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 nuclear overlap region. The elliptic (${v}_{2}$) triangular (${v}_{3}$) coefficients of final particles are expected influenced by eccentricity (${ϵ}_{2}$) triangularity (${ϵ}_{3}$) participants, respectively. In this work, we study ${v}_{2}$, ${v}_{3}$, ${ϵ}_{2}$, ${ϵ}_{3}$, correlations among them with respect event topology framework a multiphase transport model (AMPT). We use transverse spherocity reduced vector as shape classifiers study. Transverse has unique ability separate events based on geometrical shapes, i.e., jetty isotropic, which pertain pQCD non-pQCD domains particle production high-energy physics, two-particle correlation method different anisotropic coefficients. confront more widely used classifier--reduced (${q}_{n}$) they found significant (anti)correlations them. observe dependence ${ϵ}_{2}$. This work also addresses momentum dependent crossing points between ${v}_{2}$ varies for centrality percentiles.