In recent years, factorization breaking of flow coefficients in transverse momentum has been measured by CMS Collaboration  to understand the transport properties of QGP. The factorization ratio $r_n$ measured in Pb + Pb collisions at LHC represents the decorrelation of the event plane angle in different transverse momentum regions. When $r_n = 1$, which implies the coincidence of the event-plane angles along transverse momentum direction, $r_n$ can be factorized into the anisotropic flow coefficients $v_n$ in the individual transverse momentum regions. However, $r_n < 1$ means the event-plane angles differ from each other and consequently this factorization is broken. Hydrodynamic fluctuations are expected to break the factorization because they disturb the event plane.
In this study, we analyze the factorization ratio $r_n$ in the direction of transverse momentum by using an integrated dynamical model  that incorporates thermal fluctuations into the relativistic hydrodynamic model. The QGP produced in high-energy heavy-ion collisions expands rapidly, cools down and becomes a hadron gas in a short time period. Thus, the QGP cannot be measured directly. Therefore, the transport properties of QGP are explored through analysis of the hadron momentum distribution measured by the detector. Since the final state hadron observables carry the information on the whole history of the space-time evolution of the system, it is important to construct an integrated dynamical model that describes the whole reaction. Using this integrated dynamic model incorporating hydrodynamic fluctuations, we compare the analysis results of the factorization ratio in the transverse momentum direction with the experimental results and discuss the influence of the hydrodynamic fluctuations on the factorization ratio in the transverse momentum direction.
 CMS Collaboration, Phys. Rev. C 92, 034911 (2015)
 K. Murase, Ph. D thesis, The University of Tokyo (2015)