plemented MC-KLN [10, 11] and MC-Glauber [12] initial conditions at LHC energies, allowing them to be evolved by free-streaming for a time τs before switching to a viscous hydrodynamic description for the rest of the evolution

Our work focuses on the effects brought by freestreaming on both the hydrodynamic initial conditions and the final observables. We mainly focus on the MCKLN model which provides a complete prediction for the initial gluon distribution, not only in space but also in momentum. However, we show that for massless partons moving with the speed of light the shape of the initial momentum distribution is irrelevant as long as it is locally isotropic. This allows to apply our description also to

MC-Glb initial conditions although that model makes no prediction per se about the initial parton momentum distribution. Free-streaming evolves the initial conditions from an initial parton formation time τ0 (which is taken to be very close to zero) to the switching time τs when we switch to a near-equilibrium hydrodynamic description

The sudden transition to approximate local equilibrium is implemented by applying the Landau matching procedure. By tuning the switching time, we can enforce fast thermalization by setting τs τ0, or slow thermalization by setting τs τ0. The hydrodynamic initial conditions obtained from the Landau matching procedure vary with the switching time, enabling an investigation of the influence of τs on the final observables. The hydrodynamic evolution is performed with the code VISH2+1 [8, 9], without hadron cascade afterburner. For the hydrodynamic evolution, we use a constant specific shear viscosity η/s. Freeze-out is implemented at a fixed kinetic freeze-out temperature Tdec, followed by a Cooper-Frye procedure with full resonance decay cascade to convert the hydrodynamic output into final stable particle spectra

In Section II, we outline the free-streaming evolution in the pre-equilibrium stage and describe the Landau matching procedure. Its consequences on the hydrodynamic initial conditions are discussed in Section III

Section IV shows how the hydrodynamical evolution responds to initial conditions generated at different switching times. A difficulty related to the conversion of partons to hadrons that arises from a late switching time τs is discussed and resolved in VI and

VII, the energy flow anisotropy and hadron mean transverse momenta are constructed to illustrate how final observables change with switching time. Finally in Section

VIII we introduce a multidimensional parameter search procedure to systematically study the preferred ranges of

τs, η/s and Tdec. For both MC-KLN and MC-Glb initial conditions, both with and without a free-streaming pre-equilibrium stage before the onset of hydrodynamic behavior, we determine the best-fit parameters and their uncertainty ranges, and discuss their relative quality of describing the data. Conclusions are presented in Section

IX

II. FORMULATION OF FREE-STREAMING

AND LANDAU MATCHING

The evolution of partons in the free-streaming model is described by the collisionless Boltzmann equation pµ

∂µf(x, p) = 0. (1)

We work in Milne coordinates and write f(x, p) = f(x⊥, ηs, τ

p⊥, y), with longitudinal proper time

τ =

√ t2-z2, space-time rapidity ηs = 1

ln[(t+z)/(t-z)], and rapidity y = 1

ln[(E+pz)/(E-pz)]. We assume massless partons for which E = |p| = p2

⊥+p2 z. The collisionless Boltzmann equation is easily solved analytically, relating the final parton distribution f(x⊥, ηs, τs

p⊥, y) to the f(x⊥, ηs, τ0

p⊥, y) by a spatial coordinate shift, keeping the p⊥ distribution unchanged

For massless partons one finds: f(x⊥, ηs, τs

p⊥, y) = f(x⊥-(τs-τ0)ˆp⊥, ηs, τ0