Baryon chemical potential and in-medium properties of BPS skyrmions

Abstract

We continue the investigation of thermodynamical properties of the BPS Skyrme model. In particular, we analytically compute the baryon chemical potential both in the full field theory and in a mean-field approximation. In the full field theory case, we find that the baryon chemical potential is always exactly proportional to the baryon density, for arbitrary solutions. We further find that, in the mean-field approximation, the BPS Skyrme model approaches the Walecka model in the limit of high density - their thermodynamical functions as well as the equation of state agree in this limit. This fact allows to read off some properties of the $\omega$-meson from the BPS Skyrme action, even though the latter model is entirely based on the (pionic) $SU(2)$ Skyrme field. On the other hand, at low densities, at the order of the usual nuclear matter density, the equations of state of the two models are no longer universal, such that a comparison depends on some model details. Still, also the BPS Skyrme model gives rise to nuclear saturation in this regime, leading, in fact, to an exact balance between repulsive and attractive forces. The perfect fluid aspects of the BPS Skyrme model, which, together with its BPS properties, form the base of our results, are shown to be in close formal analogy with the Eulerian formulation of relativistic fluid dynamics. Within this analogy, the BPS Skyrme model, in general, corresponds to a non-barotropic perfect fluid.

arXiv commentLatex, 28 pages, 3 figures

References in corpus (66)

• Low energy hadron physics in holographic QCD
• The phase diagram of dense QCD
• Recent Progress in Quantum Hadrodynamics
• Action functionals for relativistic perfect fluids
• Null energy condition and superluminal propagation
• Rational Maps, Monopoles and Skyrmions
• Effective field theory for hydrodynamics: thermodynamics, and the derivative expansion
• Baryons as Chiral Solitons in the Nambu--Jona-Lasinio Model
• A Skyrme-type proposal for baryonic matter
• Cold Nuclear Matter In Holographic QCD
• Perfect Fluid Theory and its Extensions
• Generalized Global Defect Solutions
• Skyrmions, instantons and holography
• A BPS Skyrme model and baryons at large Nc
• First-order framework and generalized global defect solutions
• Dense matter in compact stars - A pedagogical introduction
• Skyrmions with low binding energies
• Skyrmions and the alpha-particle model of nuclei
• Light Nuclei of Even Mass Number in the Skyrme Model
• Skyrmions in a truncated BPS theory
• Skyrmions with massive pions
• Skyrmions and the pion mass
• Light Nuclei as Quantized Skyrmions
• A Unified Approach to High Density: Pion Fluctuations in Skyrmion Matter
• Skyrmions up to Baryon Number 108
• BPS Skyrmions as neutron stars
• Phase Transition and Anisotropic Deformations of Neutron Star Matter
• Interplay between ω-Nucleon Interaction and Nucleon Mass in Dense Baryonic Matter
• Incarnations of Skyrmions
• Dense Baryonic Matter in Hidden Local Symmetry Approach: Half-Skyrmions and Nucleon Mass
• Nuclei as near BPS-Skyrmions
• Multi-Skyrmion Solutions for the 6th order Skyrme Model
• Half-Skyrmions and the Equation of State for Compact-Star Matter
• Near-BPS Skyrmions: Non-shell configurations and Coulomb effects
• In-medium modified energy-momentum tensor form factors of the nucleon within the framework of a $\pi$-$\rho$-$\omega$ soliton model
• Nuclear binding energies from a BPS Skyrme model
• Effective perfect fluids in cosmology
• Skyrmions with vector mesons in the hidden local symmetry approach
• Atiyah-Manton Approach to Skyrmion Matter
• Thermodynamics of the BPS Skyrme model
• Hidden Local Symmetry and Infinite Tower of Vector Mesons for Baryons
• Mass degeneracy of the heavy-light mesons with chiral partner structure in the half-skyrmion phase
• Fractional Skyrmions and their molecules
• Classically isospinning Skyrmion solutions
• Near-BPS Skyrmions: Constant baryon density
• Kaons in Dense Half-Skyrmion Matter
• Baryonic sphere: a spherical domain wall carrying baryon number
• Baryonic torii: Toroidal baryons in a generalized Skyrme model
• Near BPS Skyrmions and Restricted Harmonic Maps
• Nucleon-antinucleon Interaction from the Modified Skyrme Model
• Magnetothermodynamics of BPS baby skyrmions
• Neutron-proton mass difference in isospin asymmetric nuclear matter
• Baby Skyrmions stabilized by vector mesons
• Spherically symmetric solutions of the 6th order SU(N) Skyrme models
• Skyrme model and Isospin Chemical Potential
• Binding energy per nucleon and hadron properties in nuclear matter
• Skyrmions in the presence of isospin chemical potential
• Solitons on tori and soliton crystals
• D-brane solitons in various dimensions
• The half-skyrmion phase in a chiral-quark model
• Skyrmions, Hadrons and isospin chemical potential
• Negative Baryon density and the Folding structure of the B=3 Skyrmion
• On Skyrmion semiclassical quantization in the presence of an isospin chemical potential
• Skyrmions, half-skyrmions and nucleon mass in dense baryonic matter
• Density versus chemical potential in holographic field theories
• Cold Compressed Baryonic Matter with Hidden Local Symmetry and Holography

Cited by in corpus (17)

• Skyrme models and nuclear matter equation of state
• Hairy black holes in the general Skyrme model
• A new consistent Neutron Star Equation of State from a Generalized Skyrme model
• The volume of a soliton
• Cosmological Einstein-Skyrme solutions with non-vanishing topological charge
• Skyrme-like models and supersymmetry in 3+1 dimensions
• Skyrmions confined as beads on a vortex ring
• The BPS sectors of the Skyrme model and their non-BPS extensions
• Neutron stars within the Skyrme model
• Gauged BPS baby Skyrmions with quantised magnetic flux
• Bogomolny equation for the BPS Skyrme model from the strong necessary conditions
• Generalized skyrmion crystals with applications to neutron stars
• The volume of a vortex and the Bradlow bound
• Fluidity of the system produced in relativistic pp and heavy-ion collisions: Hadron resonance gas model approach
• Meson's Correlation Functions in a Nuclear Medium
• Compressibility of dense nuclear matter in the $\rho$-meson variant of the Skyrme model
• Characteristic analysis for integrable soliton models on two-dimensional target spaces