$f_2(1270)\toπ+π$ as a probe of spin and vorticity in heavy-ion collisions

TL;DR

The paper investigates how spin–vorticity dynamics in heavy-ion collisions manifest in the angular distribution of pions from the decay $f_2(1270)\to\pi\pi$. Using both a phenomenological Lagrangian and the helicity formalism, it derives the general decay distribution $W(\theta,\phi,\rho_{ij})$ and connects it to the tensor meson density-matrix elements; the coupling $g_{f_{2}\pi\pi}$ is determined to reproduce the decay width. Embedding this in a blast-wave framework with elliptic flow and thermal vorticity, the authors compute the diagonal density-matrix elements and $\rho_{20}$ across centrality classes, examining the impact of a global vorticity $\Omega_{\text{global}}$. The results indicate that $f_2$'s rich spin-density structure, especially in higher-spin states, provides a sensitive probe of spin–vorticity coupling and non-equilibrium effects in hadronization, with potential experimental accessibility in heavy-ion collisions.

Abstract

The correlation between vorticity and spin alignment in heavy-ion collisions can be probed through polarization measurements of hadrons, whose total spin originates from both constituent-quark spins and orbital angular momentum in the quark-model framework. To motivate such experimental studies, we calculate the general angular distribution of produced pion in $f_2(1270)\toπ+π$ using interaction Lagrangian and helicity formalism and check that both methods yield the same result. The distribution is given as a function of angle between pion and initial quantization axis of $f_2$ and the spin density matrix element of $f_2$. Its diagonal entries and $ρ_{20}$ component were computed assuming local thermal equilibrium and blast wave model for different centrality classes, hence given as a function of azimuthal angle with respect to the impact parameter.

Figures (6)

• Figure 1: A schematic representation of the two vorticities in an event with finite impact parameter, together with the expected hadron structure at freeze-out from a coalescence type picture. The impact parameter and beam direction are the $x$ and $z$ directions, respectively.
• Figure 2: Helicity Lorentz transformation of a particle. Subscript $H$ denotes the helicity rest frame.
• Figure 3: Diagonal density matrix elements for various event centrality classes computed assuming thermal production (Eq. (\ref{['density']})) as a function of the angle w.r.t. impact parameter, assuming the blast wave picture with elliptic flow and polarization , florkblastflorkblast2 and no global vorticity .
• Figure 4: Diagonal density matrix elements for various centrality classes, computed assuming thermal production (Eq. (\ref{['density']})) as a function of the angle w.r.t. impact parameter, assuming the blast wave picture with elliptic flow and polarization , florkblastflorkblast2 as well as a global vorticity of karpenko.
• Figure 5: Diagonal density matrix elements for various centrality classes, computed assuming thermal production (Eq. (\ref{['density']})) as a function of the angle w.r.t. impact parameter, assuming the blast wave picture with elliptic flow and polarization , florkblastflorkblast2 as well as a global vorticity of karpenko multiplied by a factor of 50 .