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

TL;DR

This paper explores how the decay of the tensor meson $f_2(1270)$ into two pions can serve as a probe for studying the relationship between vorticity and spin alignment in heavy-ion collisions, providing a theoretical framework for experimental measurements.

Contribution

The paper develops a detailed angular distribution model for $f_2(1270) o \pi+\pi$ decay, linking it to spin density matrix elements and vorticity effects in heavy-ion collisions.

Findings

Derived angular distribution formula for $f_2$ decay

Computed spin density matrix elements under thermal equilibrium

Provided predictions for azimuthal angle dependence in different collision centralities

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 $f_2(1270)\to\pi+\pi$ 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 $\rho_{20}$ 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.