Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuark and pion condensates at finite isospin density in chiral perturbation theory
90
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper, we consider two-flavor QCD at zero temperature and finite isospin chemical potential ($mu_I$) using a model-independent analysis within chiral perturbation theory at next-to-leading order. We calculate the effective potential, the chiral condensate and the pion condensate in the pion-condensed phase at both zero and nonzero pionic source. We compare our finite pionic source results for the chiral condensate and the pion condensate with recent (2+1)-flavor lattice QCD results and find that they are in excellent agreement.
rate research
Read More
We reconsider the problem of calculating the vacuum free energy (density) of QCD and the shift of the quark condensates in the presence of a uniform background magnetic field using two-and-three-flavor chiral perturbation theory ($chi$PT). Using the free energy, we calculate the degenerate, light quark condensates in the two-flavor case and the up, down and strange quark condensates in the three-flavor case. We also use the vacuum free energy to calculate the (renormalized) magnetization of the QCD vacuum, which shows that it is paramagnetic. We find that the three-flavor light-quark condensates and (renormalized) magnetization are improvements on the two-flavor results. We also find that the average light quark condensate is in agreement with the lattice up to $eB=0.2 {rm GeV^{2}}$, and the (renormalized) magnetization is in agreement up to $eB=0.3 {rm GeV^{2}}$, while three-flavor $chi$PT, which gives a non-zero shift in the difference between the light quark condensates unlike two-flavor $chi$PT, underestimates the difference compared to lattice QCD.
The confinement-deconfinement transition is discussed from topological viewpoints. The topological change of the system is achieved by introducing the dimensionless imaginary chemical potential ($theta$). Then, the non-trivial free-energy degeneracy becomes the signal of the deconfinement transition and it can be visualized by using the map of the thermodynamic quantities to the circle $S^1$ along $theta$. To understand this topological deconfinement transition at finite real quark chemical potential ($mu_mathrm{R}$), we consider the isospin chemical potential ($mu_mathrm{iso}$) in the effective model of QCD. The phase diagram at finite $mu_mathrm{iso}$ is identical with that at finite $mu_mathrm{R}$ outside of the pion-condensed phase at least in the large-$N_mathrm{c}$ limit via the well-known orbifold equivalence. In the present effective model, the topological deconfinement transition does not show a significant dependence on $mu_mathrm{iso}$ and then we can expect that this tendency also appears at small $mu_mathrm{R}$. Also, the chiral transition and the topological deconfinement transition seems to be weakly correlated. If we will access lattice QCD data for the temperature dependence of the quark number density at finite $mu_mathrm{iso}$ with $theta=pi/3$, our surmise can be judged.
We present two-loop results for the quark condensate in an external magnetic field within chiral perturbation theory using coordinate space techniques. At finite temperature, we explore the impact of the magnetic field on the pion-pion interaction in the quark condensate for arbitrary pion masses and derive the correct weak magnetic field expansion in the chiral limit. At zero temperature, we provide the complete two-loop representation for the vacuum energy density and the quark condensate.
We present a calculation of the $eta$-$eta$ mixing in the framework of large-$N_c$ chiral perturbation theory. A general expression for the $eta$-$eta$ mixing at next-to-next-to-leading order (NNLO) is derived, including higher-derivative terms up to fourth order in the four momentum, kinetic and mass terms. In addition, the axial-vector decay constants of the $eta$-$eta$ system are determined at NNLO. The numerical analysis of the results is performed successively at LO, NLO, and NNLO. We investigate the influence of one-loop corrections, OZI-rule-violating parameters, and $mathcal{O}(N_c p^6)$ contact terms.
We study finite isospin chiral perturbation theory ($chi$PT) in a uniform external magnetic field and find the condensation energy of magnetic vortex lattices using the method of successive approximations (originally used by Abrikosov) near the upper critical point beyond which the system is in the normal vacuum phase. The difference between standard Ginzburg-Landau (GL) theory (or equivalently the Abelian Higgs model) and $chi$PT arises due to the presence of additional momentum-dependent (derivative) interactions in $chi$PT and the presence of electromagnetically neutral pions that interact with the charged pions via strong interactions but do not couple directly to the external magnetic field. We find that while the vortex lattice structure is hexagonal similar to vortices in GL theory, the condensation energy (relative to the normal vacuum state in a uniform, external magnetic field) is smaller (larger in magnitude) due to the presence of derivative interactions. Furthermore, we establish that neutral pions do not condense in the vortex lattice near the upper critical field.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
