# Presentation: 673036

## Limits on the Viscosity to Entropy Ratio from PHENIX Data                      on Single Electron Production

## Introduction: sQGP @ RHIC

- The matter may melt but regenerate J/’s

**Introduction: sQGP @ RHIC**

- The matter is dense

- The matter is hot

- The matter is strongly coupled

- The matter modifies jets

**PHENIX preliminary**

**QM 2005**
**strongly inter-acting Quark-Gluon Plasma (sQGP) in HI collisions at RHIC**

**recent hot topic:**
**viscosity/entropy**
******/s**

**next steps**
**quantify sQGP properties**

## Viscosity Primer

**supports a shear stress**
**viscosity ******** defined as**
**dimensional estimate**

**Viscosity**** Primer**

**large cross sections ↔ small viscosity**

**but how small is “small”?**

## Viscosity of a “Near Perfect” Fluid

**conjectured lower quantum limit **
**derived first in ****(P. Kovtun, D.T. Son, A.O. Starinets, Phys.Rev.Lett.94:111601, 2005)**** **
**motivated by AdS/CFT ****(Anti de Sitter space / Conformal Field Theory)****                                           correspondence ****(J. Maldacena: Adv. Theor. Math. Phys. 2, 231, 1998)**

**Viscosity**** of a “Near Perfect” Fluid**

**“****ordinary” fluids**
**water (at normal conditions)**
** ********/s ~ 380 ****ћ****/4******
**helium (at ******** point)**
** ********/s ~ 9 ****ћ****/4******
**“****RHIC fluid”?**

## Measuring /s

**damping (flow, fluctuations, **_**heavy quark motion**_**) ~ ********/s**
**flow**
**R. Lacey et al.: ****Phys. Rev. Lett. 98:092301, 2007**
**“****Has the QCD critical point been signaled by observations at RHIC?” **
**H.-J. Drescher et al.: ****Phys. Rev. C76:024905, 2007**
**“****The Centrality Dependence of Elliptic Flow, the Hydrodynamic Limit, and the Viscosity of Hot QCD”**
**fluctuations**
**S. Gavin and M. Abdel-Aziz: ****Phys. Rev. Lett. 97:162302, 2006**
**“****Measuring Shear Viscosity Using Transverse Momentum Correlations in Relativistic Nuclear Collisions”**
**heavy quark motion (drag, flow)**
**A. Adare et al. (PHENIX Collaboration): ****Phys. Rev. Lett. 98:092301, 2007**
**“****Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at     ****√s****NN**** = 200 GeV****”**

**Measuring ********/s**

## Heavy-Flavor in PHENIX

**near future**
**reconstruction of hadronic decays**
**upgrade: silicon vertex spectrometer**
**talk: H. van Hecke **

**Heavy-Flavor in PHENIX**

**current measurements**
**indirect via semileptonic                            heavy-flavor decays**
** ****e****±****: 6 PRL, 1 PRC papers**
**talk: Y. Morino**
** ********±****: 1 PRC paper**
**talk: D. Hornback**
** ****e****+****e****-****: 1 PRL, 1 PLB submission**
**talk: A. Toia**

| Meson | D± (D0) |
| --- | --- |
| Mass | 1.87 (1.87) GeV |
| BR D0 --> K | (3.85 ± 0.10) % |
| BR D --> e +X | 17.2 (6.7) % |
| BR D --> +X | 17.2 (6.6) % |

**posters: S. Butsyk, P. Shukla**

## Baseline: p+p at √s = 200 GeV

**Baseline: p+p at √s = 200 GeV**

**heavy-flavor e****±**** data**
**consistent with ****FONLL                                                                           ****calculation: ****F****ixed ****O****rder                                                                  ****N****ext-to-****L****eading ****L****og perturbative QCD                                                                     ****(M. Cacciari, P. Nason, R. Vogt PRL95,122001 (2005))**

**talk: Y. Morino**

## Au+Au at √sNN=200 GeV: Spectra

**Au+Au at √s****NN****=200 GeV: Spectra**

**binary scaling of total e****±**** yield from heavy-flavor decays**
**expected from heavy-quark production via hard scattering**
**high p****T**** e****±**** suppression increasing with centrality**
**footprint of medium effects**

## Nuclear Modification Factor RAA

**Nuclear Modification Factor R****AA**

**very similar to light hadron R****AA**
**careful: **
**decay kinematics!**
**p****T****(e****±****) < p****T****(D)**
**intermediate p****T**
**indication for quark mass hierarchy as expected for radiative energy loss ****(Dokshitzer and Kharzeev, PLB 519(2001)199)**
**highest p****T**
**R****AA****(e****±****) ~ R****AA****(********0****) ~ R****AA****(********)**

**R****AA **** e****±**** from heavy-flavor decays**

**crucial to understand: what is the bottom contribution?**
**ideal: R****AA**** of identified charm and bottom hadrons **

## e± RAA: a Challenge for Models 

**testing ground for various parton energy loss ********E******** models**
**radiative ********E only**
**Djordjevic et al., PLB 632(2006)81**
**Armesto et al., PLB 637(2006)362)**
**collisional ********E included**
**Wicks et al., NPA 784(2007)426**
**van Hees & Rapp, PRC 73(2006)034913)**

**or alternative approaches to interpret the suppression**
**collisional dissociation of                               heavy mesons (charm and bottom!)**
**Adil & Vitev, PLB 649(2007)139**
**contribution from baryon enhancement**
**Sorensen & Dong, PRC 74(2006)024902**

## Au+Au at √sNN = 200 GeV: Flow

**elliptic flow of e****±**** from heavy-flavor decays**
**non-zero v****2**** (RHIC Run-4)**

**Au+Au at √s****NN**** = 200 GeV: Flow**

**progress in Run-7**
**improved reaction plane resolution**
**(increased statistics)**
**data are consistent within uncertainties**
**indication for non-zero v****2**** at high p****T**** (charm vs. bottom)**
**also available:          v****2**** vs. centrality**

**good agreement with Langevin based transport calculation including resonant elastic scattering**

## Estimating /s

**at ********B**** = 0**
** ******** ****+ P = Ts**
**then**
** ********/s = (1.3-2.0)/4******

**transport models**
**Rapp & van Hees ****(PRC 71, 034907 (2005))**
**diffusion coefficient required for simultaneous fit of R****AA**** and v****2**** **
**D****HQ****x2********T ~ 4-6**

**Estimating ********/s**

**Moore & Teaney ****(PRC 71, 064904 (2005))**
**difficulties to describe R****AA**** and v****2**** simultaneously**
**calculate perturbatively (and argue that plausible also non-perturbatively)**
**D****HQ****/ (********/(********+P)) ~ 6   (for N****f ****= 3)**

## Comparison with other estimates

**Comparison with other estimates**

**estimates of ********/s based on flow and fluctuation data**
**indicate small value as well**
**close to conjectured limit**
**significantly below ********/s of helium (********s ~ 9)**

## Summary

**heavy-flavor production is a crucial probe **
**consistent ********/s estimates from single electron production, flow, and fluctuation data **

**Summary**

## The PHENIX Collaboration

- Universidade de São Paulo, Instituto de Física, Caixa Postal 66318, São Paulo CEP05315-970, Brazil
- Institute of Physics, Academia Sinica, Taipei 11529, Taiwan
- China Institute of Atomic Energy (CIAE), Beijing, People's Republic of China
- Peking University, Beijing, People's Republic of China
- Charles University, Ovocnytrh 5, Praha 1, 116 36, Prague, Czech Republic
- Czech Technical University, Zikova 4, 166 36 Prague 6, Czech Republic
- Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2,
-      182 21 Prague 8, Czech Republic
- Helsinki Institute of Physics and University of Jyväskylä, P.O.Box 35, FI-40014 Jyväskylä, Finland
- Dapnia, CEA Saclay, F-91191, Gif-sur-Yvette, France
- Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS-IN2P3, Route de Saclay,
-      F-91128, Palaiseau, France
- Laboratoire de Physique Corpusculaire (LPC), Université Blaise Pascal, CNRS-IN2P3,
- Clermont-Fd, 63177 Aubiere Cedex, France
- IPN-Orsay, Universite Paris Sud, CNRS-IN2P3, BP1, F-91406, Orsay, France
- SUBATECH (Ecole des Mines de Nantes, CNRS-IN2P3, Université de Nantes)
-     BP 20722 - 44307, Nantes, France
- Institut für Kernphysik, University of Münster, D-48149 Münster, Germany
- Debrecen University, H-4010 Debrecen, Egyetem tér 1, Hungary
- ELTE, Eötvös Loránd University, H - 1117 Budapest, Pázmány P. s. 1/A, Hungary
- KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences (MTA KFKI RMKI),
-     H-1525 Budapest 114, POBox 49, Budapest, Hungary
- Department of Physics, Banaras Hindu University, Varanasi 221005, India
- Bhabha Atomic Research Centre, Bombay 400 085, India
- Weizmann Institute, Rehovot 76100, Israel
- Center for Nuclear Study, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo,
-     Tokyo 113-0033, Japan
- Hiroshima University, Kagamiyama, Higashi-Hiroshima 739-8526, Japan
- KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan
- Kyoto University, Kyoto 606-8502, Japan
- Nagasaki Institute of Applied Science, Nagasaki-shi, Nagasaki 851-0193, Japan
- RIKEN, The Institute of Physical and Chemical Research, Wako, Saitama 351-0198, Japan
- Physics Department, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan
- Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152-8551, Japan
- Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan
- Waseda University, Advanced Research Institute for Science and Engineering, 17  Kikui-cho,
-      Shinjuku-ku, Tokyo 162-0044, Japan
- Chonbuk National University, Jeonju, Korea
- Ewha Womans University, Seoul 120-750, Korea
- KAERI, Cyclotron Application Laboratory, Seoul, South Korea
- Kangnung National University, Kangnung 210-702, South Korea
- Korea University, Seoul, 136-701, Korea
- Myongji University, Yongin, Kyonggido 449-728, Korea
- System Electronics Laboratory, Seoul National University, Seoul, South Korea
- Yonsei University, IPAP, Seoul 120-749, Korea
- IHEP Protvino, State Research Center of Russian Federation, Institute for High Energy Physics,
-      Protvino, 142281, Russia
- Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
- Russian Research Center "Kurchatov Institute", Moscow, Russia
- PNPI, Petersburg Nuclear Physics Institute, Gatchina, Leningrad region, 188300, Russia
- Saint Petersburg State Polytechnic University, St. Petersburg, Russia
- Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Vorob'evy Gory,
-      Moscow 119992, Russia
- Department of Physics, Lund University, Box 118, SE-221 00 Lund, Sweden

- Abilene Christian University, Abilene, TX 79699, U.S.
- Collider-Accelerator Department, Brookhaven National Laboratory, Upton, NY 11973-5000, U.S.
- Physics Department, Brookhaven National Laboratory, Upton, NY 11973-5000, U.S.
- University of California - Riverside, Riverside, CA 92521, U.S.
- University of Colorado, Boulder, CO 80309, U.S.
- Columbia University, New York, NY 10027 and Nevis Laboratories, Irvington, NY 10533, U.S.
- Florida Institute of Technology, Melbourne, FL 32901, U.S.
- Florida State University, Tallahassee, FL 32306, U.S.
- Georgia State University, Atlanta, GA 30303, U.S.
- University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.
- Iowa State University, Ames, IA 50011, U.S.
- Lawrence Livermore National Laboratory, Livermore, CA 94550, U.S.
- Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.
- University of Maryland, College Park, MD 20742, U.S.
- Department of Physics, University of Massachusetts, Amherst, MA 01003-9337, U.S.
- Muhlenberg College, Allentown, PA 18104-5586, U.S.
- University of New Mexico, Albuquerque, NM 87131, U.S.
- New Mexico State University, Las Cruces, NM 88003, U.S.
- Oak Ridge National Laboratory, Oak Ridge, TN 37831, U.S.
- RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973-5000, U.S.
- Chemistry Department, Stony Brook University, Stony Brook, SUNY, NY 11794-3400, U.S.
- Department of Physics and Astronomy, Stony Brook University, SUNY, Stony Brook, NY 11794, U.S.
- University of Tennessee, Knoxville, TN 37996, U.S.
- Vanderbilt University, Nashville, TN 37235, U.S.

*** ******14 Countries;  69 Institutions***

**July 2007**