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Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano

B ulk V iscous E ffects on R elativistic H ydrodynamic M odels of the Q uark- G luon P lasma. Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano. 3 rd Joint Meeting of the Nuclear Physics Divisions of the APS and the JPS

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Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano

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  1. Bulk Viscous Effects on Relativistic Hydrodynamic Models of the Quark-Gluon Plasma Akihiko Monnai Department of Physics, The University of Tokyo Collaborator: Tetsufumi Hirano 3rd Joint Meeting of the Nuclear Physics Divisions of the APS and the JPS October 15th 2009, Hawaii USA AM and T. Hirano, arXiv:0903.4436; arXiv:0907.3078

  2. Outline • Introduction Relativistic viscous hydrodynamics • Distortion of Distribution How to express in terms of dissipative currents • Numerical Estimation Effects of on observables • Summary and Outlook Summary and constitutive equations

  3. Introduction Success of ideal hydrodynamic models at relativistic heavy ion collisions Development of viscous hydrodynamic models to correctly extract information from experimental data How does bulk viscosity affects observables? It has almost been neglected, BUT bulk viscosity is not so small near Mizutani et al. (‘88) Bulk viscosity = response of pressure to volume change Paech & Pratt (‘06) … Kharzeev & Tuchin (’08)

  4. Introduction • One needs a translator of flow field into particles at freezeout How does bulk viscosity affects observables? hydro result observables Cooper-Frye formula particles freezeout hypersurface Σ hadron resonance gas variation of the flow/hypersurface modification of the distribution QGP particles freezeout hypersurface Σ Express with dissipative currents in a multi-component system hadron resonance gas QGP

  5. Macroscopic to Microscopic • Generalization of Israel-Stewart method: Express in terms of dissipative currents Israel & Stewart (‘76) Macroscopic quantities Microscopic quantities , , , Distortion of distribution (unknown) Dissipative currents (given from hydro) 14 “bridges” from Relativistic Kinetic Theory

  6. in Multi-Component System • Grad’s 14-moment method 14 unknowns , No scalar, but non-zero trace tensor : 2nd law of thermodynamics + constitutive equation New tensor structure for multi-component system • The distortion is uniquely obtained: where and arecalculated in kinetic theory.

  7. Models Inputs • Estimation of particle spectra (with bulk viscosity in ): Flow , freezeout hypersurface : (3+1)-D ideal hydrodynamic model Bulk pressure: Navier-Stokes limit Hirano et al.(‘06) Transport coefficients: , where : sound velocity : entropy density Equation of State: 16-component hadron resonance gas (hadrons up to , under ) Freezeout temperature: Weinberg (‘71) Kovtun et al.(‘05)

  8. Bulk Viscosity and Particle Spectra • Au+Au, , b = 7.2(fm), pT -spectra and v2(pT) of pT -spectra suppressed v2 (pT) enhanced *Possible overestimations due to... (i) Navier-Stokes limit (no relaxation effects) (ii) ideal hydro flow (derivatives are larger)

  9. Summary and Outlook • Determination of in a multi-component system - Viscous correction has non-zero trace. • Visible effects of on particle spectra - pT-spectra is suppressed;v2(pT) is enhanced • Bulk viscosity can be important in extracting information (e.g. transport coefficients) from experimental data. • Full Viscous hydrodynamic models need to be developed to see more realistic behavior of the particle spectra.

  10. Estimation of Dissipative Currents AM and T. Hirano, in preparation • 2nd order Israel-Stewart theory Naïve generalization to a multi-component system does NOT work • Constitutive equations in a multi-component system: Bulk pressure Shear tensor in conformal limit reduces to AdS/CFT result (Baier et al. ‘08) Navier-Stokes term Israel-Stewart 2nd order terms Post Israel-Stewart 2nd order terms

  11. Thank You • The numerical code will become available at http://tkynt2.phys.s.u-tokyo.ac.jp/~monnai/distributions.html

  12. Appendix

  13. Shear Viscosity and Particle Spectra • pT -spectra and v2(pT) of with shear viscous correction Non-triviality of shear viscosity; both pT -spectra and v2(pT) suppressed

  14. Shear & Bulk Viscosity on Spectra • pT -spectra and v2(pT) of with corrections from shear and bulk viscosity Accidental cancellation in viscous corrections in v2(pT)

  15. Quadratic Ansatz • pT -spectra and v2(pT) of when Effects of the bulk viscosity is underestimated in the quadratic ansatz.

  16. Bjorken Model • pT -spectra and v2(pT) of in Bjorken model with cylindrical geometry: Bulk viscosity suppressespT-spectra Shear viscosity enhancespT-spectra

  17. Blast wave model • pT -spectra and v2(pT) of Shear viscosity enhances pT-spectra and suppresses v2(pT).

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