Pion Condensation Research Articles

Taming the pion condensation in QCD at finite baryon density: a numerical test in a random matrix model

In the Monte Carlo study of QCD at finite baryon density based upon the phase reweighting method, the pion condensation in the phase-quenched theory and associated zero-mode prevent us from going to the low-temperature high-density region. We propose a method to circumvent them by a simple modification of the density of state method. We first argue that the standard version of the density of state method, which is invented to solve the overlapping problem, is effective only for a certain ‘good’ class of observables. We then modify it so as to solve the overlap problem for ‘bad’ observables as well. While, in the standard version of the density of state method, we usually constrain an observable we are interested in, we fix a different observable in our new method which has a sharp peak at some particular value characterizing the correct vacuum of the target theory. In the finite-density QCD, such an observable is the pion condensate. The average phase becomes vanishingly small as the value of the pion condensate becomes large, hence it is enough to consider configurations with π+ ≃ 0, where the zero mode does not appear. We demonstrate an effectiveness of our method by using a toy model (the chiral random matrix theory) which captures the properties of finite-density QCD qualitatively. We also argue how to apply our method to other theories including finite-density QCD. Although the example we study numerically is based on the phase reweighting method, the same idea can be applied to more general reweighting methods and we show how this idea can be applied to find a possible QCD critical point.

Possibility of ferromagnetic neutron matter

We study ferromagnetism at high density of neutrons in the QCD hadron phase, by using the simplest chiral effective model incorporating magnetic fields and the chiral anomaly. Under the assumption of spatial homogeneity, we calculate the energy density as a function of neutron density, with a magnetization and a neutral pion condensation a la Dautry and Neyman. We find that at a high density the energy of the ferromagnetic order is lower than that of the ordinary neutron matter, and the reduction effect is enhanced by the anomaly. Compared to the inhomogeneous phase with the alternating layer structure, our ferromagnetic phase turns out to be unfavored. However, once an axial vector meson condensation is taken into account in our simplest model, the ferromagnetic energy density is lowered significantly, which still leaves some room for a possible realization of a QCD ferromagnetic phase and ferromagnetic magnetars.

Phenomenology of high multiplicity events

Study of high multiplicity events in proton-proton (nucleus) interactions is carried out at U-70 accelerator of IHEP, Protvino. These events are extremely rare. Usually, MC codes underestimate topological cross sections in this region. Gluon dominance model has been offered to describe them. Some collective phenomena can be observed in high multiplicity events. SVD-2 Collaboration has obtained the evidence of pion condensate formation at high total multiplicity. Our future program is aimed at studying soft photon yield puzzle at U-70 and Nuclotronfacility at JINR, Dubna.

Viscosity of neutron star matter andr-modes in rotating pulsars

We study viscosity of the neutron star matter and $r$-mode instability in rotating neutron stars. Contributions to the shear and bulk viscosities from various processes are calculated with account of in-medium modifications of the nucleon-nucleon interaction. A softening of the pion mode and a possibility of the pion condensation are included. The nucleon pairing is incorporated. In the shear viscosity we include the lepton contribution calculated with account of the Landau damping in the photon exchange, the nucleon contribution described by the medium-modified one pion exchange, and other terms, such as the novel phonon contribution in the 1S$_0$ superfluid neutron phase, and the neutrino term in the neutrino opacity region. The nucleon shear viscosity depends on the density rather moderately and proves to be much less than the lepton term. Among the terms contributing to the bulk viscosity, the term from the medium modified Urca reactions possesses strongest density dependence because of the pion softening. Contributions to the bulk viscosity arising from other reactions induced by charged weak currents are included. The radiative bulk viscosity induced by charged and neutral weak currents in the region of the neutrino transparency of the star is also calculated with account for in-medium effects. The computed frequency boundary of the $r$-mode stability for the stars with the mass $\ge 1.8 M_{\odot}$ proves to be above the frequencies of all rotating young pulsars. To explain the stability of rapid rotation of old pulsars in X-ray binaries we propose a novel efficient mechanism associated with appearance of condensates of low-lying modes of bosonic excitations with finite momentum and/or with an enhancement of the inhomogeneous pion/kaon condensates in some parts of the star, if the angular velocity exceeds a critical value.

Thermal model for Pb+Pb collisions at √sNN= 2.76 TeV with explicit treatment of hadronic ground states

Various explanations of the anomalous proton to pion ratio at the LHC are discussed. The special emphasis is set on the Cracow thermal model with single freeze-out. This model allows to get a good agreement for both the mean hadron multiplicities and the spectra. Moreover, the values of the fit parameters indicate the possibility of pion Bose condensation in the most central collisions at the LHC. Therefore, a modification of the thermal framework is proposed that explicitly allows for the condensation in the ground state. The generalised model makes a link between equilibrium and non-equilibrium thermal models. It also suggests that the pion condensation may be formed in the central collisions.

On the magnetic catalysis and inverse catalysis of phase transitions in the linear sigma model

We consider the evolution of critical temperature both for the formation of a pion charged condensate as well as for the chiral transition, from the perspective of the linear sigma model, in the background of a magnetic field. We developed the discussion for the pion condensate in one loop approximation for the effective potential getting magnetic catalysis for high values of B, i.e a raising of the critical temperature with the magnetic field. For the analysis of the chiral restoration, we go beyond this approximation, by taking one loop thermo-magnetic corrections to the couplings as well as plasma screening effects for the boson's masses, expressed through the resumation of ring diagrams. Here we found the opposite behavior, i.e. inverse magnetic catalysis, i.e. a decreasing of the chiral critical temperature as function of the intensity of the magnetic field, which seems to be in agreement with recent results form the lattice community.

Equation of state in the pion condensation phase in asymmetric nuclear matter using a holographic QCD model

We study the asymmetric nuclear matter using a holographic QCD model by introducing a baryonic charge in the infrared boundary. We first show that, in the normal hadron phase, the predicted values of the symmetry energy and its slope parameter are comparable with the empirical values. We find that the phase transition from the normal phase to the pion condensation phase is delayed compared with the pure mesonic matter: the critical chemical potential is larger than the pion mass which is obtained for the pure mesonic matter. We also show that, in the pion condensation phase, the pion contribution to the isospin number density increases with the chemical potential, while the baryonic contribution is almost constant. Furthermore, the value of chiral condensation implies that the enhancement of the chiral symmetry breaking occurs in the asymmetric nuclear matter as in the pure mesonic matter. We also give a discussion on how to understand the delay in terms of the four-dimensional chiral Lagrangian including the rho and omega mesons based on the hidden local symmetry.

Magnetic structure of isospin-asymmetric QCD matter in neutron stars

We study QCD under the influence of background magnetic fields and isospin chemical potentials using lattice simulations. This setup exhibits a sign problem which is circumvented using a Taylor-expansion in the magnetic field. The ground state of the system in the pion condensation phase is found to exhibit a pronounced diamagnetic response. We elaborate on how this diamagnetism may contribute to the pressure balance in the inner core of strongly magnetized neutron stars. In addition we show that the onset of pion condensation shifts to larger chemical potentials due to the enhancement of the charged pion mass for growing magnetic fields. Finally, we sketch the magnetic structure of the QCD phase diagram in the temperature-isospin chemical potential plane.

Chaoticity parameter λ in two-pion interferometry in an expanding boson gas model

We investigate the chaoticity parameter λ in two-pion interferometry in an expanding boson gas model. The degree of Bose–Einstein condensation of identical pions, density distributions, and Hanbury–Brown–Twiss (HBT) correlation functions are calculated for expanding gas within the mean-field description with a harmonic oscillator potential. The results indicate that a source with thousands of identical pions may exhibit a degree of Bose–Einstein condensation at the temperatures encountered during the hadronic phase in relativistic heavy-ion collisions. This finite condensation may decrease the chaoticity parameter λ in two-pion interferometry measurements at low pion-pair momenta, but influence only slightly the λ value at high pion-pair momentum.

Explanation of hadron transverse-momentum spectra in heavy-ion collisions atsNN=2.76TeV within a chemical nonequilibrium statistical hadronization model

Chemical non-equilibrium version of the statistical hadronization model combined with a single-freeze-out scenario is used to analyze the transverse-momentum spectra of pions, kaons and protons produced in heavy-ion collisions at sqrt(sNN) = 2.76 TeV. With the statistical parameters found in earlier studies of hadronic ratios and two new geometric parameters determined by the absolute normalization and slopes of the spectra, we obtain a very good agreement between the data and the model predictions. In particular, the enhancement of pions observed at the very low transverse-momenta is very well reproduced. In the chemical non-equilibrium approach, this effect may be naturally interpreted as the onset of pion condensation in heavy-ion collisions. We further stress that the chemical non-equilibrium explains not only the proton yield but the proton spectra as well.

Thermal properties of supernova matter: The bulk homogeneous phase

We investigate the thermal properties of the potential model equation of state of Akmal, Pandharipande and Ravenhall. This equation of state approximates the microscopic model calculations of Akmal and Pandharipande, which feature a neutral pion condensate. We treat the bulk homogeneous phase for isospin asymmetries ranging from symmetric nuclear matter to pure neutron matter and for temperatures and densities relevant for simulations of core-collapse supernovae, proto-neutron stars, and neutron star mergers. Numerical results of the state variables are compared with those of a typical Skyrme energy density functional with similar properties at nuclear densities, but which differs substantially at supra-nuclear densities. Analytical formulas, which are applicable to non-relativistic potential models such as the equations of state we are considering, are derived for all state variables and their thermodynamic derivatives. A highlight of our work is its focus on thermal response functions in the degenerate and non-degenerate situations, which allow checks of the numerical calculations for arbitrary degeneracy. These functions are sensitive to the density dependent effective masses of neutrons and protons, which determine the thermal properties in all regimes of degeneracy. We develop the "thermal asymmetry free energy" and establish its relation to the more commonly used nuclear symmetry energy. We also explore the role of the pion condensate at supra-nuclear densities and temperatures. Tables of matter properties as functions of baryon density, composition (i.e., proton fraction) and temperature are being produced which are suitable for use in astrophysical simulations of supernovae and neutron stars.

Lattice QCD with mismatched fermi surfaces.

We study two flavor fermions with mismatched chemical potentials in quenched lattice QCD. We first consider a large isospin chemical potential, where a charged pion is condensed, and then introduce a small mismatch between the chemical potentials of the up quark and the down antiquark. We find that the homogeneous pion condensate is destroyed by the mismatch of the chemical potentials. We also find that the two-point correlation function shows spatial oscillation, which indicates an inhomogeneous ground state, although it is not massless but massive in the present simulation setup.

Temporal chiral spiral in QCD in the presence of strong magnetic fields

Vacuum properties of quantum chromodynamics in strong magnetic and finite electric fields are investigated. We show that when a uniform electric field is instantaneously applied in the parallel direction to a strong magnetic field, it induces temporal oscillation of the chiral and pion condensates. This is a temporal analog to the chiral spiral. The oscillation originates with the propagation of the collective mode, which is protected by the axial anomaly and thus nondissipative.

Enhancement of chiral symmetry breaking from the pion condensation at finite isospin chemical potential in a holographic QCD model

We study the pion condensation at finite isospin chemical potential using a holographic QCD model. By solving the equations of motion for the pion fields together with those for the iso-singlet scalar and iso-triplet vector meson fields, we show that the phase transition from the normal phase to the pion condensation phase is second order with the mean field exponent, and that the critical value of the isospin chemical potential $\mu_I$ is equal to the pion mass, consistently with the result obtained by the chiral effective Lagrangian at $O(p^2)$. For higher chemical potential, we find a deviation, which can be understood as a higher order effect in the chiral effective Lagrangian. We investigate the $\mu_I$-dependence of the chiral condensate defined by $\tilde{\sigma} \equiv \sqrt{ \langle \sigma \rangle^2 + \langle \pi^a \rangle^2 }$. We find that $\tilde{\sigma}$ is almost constant in the small $\mu_I$ region, while it grows with $\mu_I$ in the large $\mu_I$ region. This implies that the strength of the chiral symmetry breaking is not changed for small $\mu_I$: The isospin chemical potential plays a role to rotate the "vacuum angle" of the chiral circle $\tan^{-1} \sqrt{ \langle \pi^a \rangle^2 / \langle \sigma \rangle^2 } $ with keeping the "radius" $\tilde{\sigma}$ unchanged for small $\mu_I$. For large $\mu_I$ region, on the other hand, the chiral symmetry breaking is enhanced by the existence of $\mu_I$.

Linear sigma model and the formation of a charged pion condensate in the presence of an external magnetic field

We discuss the charged pion condensation phenomenon in the linear sigma model, in the presence of an external uniform magnetic field. The critical temperature is obtained as a function of the external magnetic field, assuming the transition is of second order, by considering a dilute gas at low temperature. As a result we found magnetic anti-catalysis in the Bose-Einstein condensation for lower values of the external magnetic field, and catalysis for higher values of the external magnetic field. This behavior confirms previous results with a single charged scalar field.

BCS–BEC CROSSOVER IN RELATIVISTIC FERMI SYSTEMS

We review the BCS–BEC crossover in relativistic Fermi systems, including the QCD matter at finite density. In the first part, we study the BCS–BEC crossover in a relativistic four-fermion interaction model and show how the relativistic effect affects the BCS–BEC crossover. In the second part, we investigate both two-color QCD at finite baryon density and pion superfluid at finite isospin density, by using an effective Nambu–Jona–Lasinio model. We will show how the model describes the weakly interacting diquark and pion condensates at low density and the BEC–BCS crossover at high density.

Thermodynamics of [formula omitted]-flavor strongly interacting matter at nonzero isospin

We investigate the phase structure of strongly interacting matter at non-vanishing isospin before the onset of pion condensation in the framework of the unquenched Polyakov–Quark-Meson model with 2+1 quark flavors. We show results for the order parameters and all relevant thermodynamic quantities. In particular, we obtain a moderate change of the pressure with isospin at vanishing baryon chemical potential, whereas the chiral condensate decreases more appreciably. We compare the effective model to recent lattice data for the decrease of the pseudo-critical temperature with the isospin chemical potential. We also demonstrate the major role played by the value of the pion mass in the curvature of the transition line, and the need for lattice results with a physical pion mass. Limitations of the model at nonzero chemical potential are also discussed.

Ginzburg–Landau phase diagram of QCD near chiral critical point – chiral defect lattice and solitonic pion condensate

We investigate the influence of the isospin asymmetry on the phase structure of quark matter near the chiral critical point systematically using a generalized version of Ginzburg–Landau approach. The effect has proven to be so profound that it brings about not only a shift of the critical point but also a rich variety of phases in its neighborhood. In particular, there shows up a phase with spatially varying charged pion condensate which we name the “solitonic pion condensate” in addition to the “chiral defect lattice” where the chiral condensate is partially destructed by periodic placements of two-dimensional wall-like defects. Our results suggest that there may be an island of solitonic pion condensate in the low temperature and high density side of QCD phase diagram.

Chiral pions in a magnetic background

We investigate the modification of the pion self-energy at finite temperature due to its interaction with a low-density, isospin-symmetric nuclear medium embedded in a constant magnetic background. To one loop, for fixed temperature and density, we find that the pion effective mass increases with the magnetic field. For the π−, interestingly, this happens solely due to the trivial Landau quantization shift ∼|eB|, since the real part of the self-energy is negative in this case. In a scenario in which other charged particle species are present and undergo an analogous trivial shift, the relevant behavior of the effective mass might be determined essentially by the real part of the self-energy. In this case, we find that the pion mass decreases by ∼10% for a magnetic field |eB|∼mπ2, which favors pion condensation at high density and low temperatures.

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 µI. 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.