Elliptic flow analysis with non-hydro mode in viscous hydrodynamics Nikhil Hatwar * and M. Mishra † Department of Physics, Birla Institute of Technology and Science, Pilani, Rajasthan, India (Dated: February 2, 2022) Hydrodynamics has been quite suitably used to model the thermal stage of the heavy-ion collision experiments especially in the low transverse momentum regime. But the satisfactory agreement of hydrodynamics for proton-proton collision has stirred up the discussions about the smallest volume for which the hydrodynamics can be applied. The meaning of hydrodynamics itself has been under scrutiny with non-requirement of local thermal equilibrium for its applicability. The second order viscous hydrodynamics requires a transport coefficient called relaxation time, which had to be included to avoid the causality violation in the system. This relaxation time controls the non-hydro mode in an out of equilibrium hydrodynamics theory. In phenomenological studies this relaxation time has been taken as a constant and much attention has gone into fixing shear viscosity to entropy density ratio, η/s. The dynamics of hydro and non-hydro modes govern the evolution of the system. In the present work, we study the effect of the variation of the relaxation times on the elliptic flow in Pb-Pb system, at √ sNN =2.76 TeV center-of-mass energy with optical Glauber and IPGlasma initial conditions. We find that this system operates throughout within the hydrodynamic regime. Non-hydro mode structure of the theory does not affect flow in the most central collisions and there is a noticeable increase in flow due to the initial state fluctuations. I. INTRODUCTION The fact that baryons have internal structure directly leads to the notion that a bulk medium of sub-nucleonic degrees of freedom is, in principle, possible. The en- ergy density of at least a few GeV/fm 3 is required to free up quarks from the nucleons [1]. The existance of such a medium was not very clear until the arrival of the Relativistic Heavy Ion Collider(RHIC) facility at Brookhaven National Laboratory where a deconfined state of sufficient time span was produced for observing the indirect unambiguous signatures of the Quark-Gluon Plasma(QGP). Strangeness enhancement [2] and ellip- tic flow [3] were among the preliminary indicators. The discovery of QGP in heavy ion collisions became more established with subsequent confirmation through other indicators like jet quenching and quarkonia suppression at RHIC. Efforts now are directed towards quantitatively fixing the boundaries of various regions of QCD phase di- agram [4]. With the challenges involved in the theoretical de- velopment of the non-perturbation QCD dynamics, the progress in modelling these systems have been hindered. Moreover, deconfinement of quarks in QCD is still a un- solved problem [5]. Lattice QCD has been of some help in the QGP stage [6, 7], but we are far away from getting the whole system evolution under the roof of single dynam- ics. Thankfully, phenomenology has come for the rescue, allowing us to break the evolution into pre-equilibrium QGP and freeze-out stages. The use of hydrodynamics in modelling the transient QGP stage has been quite sur- prising [8], since traditionally hydrodynamics has been associated with the establishment of the local thermal * nikhil.hatwar@gmail.com † madhukar@pilani.bits-pilani.ac.in equilibrium of fluid of some kind. However, hydrodynamics as an effective theory for ex- plaining high energy collision has been evolved tremen- dously in the last two decades. Below we provide a very brief overview of the topics leading upto the present state of affairs. For an in-depth review of the topics, please lookup references [9–15]. Hydrodynamics is the collective dynamical evolution of a suitably sized bulk medium adhering to the system’s symmetries. For the relativistic case, the conservation laws take the form, ∂ μ T μν = 0 for energy–momentum tensor and ∂ μ N μ = 0 for conserved charge. The local values of temperature, T (x), fluid velocity, u μ (x) and chemical potential, µ(x) are the chosen hydrodynamic variables. The energy-momentum tensor can be decom- posed as[16]; T μν = ǫu μ u ν + P Δ μν +(w μ u ν + w ν u μ )+Π μν . (1) Here, ǫ(energy density) and P (pressure) are scalar co- efficients. w μ represent transverse vector coefficient. Δ μν ≡ g μν + u μ u ν is the projector operator orthogonal to the fluid velocity, u μ and g μν is the spacetime metric. The above expression without the Π μν term corresponds to 0 th order ideal hydrodynamics. The Π μν tensor is in- troduced to account for the dissipative effects which is further decomposed as: Π μν = π μν +Δ μν Π. (2) Π and π μν are the bulk and shear part of the viscous stress tensor. The form of the shear stress tensor, π μν and bulk pressure, Π are set up in accordance with the covariant form of the second law of thermodynamics[9]. When we set the expression for entropy 4−current as s μ = su μ , where s is entropy density, we get; π μν = ησ μν and Π= ζ∂ μ u μ (3) arXiv:2202.00654v1 [hep-ph] 1 Feb 2022