Jun. 23~25, 2019 Novel Transport Phenomena with Chirality, Vorticity and Magnetic field Jinfeng Liao � 1
Fascinating New Frontiers of XQCD It is all about quarks & gluons — under extreme conditions! � 2
Spin: Chirality, Vorticity and Magnetic Field SPIN SPIN UP DOWN ~ ~ ~ ! P B Magnetic Rotational Chirality Polarization Polarization Polarization Interesting interplay —> highly nontrivial phenomena! � 3
Fascinating New Frontiers of XQCD ~ B QCD matter under extremely strong ~ ! vorticity and magnetic fields! � 4
A Quantum Fluid of Spin A nearly perfect fluid (of energy-momentum) What happens to the spin DoF in the fluid??? � 5
Chirality 2019 @ Tsinghua Beijing, Apr 2019 ~100 people, 4.5 days Chirality 2015,2016,2017 @ UCLA Chirality 2018 @ Univ. Florence Chirality 2019 @ Tsinghua Univ. � 6
Exciting Progress: See Recent Reviews Prog. Part. Nucl. Phys. 88, 1 (2016)[arXiv:1511.04050 [hep-ph]]. � 7
Exciting Progress: See Recent Reviews arXiv:1906.00936 � 8
Interdisciplinary Interests Weyl semimetal (non-degenerated bands) TaAs Dirac semimetal NbAs (doubly degenerated bands) NbP TaP ZrTe 5 Na 3 Bi, Cd 3 As 2 “Fluid Spintronics” Condensed matter, cold atomic gases, neutron stars, cosmology, plasma physics, etc [Chiral Matter workshops @ RIKEN, NTU] � 9
Chirality � 10
Chirality & Chiral Symmetry L = ¯ If a Dirac fermion’s Ψ ( i γ µ ∂ µ ) Ψ mass is zero Ψ → e i αγ 5 Ψ —> axial U(1) global L → L phase symmetry! Ψ γ µ γ 5 Ψ ∂ µ J µ 5 = ¯ J µ 5 = 0 Axial current Classically conserved In this case, chirality becomes well defined. Ψ R = 1 + γ 5 Ψ Right Left 2 Handed Handed Ψ L = 1 − γ 5 (RH) (LH) Ψ 2 Ψ L γ µ ∂ µ Ψ L + ¯ Ψ R γ µ ∂ µ Ψ R L → ¯ Phase symmetries: independent U(1) for RH and LH sectors! � 11
Chiral Symmetry: Explicit Breaking If a nonzero Lagrangian mass term is added: axial symmetry is explicitly broken. m ¯ � ¯ Ψ L Ψ R + ¯ � ΨΨ = m Ψ R Ψ L RH and LH get coupled together. Axial current is no longer conserved: 5 = 2 im ¯ Ψ γ 5 Ψ ∂ µ J µ The mass controls the degree of such breaking. In QCD, for light flavors (u & d), Lagrangian mass is small: m u,d ⌧ Λ QCD QCD has chiral symmetry (to very good approximation)! � 12
The QCD Vacuum: Chiral Symmetry Breaking The missing symmetries: while the Lagrangian has (approximate) chiral symmetry, the vacuum and hadron spectrum do not have that. QCD vacuum is not empty, but a complicated, nonperturbative, emergent form of condensed matter. [It accounts for 99% of the mass of our visible matter in universe.] � 13
Chiral Symmetry Restoration * Spontaneously broken chiral symmetry in the vacuum is a fundamental property of QCD. * A chirally symmetric quark-gluon plasma at high temperature is an equally fundamental property of QCD! Could we see direct experimental evidence for that? � 14
“Little Bang” in High Energy Nuclear Collision CHIRAL FERMIONS * Quark-gluon plasma (QGP) is created in such collisions. * It is PRIMORDIALLY HOT ~ trillion degrees ~ early universe. * Is chiral symmetry restored? � 15
Chiral Symmetry: Quantum Anomaly Chiral anomaly is a fundamental aspect of QFT with chiral fermions. Classical symmetry: Broken at QM level: V A V * C_A is universal anomaly coefficient * Anomaly is intrinsically QUANTUM effect [e.g. pi0—> 2 gamma] � 16
Topologically Nontrivial Gluon Fields Twisting gluon fields around spacetime boundary Mobius strip Gluon topological structures play key role in confinement and chiral symmetry breaking. How to observe their effects experimentally? � 17
From Gluon Topology to Quark Chirality Quarks QCD anomaly: gluon topology —> chirality imbalance Net chirality <—> topo fluctuations & chiral restoration � 18
Vorticity & Polarization in Heavy Ion Collisions � 19
Rotating Quark-Gluon Plasma L y = Ab √ s ∼ 10 4 ∼ 5 ~ 2 QGP’s way of accommodating this angular momentum P z = − A √ s ˆ ˆ x x 2 ˆ ˆ z z P z = + A √ s 2 � 20
Quantifying Fluid Rotation NR UR Heavy ion collisions: v ∼ 0 . 1 c ∂ ∼ fm − 1 ω ∼ 10 22 s − 1 � 21
Nontrivial Vorticity Structures Low energy High energy The local vorticity pattern is strongly influenced by the bulk flow. The averaged vorticity reflects the global orbital angular momentum. Jiang, Lin, JL, PRC2016; Shi, Li, JL, PLB2018; … � 22
Spin-Fluid Coupling How does a many-body system cope with a sizable angular momentum? Orbital motion (vorticity); Spin alignment (polarization). ??? Fluid vorticity Individual spin Macroscopic Microscopic � 23
Spin & Rotational Polarization Dirac Lagrangian in rotating frame: Under slow rotation: Rotational [CAN BE STUDIED ON THE LATTICE: polarization effect! Yamamoto, Hirono; …] � 24
Rotational Polarization in Thermal Source Rotational polarization effect! For thermally produced particles: “equal-partition” of angular momentum ! · ~ ~ J dN ∝ e T ~ ! Expect larger signal at LOW beam energy HIC! � 25
Subatomic Swirls An exciting discovery from STAR Collaboration at RHIC: The most vortical fluid! � 26 26
Fluid Spintronics in the Subatomic Swirls STAR Collaboration, Nature 2017 ω ≈ (9 ± 1) × 10 21 s − 1 The most vortical fluid! � 27
Rotational Polarization Jiang, Lin, JL, PRC2016; Shi, Li, JL, PLB2019; Becattini, et al; Csernai, et al; Q. Wang, et al; … Existing puzzles: Splitting between hyperons & anti- hyperons; Local polarization azimuthal patterns. � 28
Hydrodynamics & Transport Theory with Spin [Talks by: H. Taya, R. Ryblewski, E. Speranza, A. Kumar, Gallegos Pazos, @ Chirality 2019] [Talk by Hongo and by Yang @ this conference ] � 29
Rotational Suppression of Fermion Pairing 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. ~ J = ~ ~ L + ~ S = ~ s 1 + ~ s 2 S Rotation tends to polarize ALL ~ angular momentum, both L and S, L thus suppressing scalar pairing. ! ~ ~ L [Yin Jiang, JL, PRL2016; Huang, Fukushima, Mameda, Chernodub, …] � 30
Chiral Phase Transition Maybe in low energy collisions: In-medium mass correction due to rotation?? � 31
Color Superconducting Pairing Maybe also for nucleon-pairing?! � 32
Isospin Matter under Rotation Spin-1 Rho condensation is favored by rotation! [Hui Zhang, Defu Hou, JL, arXiv: 1812.11787.] Large isospin density in low energy collision: Possible effect from rotation? � 33
Magnetic Field & Anomalous Transport in Heavy Ion Collisions � 34
Strong Electromagnetic Fields The angular momentum together with large (+Ze) nuclear charge —> strong magnetic field! � 35
Strong Electromagnetic Fields E, B ∼ γ Z α EM ∼ 3 m 2 R 2 π A • 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] � 36
Strong Electromagnetic Fields Huang, Liao, et al PLB2012 Quantitative simulations confirm the existence of such extreme fields! [Many interesting B-field induced effects: di-electron; polarization splitting; quarkonium v2; D meson v1; …] � 37
The Chiral Magnetic Effect (CME) Chirality & Anomaly & Topology J = Q 2 ~ 2 ⇡ 2 µ 5 ~ B Electric Magnetic Current Field Q.M. Transport [Kharzeev, Fukushima, Warringa, McLerran, …] � 38
Intuitive Picture of CME Intuitive understanding of CME: Chiral imbalance —> Magnetic polarization —> ⊗ correlation between directions of correlation between micro. SPIN & MOMENTUM SPIN & EXTERNAL FORCE Transport current along magnetic field J = Q 2 ~ 2 ⇡ 2 µ 5 ~ B � 39
CME <=> 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 macroscopic chiral anomaly — a remarkable phenomenon! � 40
From Micro. Laws To Macro. Phenomena Micro. Laws: Macro. Phenomena: Symmetry; Thermodynamics; Lagrangian; Transport; Conservation laws; Fluid Dynamics; …… …… Strongly Weakly Quantum Interacting Interacting Kinetic Fluid Field Theory Dynamics Theory WHAT ABOU the “SEMI”-SYMMETRY??? i..e ANOMALY?! — classical symmetry that is broken in quantum theory � 41
Chiral Transport Theory Usual (classical) transport equation: Chiral transport equation: [Son, Yamamoto; Stephanov, Yin; Chen, Wang, et al; Hidaka, Pu, Yang; Huang, Shi, Jiang, JL, Zhuang; …] � 42
Fluid Dynamics That Knows Left & Right [Son, Surowka; Kharzeev, Yee; Hidaka, Yang; …] It would be remarkable to actually “see” this new hydrodynamics at work in real world materials! � 43
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