  The mean transverse momentum of produced particles, [pt], 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 [pt] fluctuations can be studied via multi-particle pt
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 pt
correlations, which enables the accurate study of higher-order [pt]
fluctuations without computationally heavy processing for the first time. With
this algorithm, we will examine the power of multi-particle pt 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 will demonstrate the
usefulness of multi-particle pt correlations for studying nuclear structure in
high-energy nuclei collisions at RHIC and the LHC, which could serve as
complementary to existing low-energy nuclear structure studies.
