Instanton Effects in QCD at High Baryon Density

Abstract

We study instanton effects in QCD at very high baryon density. In this regime instantons are suppressed by a large power of $({\Lambda }_{QCD}/\mu )$, where ${\Lambda }_{QCD}$ is the QCD scale parameter and $\mu$ is the baryon chemical potential. Instantons are nevertheless important because they contribute to several physical observables that vanish to all orders in perturbative QCD. We study, in particular, the chiral condensate and its contribution $m_{GB}^2\sim m<\bar{\psi }\psi >$ to the masses of Goldstone bosons in the CFL phase of QCD with $N_f=3$ flavors. We find that at densities $\rho \sim (5-10){\rho }_0$, where ${\rho }_0$ is the density of nuclear matter, the result is dominated by large instantons and subject to considerable uncertainties. We suggest that these uncertainties can be addressed using lattice calculations of the instanton density and the pseudoscalar diquark mass in QCD with two colors. We study the topological susceptibility and Witten-Veneziano type mass relations in both $N_c=2$ and $N_c=3$ QCD.

27 pages, 8 figures, minor revisions

References in corpus (7)

• The Minimal CFL-Nuclear Interface
• High Density Quark Matter under Stress
• Two-colour QCD at non-zero quark-number density
• Novel phases and transitions in Color Flavor Locked matter
• How the quark self-energy affects the color-superconducting gap
• Mass Terms in Effective Theories of High Density Quark Matter
• Instanton interactions in dense-matter QCD

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• The NJL model of dense three-flavor matter with axial anomaly: the low temperature critical point and BEC-BCS diquark crossover
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• Two-color quark matter: U(1)_A restoration, superfluidity, and quarkyonic phase
• Meson Supercurrent State in High Density QCD
• Heating (Gapless) Color-Flavor Locked Quark Matter
• Singular values of the Dirac operator in dense QCD-like theories
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• Melting Pattern of Diquark Condensates in Quark Matter
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• Bulk viscosity due to kaons in color-flavor-locked quark matter
• Chiral random matrix theory for two-color QCD at high density
• The QCD Axion at Finite Density
• Bulk viscosity in a cold CFL superfluid
• Hadron Spectrum in a Two-Colour Baryon-Rich Medium
• Viscous damping of r-mode oscillations in compact stars with quark matter
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• Kaon Condensation in a Nambu--Jona-Lasinio (NJL) Model at High Density
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• Meson current in the CFL phase
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• The Color-Superconducting {'}t Hooft Interaction
• The Myriad Uses of Instantons
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• Confinement-Deconfinement Phase Transition at Nonzero Chemical Potential
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• Effective Theory of the Color-Flavor-Locked Phase
• Phases of circle-compactified QCD with adjoint fermions at finite density
• Effective Theories of Dense and Very Dense Matter
• Bose-Einstein condensation in strong-coupling quark color superconductor near flavor SU(3) limit
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• Pseudoscalar bosonic excitations in the color-flavor locked phase at moderate densities
• Vortons in dense quark matter
• Relativistic Cooper pairing in the microscopic limit of chiral random matrix theory
• Phase transition patterns for coupled complex scalar fields at finite temperature and density
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• Chiral random matrix theory for colorful quark-antiquark condensates
• Topological Susceptibility in the Superconductive Phases of Quantum Chromodynamics: a Dyson-Schwinger Perspective
• Instanton fermionic zero mode at finite temperature and chemical potential
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• Kink properties in Lorentz-violating scalar field theory
• High density effective theory results for two and three massive flavors color-suoerconductivity
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• Chromomagnetic stability of the CFL phase with a meson current