$f_2(1270)\to\pi+\pi$ as a probe of spin and vorticity 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 $f_2(1270)\to\pi+\pi$ 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.