クォークグルーオンプラズマと高エネルギー重イオン衝突反応 信州冬の学校＠志賀高原 クォークグルーオンプラズマと高エネルギー重イオン衝突反応 上智大学理工学部 機能創造理工学科 平野哲文

講義の流れ 前半（セミナー形式） 後半（講義形式） クォークグルーオンプラズマと相対論的重イオン衝突反応の概観（１コマ） 相対論的流体力学の基礎（１コマ） 相対論的流体力学の重イオン衝突反応への応用（１コマ）

Contents Physics of the Quark Gluon Plasma Relativistic Heavy Ion Collisions Discovery of Nearly Perfect Fluidity at RHIC New Results at LHC and its Implication Summary

Physics of the quark gluon plasma

Two Aspects of Quantum ChromoDynamics QCD: Theory of strong interaction coupling vs. energy scale Asymptotic free of QCD Confinement of color charges

Physics of Many bodies Elementary Particle Physics as “Reductionism” “The whole is more than the sum of its parts.” (Aristotle) http://en.wikipedia.org/wiki/Holism “More is different” (P.W. Anderson) http://www.sciencemag.org/cgi/pdf_extract/177/4047/393 “Wholism is the way to proceed science in the 21st Century.” (T.D. Lee, one of the founders of elementary particle physics) http://www.riken.jp/r-world/info/release/news/2000/dec/index.html#fro_01 (Original article in Japanese) Elementary Particle Physics as “Reductionism”

What is the Quark Gluon Plasma? Hadron Gas Quark Gluon Plasma (QGP) Low  Temperature  High Degree of freedom: Quarks (matter) and gluons (gauge) Mechanics: Quantum ChromoDynamics (QCD) Novel matter under extreme conditions

How High? Suppose “transition” happens when a pion (the lightest hadron) gas is close-packed, 𝑟 𝜋 ≈0.5 fm 𝑛 𝜋 ≈ 1 4𝜋 𝑟 𝜋 3 3 ≈3.6 𝑇 3 𝑇 𝐶 ≈100 MeV ≈ 10 12 K Note 1: T inside the Sun ~ 107 K Note 2: Tc from the 1st principle calculation ~2x1012 K

Equation of State from 1st Principle scaled energy density ~ degree of freedom temperature 𝑇~160 MeV, 𝜖~1 GeV/ fm 3 Wuppertal-Budapest (2010)

Where/When was the QGP? History of the Universe ~ History of form of matter Micro seconds after Big Bang Our Universe was filled with the QGP!

relativistic heavy ion collisions

The QGP on the Earth Front View Side View Relativistic heavy ion collisions Turn kinetic energy (v > 0.99c) into thermal energy

Standard Scenario of Relativistic Heavy Ion Collisions Approach “Form” of matter 4. Relativistic kinetic theory time 4. Hadron gas 3. Relativistic hydrodynamics 3. QGP fluid 2. Non-equilibrium statistical physics 2. Glasma collision axis 1. QCD aspects of nuclear structure 1. Color glass condensate

Hydrodynamic Simulation of a Au+Au Collision http://youtu.be/p8_2TczsxjM Time scale ~ 10-22 sec quark gluon plasma

New Era Started! Multiplicity of charged hadrons ~ 1600 per unit rapidity in a head-on collision at sqrt(sNN)=2.76 TeV

Conjectured Phase Diagram of QCD Understanding of phase diagram  “Condensed matter physics of QCD” The region in which we can investigate by relativistic heavy ion collisions

Big Bang vs. Little Bang Figure adapted from http://www-utap.phys.s.u-tokyo.ac.jp/~sato/index-j.htm

Big Bang vs. Little Bang (contd.) Time scale 10-5 sec >> m.f.p./c 10-23 sec ~ m.f.p./c Expansion rate 105-6/sec 1022-23/sec Spectrum Red shift (CMB) Blue shift (hadrons) Non-trivial issue on thermal equilibration m.f.p. = Mean Free Path

Jargon: Centrality central event peripheral event “Centrality” characterizes a collision and categorizes events. central event peripheral event Participant-Spectator picture is valid

Discovery of nearly perfect fluidity at RHIC

Hydrodynamics for QGP at Work

Elliptic Flow Momentum anisotropy as a response to spatial anisotropy J.-Y. Ollitrault (’92) Elliptic Flow Momentum anisotropy as a response to spatial anisotropy Known to be sensitive to properties of the system (Shear) viscosity Equation of state ~1035Pa 2v2 dN/df 2nd harmonics (elliptic flow)  Indicator of hydrodynamic behavior f 2p

Relativistic Boltzmann Simulations 𝜆= 1 𝜎𝜌 ∝𝜂 l: mean free path h: shear viscosity generated through secondary collisions saturated in the early stage sensitive to cross section (~1/m.f.p.~1/viscosity) v2 is Zhang-Gyulassy-Ko(’99)

“Hydrodynamic Limit” y Eccentricity 𝜀= 𝑦 2 − 𝑥 2 𝑦 2 + 𝑥 2 x 𝜀= 𝑦 2 − 𝑥 2 𝑦 2 + 𝑥 2 x 𝑣 2 𝜀 = Momentum Anisotropy Spatial Anisotropy Response of the system reaches “hydrodynamic limit” 𝑣 2 𝜀 vs. transverse particle density

Ideal Hydrodynamics at Work 𝑣 2 vs. centrality Au+Au Cu+Cu T.Hirano et al. (in preparation)

Viscous Fluid Simulations H.Song et al. (’11) Viscous Fluid Simulations 𝑣 2 𝜀 vs. transverse particle density Ratio of shear viscosity to entropy density 𝜂 𝑠 QGP = 0.08~0.16 ℏ 𝑘 𝐵 ≈ 1 380 𝜂 𝑠 Water ≈ 1 9 𝜂 𝑠 Liquid He

New Results at LHC and its implication

Elliptic Flow ~30% increase Almost identical from RHIC to LHC to RHIC!? ALICE (2011)

Initial Fluctuation Initial spatial fluctuation 𝚺2 𝚺𝟑 𝚺4 Initial spatial fluctuation  higher order harmonics. Profile itself determines “event” planes to respond Adapted from talk by J.Jia at QM2011

Higher Order Harmonics vn (n=2,3,4,5 and 6) are observed at LHC v3 as large as v2 in central collisions Adapted from talk by J.Jia (ATLAS) at QM2011

Higher Order Harmonics from Event-by-Event Hydro Model K.Murase, M.Sci. thesis the Univ. of Tokyo (2012) Higher Order Harmonics from Event-by-Event Hydro Model Initial hydrodynamic field Bumpiness from nucleon position in a nuclei Finite higher order harmonics  Response to fine structure  New tool to diagnose QGP

QGP as Opaque QCD Matter Perfect liquid is something like a black ink in a sense of QED.

Jet Tomography 1. Suppression of inclusive yields at high pT 2. Modification of back-to-back correlation Adapted from http://www.lbl.gov/Science-Articles/Archive/sabl/2008/Feb/jets.html

Suppression of Yields at High pT Adapted from talk by Y.-J. Lee(CMS) at QM2011 Suppression of Yields at High pT SPS RHIC, low E RHIC, maximum E D.d’Enterria, 0902.2011[nucl-ex] 𝑅 𝐴𝐴 ≈ Observed yield "Expected" yield High pT hadrons are suppressed again!

Jet Quenching As Missing pT Adapted from talk by C.Roland (CMS) at QM2011 Jet Quenching As Missing pT in-cone out-of- cone Jet momentum balanced by low pT hadrons out of jet cone!

Momentum Balance Restored Adapted from talk by C.Roland (CMS) at QM2011 Momentum Balance Restored Lost energy goes to low pT particles

Towards Understanding of Jet-Medium Interaction: Wake by Jet Y.Tachibana, M.Sci. thesis, the Univ. of Tokyo (2012) Towards Understanding of Jet-Medium Interaction: Wake by Jet A 50 GeV jet traverses a background with T=0.5 GeV  Mach-cone like structure Vortex ring behind a jet

Large Angle Emission from Expanding Medium Y.Tachibana, M.Sci. thesis, the Univ. of Tokyo (2012) Large Angle Emission from Expanding Medium Δ 𝑑𝑁 𝑑 cos 𝜃 = 𝑑𝑁 w.jet 𝑑 cos 𝜃 − 𝑑𝑁 w.o.jet 𝑑 cos 𝜃 cos 𝜃 =1 q out-of-cone cos 𝜃 =−1 Jet pair created at off central position Spherical QGP for simplicity Enhancement of low momentum particles at large angle from jet axis

Summary QGP behaves like a perfect fluid. Large anisotropic flow and finite harmonics at higher order Response to fine structure of initial profiles QGP is opaque. Huge stopping power against a few hundred GeV jet Response to large energy loss by jets Transport of wake Towards more quantitative understanding of the QGP by means of heavy ion collisions