Factorization breaking of flow coefficients is actively studied to understand longitudinal dynamics of the quark-gluon plasma produced in high-energy nuclear collisions, yet no hydrodynamic models have successfully described the centrality dependence of the factorization breaking in various collisions systems. In this study, we reproduce the centrality dependence of rapidity decorrelation in Pb+Pb collision at LHC by constructing an integrated dynamical model with hydrodynamic fluctuations [1,2] and initial longitudinal fluctuations.
Hydrodynamic fluctuations are thermal fluctuations arising during the hydrodynamic stage of high-energy nuclear collisions. We include hydrodynamic fluctuations obeying the fluctuation-dissipation theorem . For initial longitudinal fluctuations, we employ an initial model discussed in Ref. . In this model, we run PYTHIA for each binary $p+p$ collision, scale it by the number of participants and regard the distribution of produced particles as entropy density distribution. We switch on and off the initial longitudinal fluctuations and hydrodynamic fluctuations to understand the origin of longitudinal rapidity decorrelation.
 Koichi Murase, “Causal hydrodynamic fluctuations and their effects on high-energy nuclear collisions”, Ph. D thesis, the University of Tokyo (2015).
 Koichi Murase, “Causal hydrodynamic fluctuations in non-static and inhomogeneous backgrounds”, arXiv:1904.11217 (2019).
 Michito Okai, Koji Kawaguchi, Yasuki Tachibana, and Tetsufumi Hirano, “New approach to initializing hydrodynamic fields and mini-jet propagation in quark-gluon fluids”, Phys. Rev. C 95, 054914 (2017)