Bose-Einstein condensation in dense quark matter

We consider the problem of Bose condensation of charged pions in QCD at finite isospin chemical potential μ_I using the O(4)-symmetric linear sigma model as an effective field theory for two-flavor QCD. Using the 2PI 1/N-expansion, we determine the quasiparticle masses as well as the pion and chiral condensates as a function of the temperature and isospin chemical potential in the chiral limit and at the physical point. The calculations show that there is a competition between the condensates. At T=0, Bose condensation takes place for chemical potentials larger than μ_π. In the chiral limit, the chiral condensate vanishes for any finite value of μ_I.     

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.     

Chiral Phase Transition at Finite Isospin Density in Linear Sigma Model

Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ-T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the Bose-Einstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.     

Survival of charged ρ condensation at high temperature and density

The charged vector ρ mesons in the presence of external magnetic fields at finite temperature T and chemical potential μ have been investigated in the framework of the Nambu-Jona-Lasinio model.We compute the masses of charged ρ mesons numerically as a function of the magnetic field for different values of temperature and chemical potential.The self-energy of the ρ meson contains the quark-loop contribution,i.e.the leading order contribution in 1/N_C expansion.The charged ρ meson mass decreases with the magnetic field and drops to zero at a critical magnetic field eB_c,which indicates that the charged vector meson condensation,i.e.the electromagnetic superconductor can be induced above the critical magnetic field.Surprisingly,it is found that the charged ρ condensation can even survive at high temperature and density.At zero temperature,the critical magnetic field just increases slightly with the chemical potential,which indicates that charged ρ condensation might occur inside compact stars.At zero density,in the temperature range 0.2 — 0.5 GeV,the critical magnetic field for charged ρ condensation is in the range of 0.2 — 0.6 GeV~2,which indicates that a high temperature electromagnetic superconductor might be created at LHC.     

Pion condensation of quark matter in a static Einstein universe

In the framework of an extended Nambu–Jona-Lasinio model we study pion condensation in quark matter with an asymmetric isospin composition. We treat this against the gravitational field of a static Einstein universe at finite temperature and chemical potential. This particular choice of the gravitational field configuration enables us to investigate phase transitions of the system with exact consideration of the role of this field in the formation of quark and pion condensates. Also, we point out its influence on the phase portraits. We demonstrate the effect of oscillations of the thermodynamic quantities as functions of the curvature and also refer to a certain similarity between the behavior of these quantities as functions of curvature and finite temperature. Finally, the role of quantum fluctuations for spontaneous symmetry breaking in the case of a finite volume of the universe is briefly discussed.     

Charge-constrained coherent pion states produced in nuclear matter

In a recent article, Bloss, Hone and Scalapino have used a simplified model Hamiltonian and Keldysh field theoretic methods to approximately calculate the power radiated as Cherenkov charged pions whose emission is triggered when a fast nucleon traverses nuclear matter. The model used by these authors conserves charge by flipping the isospin state of the fast nucleon alone for each charged pion emitted. Since it is the nuclear matter excited by the fast nucleon which should be largely reponsible for emitting the Cherenkov charged pions, we investigate an alternate model that allows all the disturbed nuclear matter to change its charge state when a charged pion is emitted—as an idealization, the emitting matter is assumed to have an infinite number of charge states, in contrast to the two of the fast nucleon. This modified model is shown to be exactly solvable in terms of charge-constrained coherent pion states; the power radiated as charged pions is found to be approximately twice that calculated by Bloss et al. from their model.     

QCD at finite isospin density

QCD at finite isospin chemical potential mu(I) has no fermion sign problem and can be studied on the lattice. We solve this theory analytically in two limits: at low mu(I), where chiral perturbation theory is applicable, and at asymptotically high mu(I), where perturbative QCD works. At low isospin density the ground state is a pion condensate, whereas at high density it is a Fermi liquid with Cooper pairing. The pairs carry the same quantum numbers as the pion. This leads us to conjecture that the transition from hadron to quark matter is smooth, which passes several tests. Our results imply a nontrivial phase diagram in the space of temperature and chemical potentials of isospin and baryon number.     

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.     

QCD inequalities for the nucleon mass and the free energy of baryonic matter

The positivity of the integrand of certain Euclidean space functional integrals for two flavor QCD with degenerate quark masses implies that the free energy per unit volume for QCD with a baryon chemical potential mu(B) (and zero isospin chemical potential) is greater than the free energy with an isospin chemical potential mu(I)=(2 mu(B)/N(c)) (and zero baryon chemical potential). The same result applies to QCD with any number of heavy flavors in addition to the two light flavors so long as the chemical potential is understood as applying to the light quark contributions to the baryon number. This relation implies a bound on the nucleon mass: there exists a particle X in QCD (presumably the pion) such that M(N)> or =(N(c) m(X)/2 I(X)) where m(X) is the mass of the particle and I(X) is its isospin.     

Meson screening mass in a strongly coupled pion superfluid

We calculate the meson screening mass in a pion superfluid in the framework of Nambu–Jona-Lasinio model. The minimum of the attractive quark potential is always located at the phase boundary of pion superfluid. Different from the temperature and baryon density effect, the potential at finite isospin density cannot be efficiently suppressed and the matter is always in a strongly coupled phase due to the Goldstone mode in the pion superfluid.     

Restrictions on the cluster decay multiplicity distribution in the independent cluster emission model due to crossing symmetry and isospin invariance

We discuss multiparticle production in high energy proton-proton scattering under the assumption that all produced secondaries are pions. We take into account the pion isospin but neglect the isospin of the protons. In the first part of the paper it is shown that the multiplicity distribution of the independent cluster emission model can be derived from a unitary, crossing symmetric, isospin invariant, impact parameter model. This part is a straight forward generalization of a previous work where similar results were obtained for isospin-zero mesons. In the second part of the paper we shall discuss the restrictions on the cluster decay multiplicity distribution due to crossing symmetry in the meson variables and to isospin invariance. In particular, we shall derive a non-trivial lower bound for the dispersion of the charged particles in the cluster decay multiplicity distribution.     

核物质中内介质等效手征Lagrange量和π介子质量

在核物质中从手征等效Lagrange量得到的π介子有效质量是单值的,并且与π介子场的离壳扩展无关,例如PCAC选择.同位旋对称核物质中的有效π介子质量随增加的核密度有些上升,因此有效类时π介子衰变常数和密度相关的夸克凝聚渐渐下降.另外研究了内介质Gell–Mann–Oakes–Renner关系和其它内介质同一性.最后讨论了同位旋对称、各向同性和均匀的核物质中关于介子传播的等效Lagrange量的几个限制.     

Spontaneous CP violation in the NJL model at θ = π

As is well-known, spontaneous CP-violation in the strong interaction is possible at θ = π, which is commonly referred to as Dashen's phenomenon. This phenomenon has been studied extensively using chiral Lagrangians. Here the two-flavor NJL model at θ = π is discussed. It turns out that the occurrence of spontaneous CP-violation depends on the strength of the 't Hooft determinant interaction, which describes the effect of instanton interactions. The dependence of the phase structure, and in particular of the CP-violating phase, on the quark masses, temperature, baryon and isospin chemical potential is examined in detail. The latter dependence shows a modification of the charged pion condensed phase first discussed by Son and Stephanov.     

A phenomenological approach to pion condensation

The threshold of π-condensation in isospin symmetric nuclear matter is studied with a field theoretic model which reproduces the low energy πN data. We find a critical density around normal nuclear matter density. Besides the role of the nucleon-nucleon correlations we investigate the effect of the s-wave πN interaction on- and off-mass-shell. The chiral symmetry breaking Σ-term may impede pion condensation.     

Phase structure of the linear sigma model with the standard symmetry breaking term

The linear sigma model at finite isospin chemical potential μ and temperature T is systematically studied by means of the Cornwal–Jackiw–Tomboulis (CJT) effective potential calculated in the improved Hartree–Fock (HF) approximation, where the Goldstone theorem and the thermodynamic consistency are respected. It results that in the chiral limit, for μ=0 the chiral phase transition is second order as expected from the general universality arguments, and for μ≠0 the phase diagram for the pion condensation in the (T,μ) plane exhibits a tricritical point which is crossover from first-order to second-order phase transitions. In the physical world, where the chiral symmetry is explicitly broken, the pion condensation occurs at μ=m _π , the pion mass in vacuum, and its phase diagram is basically in agreement with those found from the chiral perturbation theory. The chiral symmetry gets restored at high values of T for fixed μ and of μ for fixed T.     

A two-step model of pion induced nucleon knockout reactions

A two-step model is utilized to explain the puzzling isospin dependence of pion induced nucleon knockout reactions. The model treats the pions as strongly absorbed by nuclei. The pion is assumed to interact only once, even in the two-step mechanism. Energy transfer systematics suggest the pion interaction is with a four-nucleon cluster. If so, this helps to explain the surprisingly large pion induced α-knockout cross sections seen recently.     

Charged pion photoproduction from light nuclei

The photoproduction of 0–150-MeV charged pions from light nuclei is studied from a distorted wave impulse approximation (DWIA) approach. The final nuclear states are restricted to a finite set of isospin analogs of excited states of the target nucleus. The final state interactions of the pion with the residual nucleus are incorporated via optical potentials. The elementary photoproduction operator used is that of Blomqvist and Laget which is derived in a general reference frame. To gain insight into the predictive power of this DWIA approach, total and differential cross sections for π^± production from ⁶Li, ⁷Li, ¹⁰B, ¹²C, and ¹⁴N are calculated and compared with available data. It is found that, with a few exceptions, reasonable agreement is obtained between theory and experiment as long as the nuclear wave functions are constrained to fit other electromagnetic and weak processes and the optical potentials are constrained to fit pion-nucleus elastic scattering data. We conclude that, at this stage, using the Blomqvist-Laget operator in a DWIA calculation adequately describes the dynamics of charged pion photoproduction from complex nuclei. We illustrate how this reaction can be used to obtain information on the short range nature of the pion wave function and on nuclear wave functions. Shortcomings of and improvements on this calculation are also suggested.     

Pion production by fragmentation of weak currents in Weinberg theory

The Feynman quark parton model is used to study inclusive single-pion production by the fragmentation of the neutral and charged weak currents of Weinberg theory. The structure functions for the neutral current-induced reactions are related to those for the electromagnetic and charged weak current processes. Analogues of inclusive deep-inelastic sum rules are derived. The ratios of neutral current to charged current cross sections for semi-inclusive pion production are studied. In the approximation of neglect of “core” partons, these ratios are given in terms of average pion multiplicities in the charged current-induced reaction. We finally specialise to the quark parton distributions of McElhaney and Tuan to calculate these ratios as functions of the Weinberg angle.     

Pion and chiral density waves in a (1 + 1)-dimensional Nambu-Jona-Lasinio model

A (1 + 1)-dimensional massless Nambu-Jona-Lasinio model is investigated in the limit of a large number of colors. The model describes a system with two quark flavors if μ baryon and μ _I isospin chemical potentials occur. The question of whether spatially inhomogeneous chiral and pion condensates can form in a dense quark environment is also examined.