetric cumulant, measuring correlations between the elliptic and triangular deformations. We note a similar behavior in 16 O- 16 O as in Pb-Pb or Xe-Xe, albeit, as expected, moved to lower values of the number of wounded nucleon, N W . Further results are given in [10].

Signature of intrinsic correlations
Over the past few years we have been pursuing the idea [14,15,16,17] that clustering in light nuclei may produce specific signals in harmonic flow correlations in reactions with heavy nuclei. The issue is fundamentally interesting, as in collisions at highest available energies the reaction time is so short that the existing nucleon cluster structures (such as the α particles present in the ground state) are effectively frozen when the nuclear wave function collapses. As a result, the shape of the formed fireball in the transverse plane is, event-by-event, revealing the information on the lowest-energy ground-state of the light nucleus colliding with a "wall" of a heavy nucleus.
Most promising signals for the cluster effects would originate from 12 C -heavy nucleus collisions, since the 12 C nucleus is believed to have a prominent cluster structure, with three α particles placed in corners of an equilateral triangle. In our GLISSANDO [13] simulations we have used configurations from state-of-the-art cluster Variational Monte Carlo simulations [18], as supplied in files in [19]. Similar studies were reported in [20]. We stress that the used dynamically generated distributions contain realistic nuclear correlations.
An example of a measure sensitive to the cluster correlations in the light nucleus is the double ratio of triangular and elliptic eccentricities evaluated with cumulants with 2 and 4 particles, It is plotted in the right panel of Fig. 2 as a function of the number of wounded nucleons. We note a characteristic non-monotonic behavior for the case where the 12 C nucleus is clustered (solid line), as opposed to the case of a uniform distribution (dotted line). An analogous behavior is expected for the corresponding double ratio of the elliptic and triangular flow coefficients. More details can be found in [14,15,16,17].
To summarize, various intriguing and hitherto unexplored physical effects may be explored in future heavy-light ultrarelativistic nuclear collisions, which may further probe the issue of the origin of collectivity in the fireball dynamics and its limits, as well as investigate the nuclear structure correlation effects in the initial state. The observation of the discussed effects would confirm the scenario of the late stage generation of collective flow in small systems, which, while plausible, needs independent and unique tests.