“QCD Kondo effect” KH, K. Itakura, S. Ozaki, S. Yasui, “QCD Kondo effect: quark matter with heavy-flavor impurities”, Phys. Rev. D 92 (2015) 065003. arXiv:1504.07619 [hep-ph] “QCD Kondo effect in two-flavor superconducting phase”, KH, X.-G. Huang, R. Pisarski, In progress.

+ 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)

(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

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) 065003. arXiv:1504.07619 [hep-ph] 2. In strong magnetic field with heavy-quark impurities Cf) S. Ozaki, K. Itakura, Y. Kuramoto, “Magnetically Induced QCD Kondo Effect ”, arXiv:1509.06966 [hep-ph] KH, X.-G. Huang, R. Pisarski, In progress. 3. In two-flavor superconducting phase (2SC) without a heavy-quark impurity

Heavy-light scattering near Fermi surface Q Large Fermi sphere q Q

-- 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

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

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

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.

Logs from the longitudinal integrals

Color structure

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

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

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:1509.06966 [hep-ph] Cf. K. Fukushima, KH, H.-U. Yee, Y. Yin, Phys. Rev. D 93 (2016) 074028. arXiv:1512.03689 [hep-ph]

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

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:1504.07619 [hep-ph] “Magnetically Induced QCD Kondo Effect” S. Ozaki, K. Itakura, Y. Kuramoto, “Magnetically Induced QCD Kondo Effect ”, arXiv:1509.06966 [hep-ph]

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

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?

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

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

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

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

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

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

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.

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

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).

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

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

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

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

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.