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The correlation between the mean transverse momentum and the harmonic flowcoefficients is an observable which is of great interest, it is sensitive toshape fluctuations in the initial state of a relativistic nuclear collision.The measurement of that correlation coefficient in central collisions allowsone to infer on the intrinsic deformation and structure of the collidingnuclei. We propose to study the momentum dependent covariance and correlationcoefficient between the mean transverse momentum and the harmonic flow in agiven transverse momentum bin. Two possible constructions of such observableare provided and predictions are obtained from a viscous hydrodynamic model. Wefind that such momentum dependent correlation coefficient between the meantransverse momentum and the harmonic flow shows a very strong and nontrivialmomentum dependence. We also explore the effect of granularity (nucleon width)in the initial state on this momentum dependent correlation coefficient. Inparticular, this momentum dependence could be used to constrain the size ofsmall scale fluctuations in the initial state.

Momentum dependent measures of correlations between mean transverse momentum and harmonic flow in heavy ion collisions