Generic multi-particle transverse momentum correlations as a new tool for studying nuclear structure at the energy frontier

The mean transverse momentum of produced particles, [p${}_T$], and its event-by-event fluctuations give direct access to the initial conditions of ultra-relativistic heavy-ion collisions and help probe the colliding nuclei's structure. The [p${}_T$] fluctuations can be studied via multi-particle p${}_T$ correlations; so far, only the lowest four orders have been studied. Higher-order fluctuations can provide stronger constraints on the initial conditions and improved sensitivity to the detailed nuclear structure; however, their direct implementation can be challenging and is still lacking. In this paper, we apply a generic recursive algorithm for the genuine multi-particle p${}_T$ correlations, which enables the accurate study of higher-order [p${}_T$] fluctuations without heavy computational cost for the first time. With this algorithm, we will examine the power of multi-particle p${}_T$ correlations through Monte Carlo model studies with different nuclear structures. The impact on the nuclear structure studies, including the nuclear deformation and triaxial structure, will be discussed. These results demonstrate the usefulness of multi-particle p${}_T$ correlations for studying nuclear structure in high-energy nuclei collisions at RHIC and the LHC, which could serve as a complementary tool to existing low-energy nuclear structure studies.