1. “QCD Kondo effect” KH, K. Itakura, S. Ozaki, S. Yasui,
“QCD Kondo effect: quark matter with heavy-flavor impurities”,
Phys. Rev. D 92 (2015) arXiv: [hep-ph]
“QCD Kondo effect in two-flavor superconducting phase”,
KH, X.-G. Huang, R. Pisarski, In progress.

2. + Brief Introduction to Kondo effect electron Quantum Classical hole
GTT
T (K)
Lattice vibration
Electron scatterings (classical) +
electron
hole
Quantum
Classical
Log T/TK
(quantum)
TK: Kondo Temp. (Location of the minima)

3. (1+1)-dimensional low-energy effective theory in dense systems
+ Low energy excitation along radius (1+1 D)
+ Degenerated states in the tangential plane (2D)
Enhancement of IR dynamics
cf. superconductivity and magnetic catalysis

4. QCD Kondo effect in various systems
1. Dense quark matter with heavy-quark impurities
KH, K. Itakura, S. Ozaki, S. Yasui,
“QCD Kondo effect: quark matter with heavy-flavor impurities”,
Phys. Rev. D 92 (2015) arXiv: [hep-ph]
2. In strong magnetic field with heavy-quark impurities
Cf) S. Ozaki, K. Itakura, Y. Kuramoto, “Magnetically Induced QCD Kondo Effect ”, arXiv: [hep-ph]
KH, X.-G. Huang, R. Pisarski, In progress.
3. In two-flavor superconducting phase (2SC)
without a heavy-quark impurity

5. Heavy-light scattering near Fermi surfaceQ
Large Fermi sphere q Q

6. -- Renormalizaiton of the low energy dynamics
Scattering in the NLO
-- Renormalizaiton of the low energy dynamics
Large Fermi sphere
Large Fermi sphere
Logarithmic enhancement in special
kinematic and circumstances.
 BCS, Kondo effect

7. High-Density Effective Theory (LO)
Expansion around the large Fermi momentum
The LO Fermion propagator for particle and hole excitations near the Fermi surface
(1+1)-dimensional dispersion relation
Large Fermi sphere
Interaction vertex in the LO

8. Heavy-Quark Effective Theory (LO)
HQ-momentum decomposition
HQ velocity Q
The LO HQ propagator
Dispersion relation

9. Gluon propagator in dense matter
Screening of the longitudinal gluons from HDL
 Contact-interaction limit in the low-energy dynamics.
Son, Schaefer, Wilczek, Hsu, Schwetz, Pisarski, Rischke, ……,
showed that unscreened magnetic gluons play a role in the cooper paring.

10. Logs from the longitudinal integrals

11. Color structure

12. Important ingredients for Kondo effect
1. Quantum corrections
Particle
hole
2. Log div. from the IR dynamics
3. Incomplete cancellation due to non-Abelian interactions
Particle contribution
Hole contribution

13. RG analysis for “QCD Kondo effect”Λ
Λ-dΛ
G(Λ-dΛ) = + +
G(Λ)
E = 0 Λ
Fermi energy
Landau pole (“Kondo scale”)
Effective coupling: G(Λ)
Strong coupling
RG equation
Asymptotic-free solution

14. Similarity between (1+1)-dimensional dynamics
in high-density matter and in strong magnetic field
Cf. S. Ozaki, K. Itakura, Y. Kuramoto, “Magnetically Induced QCD Kondo Effect ”, arXiv: [hep-ph]
Cf. K. Fukushima, KH, H.-U. Yee, Y. Yin,
Phys. Rev. D 93 (2016) arXiv: [hep-ph]

15. Schematic picture of the strong field limit
Fermions in 1+1 dimension
Wave function (in symmetric gauge)
Large Fermi sphere
Strong B

16. Important ingredients revisited -- In strong B fields
1. Quantum corrections (loop effects)
2. Log div. from the IR dynamics
 dimensional reduction in strong B
3. Incomplete cancellation due to non-Abelian interactions
 Color-exchange interactions
“QCD Kondo Effect”
KH, K. Itakura, S. Ozaki, S. Yasui, arXiv: [hep-ph]
“Magnetically Induced QCD Kondo Effect”
S. Ozaki, K. Itakura, Y. Kuramoto, “Magnetically Induced QCD Kondo Effect ”, arXiv: [hep-ph]

17. Possible implication for heavy-ion collisions
Initial distribution (τ = 0)
from pQCD
Thermal (τ = ∞)
Momentum distribution of HQs in log scale
Relaxation time is controlled by transport coefficients (Drag force, diffusion constant)
Deng & Huang (2012), KH, & Huang (2016)
Impact parameter

18. Perturbative computation of momentum diffusion constant
Fukushima, KH, H.-U. Yee, Y. Yin
Momentum transfer rate in LO Coulomb scatterings 2
Thermal quarks
Thermal gluons + HQ 2
Thermal quarks
Thermal gluons + HQ
c.f.) LO and NLO without B (Moore & Teaney, Caron-Huot & Moore)
Kondo effect in NLO?

19. Emergent QCD Kondo Effect in 2SC phase
-- Interaction btw gapped and ungapped excitations
Very preliminary results
KH, X.-G. Huang, R. Pisarski, In progress.

20. Gapped and ungapped quasiparticles in 2SC phase
Attraction in color 3
S-wave
Spin-0
Flavor antisymmetric

21. Debye and Meissner mass in 2SC phase
Rischke
Pure gluodynamics
Rischke, Son, Stephanov

22. Possible diagrams for the scattering between 1 and 3
Some more if one includes interactions with the condensate
by Nambu Gorkov formalism.

23. Propagator for the gapped quasiparticles and quasiholes
Rischke, Pisarski, ...
LO expansion by 1/μ

24. Strong coupling between gapped and ungapped excitationsΛ
Fermi energy
Landau pole (“Kondo scale”)
Effective coupling: G(Λ)
Strong coupling

25. Summary Prospects QCD Kondo effect may appear in various systems.
Dense quark matter with heavy-quark impurities
In strong magnetic field
Between gapped and ungapped excitations in 2SC
Prospects
- Effects on specific transport coefficients
E.g., heavy-quark transport, conductivity.
- Observable consequences in heavy-ion collisions
including FAIR, J-PARC as well as RHIC, LHC.

27. Liu, C. Greiner, and C. M. Ko
KH, X.-G. Huang

28. Heavy quark (HQ) dynamics in the QPG
Random kick (white noise)
Langevin equation
Drag force coefficient: ηD
Momentum diffusion constant: κ
- Mean-square momentum transfer / unit time
Einstein relation
Perturbative calculation by finite-T field theory (Hard Thermal Loop resummation)
LO and NLO without B are known (Moore & Teaney, Caron-Huot & Moore).

29. Perturbative computation of momentum diffusion constant
Momentum transfer rate in LO Coulomb scatterings 2
Thermal quarks
Thermal gluons + HQ 2
Thermal quarks
Thermal gluons + HQ
c.f.) LO and NLO without B (Moore & Teaney, Caron-Huot & Moore)
Effects of a strong magnetic field: eB >> T^2
+ Modification of the dispersion relation of thermal quarks
+ Modification of the gluon self-energy and the Debye screening mass

30. Longitudinal diffusion constant
Light-quark mass correction
Gluon contribution
From Moore & Teaney, Caron-Huot & Moore
Comparison between two contributions

31. Kinematics in the strong field limit
Massless limit
Linear dispersion relation
Spatial momentum transfer in the direction of B
From the chirality conservation
Static limit (or HQ limit)
Anisotropy of diffusion constant

32. Transverse diffusion constant in massless limit
Screened Coulomb scattering amplitude (squared)
Spectral density
Distribution of the scatterers

33. Implication to v2 of heavy flavors
Moore & Teaney, Caron-Huot & Moore
Gluon contribution
Magnetic anisotropy of diffusion constant
(1) does not significantly change R_AA.
(2) give rise to v2 of HQs even without v2 of medium.
 Possible to generate v2 of HQs in the early QGP stage.