1. 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

2. 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）

3. 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

4. Physics of the quark gluon plasma

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

6. Physics of Many bodies Elementary Particle Physics as “Reductionism”
“The whole is more than the sum of its parts.” (Aristotle)
“More is different” (P.W. Anderson)
“Wholism is the way to proceed science in the 21st Century.” (T.D. Lee, one of the founders of elementary particle physics) (Original article in Japanese)
Elementary Particle Physics
as “Reductionism”

7. 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

8. 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 ≈3.6 𝑇 3
𝑇 𝐶 ≈100 MeV ≈ K
Note 1: T inside the Sun ~ 107 K
Note 2: Tc from the 1st principle calculation ~2x1012 K

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

10. 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!

11. relativistic heavy ion collisions

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

13. 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

14. Hydrodynamic Simulation of a Au+Au Collision
Time scale ~ sec
quark gluon plasma

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

16. 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

17. Big Bang vs. Little Bang Figure adapted from

18. 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
/sec
Spectrum
Red shift (CMB)
Blue shift (hadrons)
Non-trivial issue on thermal equilibration
m.f.p. = Mean Free Path

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

20. Discovery of nearly perfect fluidity at RHIC

21. Hydrodynamics for QGP at Work

22. 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

23. 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)

24. “Hydrodynamic Limit” y Eccentricity 𝜀= 𝑦 2 − 𝑥 2 𝑦 2 + 𝑥 2 x
𝜀= 𝑦 2 − 𝑥 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

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

27. 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 ≈ 𝜂 𝑠 Water ≈ 𝜂 𝑠 Liquid He

28. New Results at LHC and its implication

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

30. Initial Fluctuation Initial spatial fluctuation𝚺2 𝚺𝟑 𝚺4
Initial spatial fluctuation
 higher order harmonics.
Profile itself determines
“event” planes to respond
Adapted from talk
by J.Jia at QM2011

31. 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

32. 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

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

34. Jet Tomography 1. Suppression of inclusive yields at high pT
2. Modification
of back-to-back
correlation
Adapted from

35. 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, [nucl-ex]
𝑅 𝐴𝐴 ≈ Observed yield "Expected" yield
High pT hadrons are suppressed again!

36. 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!

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

38. 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

39. 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

40. 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