Sensitivity of flow harmonics to sub-nucleon scale fluctuations in heavy ion collisions

In this paper a new procedure to smooth out the initial energy densities of hydrodynamics is employed to show that the initial spatial eccentricities $\varepsilon_{m,n}$, which drive the final state flow harmonics $v_n$, are remarkably robust with respect to variations of the underlying scale of initial energy density spatial gradients, $\lambda$, in nucleus-nucleus collisions. For $\sqrt{s}=2.76$ TeV Pb+Pb collisions, the $\varepsilon_{m,n}$'s (across centrality classes) change by less than $10\%$ if the scale of fluctuations is varied from $0.1$ to $1$ fm. We show, using the 2+1 Lagrangian hydrodynamic code, v-USPhydro, that this robustness is transferred to the final $v_n$'s computed within event by event viscous hydrodynamics. This indicates that the flow harmonics in nucleus-nucleus collisions are not yet particularly sensitive to the underlying microscopic sub-nucleon physics below the confinement scale. On the other hand, the eccentricities of top $1\%$ high multiplicity $\sqrt{s}=5.02$ TeV p+Pb collisions are found to be very sensitive to sub-nucleonic scale fluctuations, which should be contrasted with the robustness found in peripheral Pb+Pb collisions with the same multiplicity.