Novel Quantum Phenomena in the Subatomic Swirls

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Novel Quantum Phenomena in the Subatomic Swirls

Chiral Matter Workshop @ NTU Dec. 6~9, 2018

Jinfeng Liao

Indiana University, Physics Dept. & CEEM

Research Supported by NSF & DOE


The Subatomic Swirls

An exciting discovery from STAR Collaboration at RHIC:

The most vortical fluid!





Nuclear Physics: Exploring the Heart of Matter

nuclear force

matter molecule atoms

atomic nucleus proton


[a millionth of a mm]

[a trillionth of a mm]

The physical world has a hierarchy of structures.

Most basic entities:

quarks and gluons.


Chromodynamics (QCD)


Quantum Chromodynamics (QCD)

The fundamental theory of strong nuclear force:

QCD, a non-Abelian gauge theory of quarks and gluons

Asymptotic Freedom: coupling becomes large at low energy or long distance scale.

QCD ⇠ 200MeV R ⇠ 1 fm

Nobel Prize 2004


QCD Confinement: “The Missing Particles"

This null result is by itself a remarkable FACT of Nature.

Confinement problem:

Biggest challenge withinStandard Model!

Mathematics: one of the seven Millennium Problems!

from Particle Data Group

QCD vacuum as “dual superconductor” with dual Meissner effect?

Color-magnetic topological condensate?

QCD dipole field


Chiral Symmetry: Spontaneous Breaking

Dirac Sea

Lagrangian (SM) mass Constituent


m ⇡ 140MeV , mn ⇡ 940MeV

Vacuum condensate

It accounts for 99% of the mass of our visible

matter in universe.


QCD as Topological Material



Emergent Phenomena in QCD

F. Wilczek

@ QM2014


NP as Quantum Chromo Material Science

This talk will focus on the “hot frontier”.


Baryon Density



“Force Frontier

“Dense Frontier”


Quark-Gluon Plasma (QGP):

A Subatomic Quantum Fluid


QCD in Hot Environment

The “super” side is hard, and let’s attack the lambda point from the “right side”, when the system is just about to condense!

Why don’t we do the same for QCD?!

QCD at extreme temperatures:

At high enough T >> Lambda_QCD

A transition to a quark-gluon plasma (QGP) ! [mid ~ late 1970’s]


QGP: A New Phase of Matter

from Lattice QCD

a relativistic pion gas

More precisely,

Hadron Resonance Gas

free QGP


* Two benchmarks at low/high T

* A transition regime in the middle

* Crossover (instead of a phase transition)


QGP: A New Phase of Matter

The high T phase of QCD matter (a few hundred MeV & up) is a distinctive new phase, the quark-gluon plasma (QGP).

The liberated quarks & gluons

The restored chiral symmetry

Wuppertal- Budapest



Little Bangs in Heavy Ion Collisions (HIC)

Relativistic Heavy Ion Collider

An artistic presentation:

“nuclei as heavy as bulls,

colliding into new phase of matter”

Large Hadron Collider


The Setup of Heavy Ion Collision

A typical off-central collision.

In-Plane Out-of-Plane

Quark-gluon plasma is created in such collisions!


QGP Shining Brightly!

QGP is hot stuff: about trillion degrees ! Official Guinness World Record:

the highest man-made temperature!



QGP: An Old Phase of Matter

The quark-gluon plasm is an old phase of matter!

The highest ever temperature was in the beginning of universe.

The QGP temperature was available back then.


Anisotropic Explosion: Elliptic Flow

relativistic hydrodynamics

@ 1~ 10 fm scale.

This response is very sensitive to fluid dissipation

from STAR


QGP: Nearly Perfect Quantum Liquid

QGP is a quantum fluid:

s ⇠ n

⌘/s ⇠ pT ⇠ / dB

It has nearly perfect fluidity:

less dissipative than known substance;

very close to conjectured lower bound.

[A recent ravel: cold atomic gas with infinite scattering length]


Vorticity & Magnetic Field


Fascinating New Frontiers

B ~



QGP fluid in extremely strong vorticity and magnetic fields


Rotating Quark-Gluon Plasma Ly = Abp


2 ⇠ 104⇠5~

ˆ z ˆ

x Pz = Aps


Pz = +Ap s 2

ˆ z ˆ


QGP’s way of accommodating this angular momentum


Quantifying Fluid Rotation


Heavy ion collisions:

@ ⇠ fm 1

! ⇠ 1022 s 1

v ⇠ 0.1 c


The averaged vorticity strongly increases toward low beam energy!

Jiang, Lin, JL, PRC2016; Deng & Huang, PRC2016;

Xia, Li, Wang, et al, PRC; Shi, Li, JL, PLB2018; …

Rotating Quark-Gluon Plasma


The angular momentum together with large (+Ze) nuclear charge

—> strong magnetic field!

Strong Electromagnetic Fields


Strong Electromagnetic Fields

Strongest B field (and strong E field as well) naturally arises!

[Kharzeev,McLerran,Warringa;Skokov,et al; Bzdak-Skokov;

Deng-Huang; Skokov-McLerran; Tuchin; ...]

“Out-of-plane” orientation (approximately) [Bloczynski-Huang-Zhang-Liao]


R2A ⇠ 3m2


Quantitative simulations confirm the existence of such extreme fields!

Strong Electromagnetic Fields

[STAR measurements of dielectron directly from such fields, PRL2018]

Huang, Liao, et al PLB2012


Spin & Rotational Polarization


Spin-Fluid Coupling

How does a many-body system cope with a sizable angular momentum?

Orbital motion (vorticity);

Spin alignment (polarization).

Fluid vorticity Macroscopic

Individual spin

Microscopic, quantum



Spin & Rotational Polarization

Dirac Lagrangian in rotating frame:

Under slow rotation:


polarization effect!


Rotational Polarization


polarization effect!

For thermally produced particles:

“equal-partition” of angular momentum



dN / e

!~T· ~J


“Fluid Spintronics”

From Vorticity to Spin Polarization

Viscous fluid flow

—> vorticity

—> spin polarization


Fluid Spintronics in the Subatomic Swirls

STAR Collaboration, Nature 2017


Fluid Spintronics in the Subatomic Swirls

STAR Collaboration, Nature 2017

! ⇡ (9 ± 1) ⇥ 1021s 1

The most vortical fluid!

Low energy

High energy

Jiang, Lin, JL, PRC2016


Rotational Suppression of Fermion Pairing

[Yin Jiang, JL, PRL2016]

[Rotational Inhabitation: Chen, Fukushima, Huang, Mameda, PRD2016]

Let us consider pairing phenomenon in fermion systems.

There are many examples:

superconductivity, superfluidity, chiral condensate, diquark, … We consider scalar pairing state, with J=0.

S = ~s~ 1 + ~s2 J = ~~ L + ~S

Rotation tends to polarize ALL

angular momentum, both L and S, thus suppressing scalar pairing.






Chiral Magnetic Effect in the Subatomic Chiral Matter


Exciting Progress: See Recent Reviews

Prog. Part. Nucl. Phys. 88, 1 (2016)[arXiv:1511.04050 [hep-ph]].

J. Liao, Pramana 84, no. 5, 901 (2015)  [arXiv:1401.2500 [hep-ph]].

X.G. Huang, ROPP2016; Hattori, Huang, 2017.


Chiral Anomaly

* C_A is universal anomaly coefficient

* Anomaly is intrinsically QUANTUM effect Chiral anomaly is a fundamental aspect of QFT with chiral fermions.



Broken at QM level:

Classical symmetry:

[e.g. pi0—> 2 gamma]


Chiral Restoration in QGP

* Spontaneously broken chiral symmetry in the vacuum is a fundamental property of QCD.

* A chirally symmetric quark-gluon plasma at high temperature is also a fundamental property of QCD!

Can we see direct experimental evidence for that?


Chiral Restoration via Chiral Anomaly

J5µ = JRµ JLµ





= 2iM ¯




~E · ~B

Low T

Strong spon. breaking

High T

Quantum Anomaly

Look for pure quantum anomaly effect in hot QGP with chiral symmetry restoration!


The Chiral Magnetic Effect (CME)

J = ~ Q 2

2⇡ 2 µ 5 B ~

Chirality & Anomaly & Topology

Magnetic Field Electric


Q.M. Transport


Intuitive Picture of CME

Intuitive understanding of CME:

Magnetic polarization —>

correlation between micro.


Chiral imbalance —>

correlation between directions of SPIN & MOMENTUM

Transport current along magnetic field

J =~ Q2

2⇡2 µ5 B~


From Micro. Laws To Macro. Phenomena

Micro. Laws:



Conservation laws;


Macro. Phenomena:



Fluid Dynamics;


Quantum Field Theory


Theory Fluid


Weakly Interacting

Strongly Interacting


i..e ANOMALY?!

— classical symmetry that is broken in quantum theory


CME = Macroscopic Chiral Anomaly

Anomaly -->

Chirality -->

* This is a non-dissipative current!

* Indeed the chiral magnetic conductivity is P-odd but T-even!

(In contrast the Ohmic conductivity is T-odd and dissipative.) CME is a quantum/anomalous transport current

as macroscopic manifestation of microscopic quantum anomaly.


Fluid Dynamics That Knows Left & Right

[Son, Surowka, 2009;…]

conservation law:

constituent relation:


Microscopic quantum anomaly emerges as macroscopic anomalous hydrodynamic currents!

It would be remarkable to actually “see” this new hydrodynamics at work in real world materials!


Looking for CME in Heavy Ion Collisions

The quark-gluon plasma is a subatomic CHIRAL MATTER.

In-Plane Out-of-Plane

Can we observe CME in heavy ion collisions??

1) (nearly) chiral quarks 2) chirality imbalance 3) strong magnetic field


From Gluon Topology to Quark Chirality

QCD anomaly: gluon topology —> chirality imbalance


From CME Current to Charge Separation

[Kharzeev 2004; Kharzeev, McLerran, Warringa,2008;…]

strong radial blast:

position —> momentum

+ +

- -

Very difficult measurement:

* Zero average, only nonzero variance;

* Correlation measurement with significant backgrounds;

* Signal likely small


Latest Exp. Search Status

[From Z. Ye, STAR Summary Talk @ QM2018]

ALICE @ LHC 2.76TeV: signal level possibly about 8~10%

(upper limit ~30%)

CMS @ LHC 5.02TeV: signal level no more than 7%

The trend with beam energy seems in line with expectation!

STAR @ RHIC 200GeV: “

naive” statistical interpretation: ( 8.5 +/- 1.2 ) %




Badly needed:

Quantitative predictions for CME signal in heavy ion



Anomalous Viscous Fluid Dynamics (AVFD)


Anomalous-Viscous Fluid Dynamics


The AVFD Framework

arXiv:1611.04586 arXiv:1711.02496 We now have a versatile tool to

quantitatively understand and answer many important questions about CME in heavy ion collisions!


The AVFD Framework

[We now also have MUSIC-AVFD!]


The AVFD At Work

[arXiv:1611.04586; arXiv:1711.02496]

Zero B Field Nonzero B Field


The AVFD At Work

[arXiv:1611.04586; arXiv:1711.02496]

Left-handed Right-handed


The Charge Separation from AVFD


AVFD Predictions v.s Experimental Data

Excellent agreement!

Shi, Jiang, JL, et al: arXiv:1611.04586 [CPC];

arXiv:1711.02496 [Annals of Physics]


Chiral Magnetic Wave (CMW)

CMW: gapless collective excitation in chiral fluid

—> charge quadrupole of QGP —> elliptic flow splitting [Burnier, Kharzeev, JL, Yee, PRL2011;

& arXiv: 1208.2537]

[STAR, PRL2015]

charge quadrupole due to CMW transport


[Also seen by ALICE@LHC]


There Are Electric Fields Too!

Chiral matter in strong electric field:

Chiral Electric Separation Effect (CESE) [Huang, JL, PRL2013; Jiang, Huang, Liao, PRD2014]

QED plasma QCD plasma


Summary & Outlook


Summary: the Subatomic Swirls

Subatomic swirls as the most vortical fluid with the strongest B field

Quark-Gluon Plasma:

A Subatomic Chiral Fluid

The hottest material

The new, 5th state of


The oldest state of matter:

early cosmos

The most perfect fluid

Spin Polarization





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