QCD at a Finite isospin density: From the pion to quark-antiquark condensation

QCD at a finite isospin chemical potential μ _I is studied. This theory has no fermion-sign problem and can be simulated on a lattice by using present-day techniques. We solve this theory analytically in two limits: low μ _I, where chiral perturbation theory is applicable, and asymptotically high μ _I, where perturbative QCD is at work. At a low isospin density, the ground state is a superfluid pion condensate. At a very high density, it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum numbers as the pions. Motivated by this observation, we put forward a conjecture that the transition from hadron to quark matter is smooth. The conjecture passes several nontrivial tests. Our results imply a nontrivial phase diagram in the space of the temperature and chemical potentials of isospin and baryon number. At asymptotically large values of μ _I and small values of the baryon chemical potential, the ground state is in a phase similar to the Fulde-Ferrell-Larkin-Ovchinnikov phase. It is characterized by a spatially modulated superfluid order parameter 〈ūγ ₅ d〉 and may be the asymptotic limit of the inhomogeneous pion-condensation phase advocated by Migdal and others.     

Diquark condensate and quark interaction with an instanton liquid

The interaction of light quarks with an instanton liquid is considered at nonzero density of quark/baryon matter in a phase where the diquark condensate is nonzero. It is shown that the inclusion of the relevant perturbation of the instanton liquid leads to an increase in the quark chemical potential μ_c. This in turn induces a considerable growth of the threshold quark-matter density at which one expects the emergence of color superconductivity.     

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 0 and μI 0 in the phase diagram, and different values for the charged pion mass(or decay constant) and neutral pion mass(or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.     

Emergence of a nonuniform pion condensate in the (1 + 1)-dimensional Nambu-Jona-Lasinio model

The (1 + 1)-dimensional Nambu-Jona-Lasinio model describing the system of two-flavor quarks is studied in the limit of a large number of colors in the presence of a baryon chemical potential µ and an isospin chemical potential µ _I . The possible formation of a nonuniform pion condensate in dense quark matter is considered for the cases of both the massive and the massless model.     

On the chiral phase transition in hadronic matter

A qualitative analysis of the chiral phase transition in QCD with two massless quarks and nonzero baryon density is performed. It is assumed that, at zero baryonic density, ρ=0, the temperature phase transition is of the second order. Due to a specific power dependence of baryon masses on the chiral condensate, the phase transition becomes of the first order at the temperature T=T_ph(ρ) for ρ>0. At temperatures T_cont(ρ)> _T>_Tph(ρ), there is a mixed phase consisting of the quark phase (stable) and the hadron phase (unstable). At the temperature T=T_cont(ρ), the system experiences a continuous transition to the pure chirally symmetric phase.     

Screening of instantons in the quark gas

The grand partition function of quark matter is developed about an arbitrary classical gauge field configuration in a systematic weak coupling expansion. In the presence of a finite density massless quark gas the instanton induced effective quark interaction is modified by a factor exp[?2N_F(ω?)²], i.e. the baryon number chemical potential μ acts as an intrinsic infrared cutoff on the instanton scale size ?. The equation of state of the quark matter is also briefly discussed.     

A consistent formulation of the excluded volume effect in hadron gas at high densities

Thermodynamics of a gas of nucleons and antinucleons at nonzero temperatureT and nonzero chemical potential μ is formulated by taking into account the nuclear repulsive force as an excluded volume effect. A thermodynamical potential Ω(T, μ, V) is constructed by replacing the true volumeV of the system with the effective volume in a formula which is valid for a free pointlike hadron gas. The general thermodynamical relationV ^?1?Ω/?μ=?n (n is the net baryon number density) yields a differential equation forn. The equation is solved in a compact integral form. The behavior of the solution is examined numerically for typical ranges ofT and μ which are relevant to the hadron-quark phase transition. The numerical results show that our previous formalism of the excluded volume effect is a good approximation of the present rigorous formalism. The baryon number susceptibility ?n/?μ|_μ=0 is also calculated numerically, and is compared with the result from the QCD Monte Carlo simulation by Gottlieb et al. [5].     

Strange-quark matter within the Nambu-Jona-Lasinio model

The equation of state of baryon-rich quark matter is studied within the SU(3) Nambu-Jona-Lasinio model with flavor-mixing interaction. Possible bound states (strangelets) and chiral phase transitions in this matter are investigated at various values of the strangeness fraction r _s. Model predictions are very sensitive to the ratio of the vector and scalar coupling constants, ξ=G _V/G _S. At ξ=0.5 and zero temperature, the binding energy takes a maximum value of about 15 MeV per baryon at r _s?0.4. Such strangelets are negatively charged and have typical lifetimes of about 10^?7s. Calculations are performed at finite temperatures as well. According to these calculations, bound states exist up to temperatures of about 15 MeV. The model predicts a first-order chiral phase transition at finite baryon densities. The parameters of this phase transition are calculated as functions of r _s.     

Molecular dynamics simulation for the baryon-quark phase transition at finite baryon density

We study the baryon-quark phase transition in the molecular dynamics (MD) of the quark degrees of freedom at finite baryon density. The baryon state at low baryon density, and the deconfined quark state at high baryon density are reproduced. We investigate the equations of state of matters with different u-d-s compositions. It is found that the baryon-quark transition is sensitive to the quark width.     

Stars of strange matter?

We investigate suggestions that quark matter with strangeness per baryon of order unity may be stable. We model this matter at nuclear matter densities as a gas of close packed Λ-particles. From the known mass of the Λ-particle we obtain an estimate of the energy and chemical potential of strange matter at nuclear densities. These are sufficiently high to preclude any phase transition from neutron matter to strange matter in the region near nucleon matter density. Including effects from gluon exchange phenomenologically, we investigate higher densities, consistently making approximations which underestimate the density of transition. In this way we find a transition density ρ_tr≳7ρ₀, where ρ₀ is nuclear matter density is not far from the maximum density in the center of the most massive neutron stars that can be constructed. Since we have underestimated ρ_tr and still find it to be ∼7ρ₀, we do not believe that the transition from neutron to quark matter is likely in neutron stars. Moreover, measured masses of observed neutron stars are ≅1.4 M_⊙, where M_⊙ is the solar mass. For such masses, the central (maximum) density is ρ_c<5ρ₀. Transition to quark matter is certainly excluded for these densities.     

A note on the massive quark matter phase

Using an equation of state which is based on a many-body treatment of a constituent quark model with confinement interaction, the phase transition to a massive quark phase is studied. It is found that in the case of bag constantsB ^1/4>200 MeV and baryon number density of about 5ρ₀ a phase of massive deconfined quarks may become stable.     

Spectra of charmed and bottom baryons with hyperfine interaction

Up to now,the excited charmed and bottom baryon states have still not been well studied experimentally or theoretically.In this paper,we predict the mass of ?*b,the only L=0 baryon state which has not been observed,to be 6069.2 Me V.The spectra of charmed and bottom baryons with the orbital angular momentum L = 1 are studied in two popular constituent quark models,the Goldstone boson exchange(GBE) model and the one gluon exchange(OGE) hyperfine interaction model.Inserting the latest experimental data from the "Review of Particle Physics",we find that in the GBE model,there exist some multiplets(Σc(b),Ξ c(b)and ?c(b)) in which the total spin of the three quarks in their lowest energy states is 3/2,but in the OGE model there is no such phenomenon.This is the most important difference between the GBE and OGE models.These results can be tested in the near future.We suggest more efforts to study the excited charmed and bottom baryons both theoretically and experimentally,not only for the abundance of baryon spectra,but also for determining which hyperfine interaction model best describes nature.     

The B=2 sector of the Skyrme model in S3(L)

We consider baryon-number-two solutions to the Skyrme effective lagrangian on the surface of a hypersphere, S₃(L). At high densities we find solutions with “radially” uniform energy and baryon densities analogous to solutions previously found for the baryon-number-one problem on S₃(L) and for the dense matter problem in R₃. The density for this phase transition is essentially the same in the three cases. An interpretation of this phase transition as a simulation of “deconfinement” is offered.     

Bulk viscosity of quark-gluon matter in a magnetic field

On the basis of low-energy QCD theorems, the bulk viscosity ζ(T, µ, H) is expressed in terms of basic thermodynamic quantities that characterizes quark-gluon matter at finite temperature and a finite baryon density in a magnetic field. Various limiting cases are considered.     

The thermodynamic properties of weakly interacting quark-gluon plasma via the one-gluon exchange interaction

The thermodynamic properties of the quark-gluon plasma (QGP), as well as its phase diagram, are calculated as a function of baryon density (chemical potential) and temperature. The QGP is assumed to be composed of the light quarks only, i.e., the up and down quarks, which interact weakly, and the gluons which are treated as they are free. The interaction between quarks is considered in the framework of the one gluon exchange model which is obtained from the Fermi liquid picture. The bag model is used, with fixed bag pressure (B)for the nonperturbative part, and the quantum chromodynamics (QCD) coupling is assumed to be constant, i.e., with no dependence on the temperature or the baryon density. The effect of weakly interacting quarks on the QGP phase diagram are shown and discussed. It is demonstrated that the one-gluon exchange interaction for the massless quarks has considerable effect on the QGP phase diagram and it causes the system to reach to the confined phase at the smaller baryon densities and temperatures. The pressure of excluded volume hadron gas model is also used to find the transition phase diagram. Our results depend on the values of bag pressure and the QCD coupling constant. The latter does not have a dramatic effect on our calculations. Finally, we compare our results with the thermodynamic properties of strange quark matter and the lattice QCD prediction for the QGP transition critical temperature.     

Neutron star matter in a modified PNJL model

We discuss a three-flavor Nambu-Jona-Lasinio model for the quark matter equation of state with scalar diquark interaction, isoscalar vector interaction and Kobayashi-Maskawa-??t Hooft interaction. We adopt a phenomenological scheme to include possible effects of a change in the gluon pressure at finite baryon density by including a parametric dependence of the Polyakov-loop potential on the chemical potential. We discuss the results for the mass-radius relationships for hybrid neutron stars constructed on the basis of our model EoS in the context of the constraint from the recently measured mass of (1.97 ± 0.04) M _?? for the pulsar PSR J1614-2230.     

No-go theorem for critical phenomena in large-N(c) QCD

We derive some rigorous results on the chiral phase transition in QCD and QCD-like theories with a large number of colors, N(c), based on the QCD inequalities and the large-N(c) orbifold equivalence. We show that critical phenomena and associated soft modes are forbidden in flavor-symmetric QCD at finite temperature T and finite but not so large quark chemical potential μ for any nonzero quark mass. In particular, the critical point in QCD at a finite baryon chemical potential μ(B)=N(c)μ is ruled out, if the coordinate (T, μ) is outside the pion condensed phase in the corresponding phase diagram of QCD at a finite isospin chemical potential μ(I)=2μ.     

Chiral quarks,chiral limit,nonanalytic terms and baryon spectroscopy

It is shown that the principal pattern in baryon spectroscopy, which is associated with the flavor-spin hyperfine interactions, is due to the spontaneous breaking of chiral symmetry in QCD and persists in the chiral limit. All corrections, which are associated with a finite quark (Goldstone boson) mass are suppressed by the factor (μ/Λ_χ)² and higher.     

Fabrication of thin-film transistor based on self-assembled single-walled carbon nanotube network

Thin-film transistor based on controllable electrostatic self-assembled monolayer single-wall carbon nanotubes (SWNTs) network has been fabricated by varying the density of nanotubes on the silicon substrate. The densities of SWNTs network have been investigated as a function of concentration and assembly time. It has been observed that the density of SWNTs network increases from 0.6 µm⁻² to 2.1 µm⁻², as the average on-state current (I_on) increases from 0.5 mA to 1.47 mA. The device has a current on/off ratio (I_on/I_off) of 1.3×10⁴ when I_on reaches to 1.34 mA.     

On the possibility of P-violation at finite baryon-number densities

We show how the introduction of a finite baryon density may trigger spontaneous parity violation in the hadronic phase of QCD. Since this involves strong interaction physics in an intermediate energy range we approximate QCD by a σ model that retains the two lowest scalar and pseudoscalar multiplets. We propose a novel mechanism based on interplay between lightest and heavy meson states which cannot be realized solely in the Goldstone boson (pion) sector and thereby is unrelated to the one advocated by Migdal some time ago. Our approach is relevant for dense matter in an intermediate regime of few nuclear densities where quark percolation does not yet play a significant role.