Abstract
The quantum chromodynamics (QCD) Kondo effect is a quantum phenomenon in which heavy quarks ($c$, $b$) exist as impurity particles in quark matter composed of light quarks ($u$, $d$, $s$) at extremely high density. This is analogous to the famous Kondo effect in condensed matter physics. In the present paper, we show theoretically the existence of the "QCD Kondo excitons", i.e., the bound states of light quarks and heavy quarks, as the lowest-excitation modes above the ground state of the quark matter governed by the QCD Kondo effect. These are neutral for color and electric charges, similarly to the Kondo excitons in condensed matter, and they are new type of quasiparticles absent in the normal phase of quark matter. The QCD Kondo excitons have various masses and quantum numbers, i.e., flavors and spin parities (scalar, pseudoscalar, vector, and axialvector). The QCD Kondo excitons lead to the emergence of the neutral currents in transport phenomena, which are measurable in lattice QCD simulations. The study of the QCD Kondo excitons will provide us with understanding of new universal properties shared by quark matter and condensed matter.
Highlights
The Kondo effect is caused by a strong coupling between an itinerant electron and a spin impurity in metal, which leads to the enhancement of the electric resistance in the low-temperature region, and it still provides us with universal problems in various systems with a non-Abelian interaction like spin exchange [1]
We show theoretically the existence of the “quantum chromodynamics (QCD) Kondo excitons,” i.e., the bound states of light quarks and heavy quarks, as the lowest-excitation modes above the ground state of the quark matter governed by the QCD Kondo effect
We have shown the properties of the QCD Kondo excitons as the excited states in the QCD Kondo insulator (KI), and that they can induce neutral currents for color and/or electric charge
Summary
The Kondo effect is caused by a strong coupling between an itinerant electron and a spin impurity in metal, which leads to the enhancement of the electric resistance in the low-temperature region, and it still provides us with universal problems in various systems with a non-Abelian interaction like spin exchange [1] (see Refs. [2,3,4,5]). The gluon exchange between a light quark and a heavy quark provides the non-Abelian interaction with the color SU(Nc) symmetry, where Nc is the number of colors This is called the QCD Kondo effect [43,44]. We study the mass spectrum and the energy-momentum dispersion relations of the QCD Kondo excitons, and show that there exist various types with different quantum numbers (JP: the total spin J and parity P). Ki ≡ ki/k (k ≡ |k|) is a unit vector along the direction of the (residual) momentum With this ansatz, we find that the light quark for a = 1 and the heavy quark are superposed to form the Bogoliubov quasiparticle, and that the energy-momentum dispersions are. The detailed computations to derive the dispersion relations for the Bogoliubov quasiparticle and to search for the ground state are provided in Appendix A
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