Probing initial geometrical anisotropy and final azimuthal anisotropy in heavy-ion collisions at Large Hadron Collider energies through event-shape engineering

Anisotropic flow is accredited to have effects from the initial state geometry and fluctuations in the nuclear overlap region. The elliptic flow ($v_2$) and triangular flow ($v_3$) coefficients of the final state particles are expected to have influenced by eccentricity ($\varepsilon_2$) and triangularity ($\varepsilon_3$) of the participants, respectively. In this work, we study $v_2$, $v_3$, $\varepsilon_2$, $\varepsilon_3$ and the correlations among them with respect to event topology in the framework of a multi-phase transport model (AMPT). We use transverse spherocity and reduced flow vector as event shape classifiers in this study. Transverse spherocity has the unique ability to separate events based on geometrical shapes, i.e., jetty and isotropic, which pertain to pQCD and non-pQCD domains of particle production in high-energy physics, respectively. We use the two-particle correlation method to study different anisotropic flow coefficients. We confront transverse spherocity with a more widely used event shape classifier -- reduced flow vector ($q_n$) and they are found to have significant (anti-)correlations among them. We observe significant spherocity dependence on $v_2$, $v_3$ and $\varepsilon_2$. This work also addresses transverse momentum dependent crossing points between $v_2$ and $v_3$, which varies for different centrality and spherocity percentiles.