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Spectral shapes in pp collisions

This article explores the use of hydrodynamics in high energy collisions and its connection to lattice QCD. It covers the basics of hydrodynamics, including the hydrodynamic equations and energy-momentum conservation. The equation of state is discussed as a means to close the system of equations, and the importance of collective flow in understanding the equation of state is highlighted. The article also addresses the challenges of thermalization and decoupling in hydrodynamic simulations.

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Spectral shapes in pp collisions

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  1. Spectral shapes in pp collisions Mt-scaling for soft particles Power-law tail from hard scattering Increasing with energy

  2. Scaling of spectra in dA and AA collisions • mT scaling in pp and dA, but NOT in AA. Signature of radial flow.

  3. Fitting p,K,p with hydrodynamics model 40-50% 80-92% 0-5%

  4. Blast wave fits: Tfo and flow velocity

  5. Flow velocity vs energy < bT > slowly increasing from AGS to SPS to RHIC

  6. Basics of Hydrodynamics Hydrodynamic Equations Energy-momentum conservation Charge conservations (baryon, strangeness, etc…) Need equation of state (EoS) P(e,nB) to close the system of eqs.  Hydro can be connected directly with lattice QCD For perfect fluids (neglecting viscosity), Energy density Pressure 4-velocity Within ideal hydrodynamics, pressure gradient dP/dx is the driving force of collective flow.  Collective flow is believed to reflect information about EoS!  Phenomenon which connects 1st principle with experiment Caveat:Thermalization,l << (typical system size)

  7. Inputs to Hydrodynamics Final stage: Free streaming particles  Need decoupling prescription t Intermediate stage: Hydrodynamics can be valid if thermalization is achieved.  Need EoS z • Initial stage: • Particle production and • pre-thermalization • beyond hydrodynamics • Instead, initial conditions for hydro simulations Need modeling (1) EoS, (2) Initial cond., and (3) Decoupling

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