Plasma polarised by spin-orbit effect

Spin-orbit coupling causes fine structure in atomic physics and shell structure in nuclear physics, and is a key ingredient in the field of spintronics in materials sciences. It is also expected to affect the development of the quickly rotating quark–gluon plasma (QGP) created in non-central collisions of lead nuclei at LHC energies. As such plasmas are created by the collisions of lead nuclei that almost miss each other, they have very high angular momenta of the order of 10⁷ħ – equivalent to the order of 10²¹ revolutions per second. While the extreme magnetic fields generated by spectating nucleons (of the order of 10¹⁴ T, CERN Courier Jan/Feb 2020 p17) quickly decay as the spectator nucleons pass by, the plasma’s angular momentum is sustained throughout the evolution of the system as it is a conserved quantity. These extreme angular momenta are expected to lead to spin-orbit interactions that polarise the quarks in the plasma along the direction of the angular momentum of the plasma’s rotation. This should in turn cause the spins of vector (spin-1) mesons to align if hadronisation proceeds via the recombination of partons or by fragmentation. To study this effect, the ALICE collaboration recently measured the spin alignment of the decay products of neutral K^* and φ vector mesons produced in non-central Pb–Pb collisions.

Spin alignment can be studied by measuring the angular distribution of the decay products of the vector mesons. It is quantified by the probability ρ₀₀ of finding a vector meson in a spin state 0 with respect to the direction of the angular momentum of the rotating QGP, which is approximately perpendicular to the plane of the beam direction and the impact parameter of the two colliding nuclei. In the absence of spin-alignment effects, the probability of finding a vector meson in any of the three spin states (–1, 0, 1) should be equal, with ρ₀₀ = 1/3.

The ALICE collaboration measured the angular distributions of neutral K^* and φ vector mesons via their hadronic decays to Kπ and KK pairs, respectively. ρ₀₀ was found to deviate from 1/3 for low-p_T and mid-central collisions at a level of 3σ (figure 1). The corresponding results for φ mesons show a deviation of ρ₀₀ values from 1/3 at a level of 2σ. The observed p_T dependence of ρ₀₀ is expected if quark polarisation via spin-orbit coupling is subsequently transferred to the vector mesons by hadronisation, via the recombination of a quark and an anti-quark from the quark–gluon plasma. The data are also consistent with the initial angular momentum of the hot and dense matter being highest for mid-central collisions and decreasing towards zero for central and peripheral collisions.

The results are surprising as studies with Λ hyperons are compatible with zero

The results are surprising, however, as corresponding quark-polarisation values obtained from studies with Λ hyperons are compatible with zero. A number of systematic tests have been carried out to verify these surprising results. K⁰_S mesons do indeed yield ρ₀₀ = 1/3, indicating no spin alignment, as must be true for a spin-zero particle. For proton–proton collisions, the absence of initial angular momentum also leads to ρ₀₀ = 1/3, consistent with the observed neutral K^* spin alignment being the result of spin-orbit coupling.

The present measurements are a step towards experimentally establishing possible spin-orbit interactions in the relativistic-QCD matter of the quark–gluon plasma. In the future, higher statistics measurements in Run 3 will significantly improve the precision, and studies with the charged K^*, which has a magnetic moment seven times larger than neutral K^*, may even allow a direct observation of the effect of the strong magnetic fields initially experienced by the quark–gluon plasma.