Intriguing aspects of meson condensation (original) (raw)
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Fate of pion condensation in quark matter: From the chiral limit to the physical pion mass
Physical Review D, 2009
We study aspects of the pion condensation in two-flavor neutral quark matter using the Nambu-Jona-Lasinio model of QCD at finite density. We investigate the role of electric charge neutrality, and explicit symmetry breaking via quark mass, both of which control the onset of the charged pion (π c ) condensation. We show that the equality between the electric chemical potential and the in-medium pion mass, µe = M π − , as a threshold, persists even for a composite pion system in the medium, provided the transition to the pion condensed phase is of the second order. Moreover, we find that the pion condensate in neutral quark matter is extremely fragile to the symmetry breaking effect via a current quark mass m, and is ruled out for m larger than the order of 10 keV.
Scrutinizing the pion condensed phase
The European Physical Journal A, 2017
When the isospin chemical potential exceeds the pion mass, charged pions condense in the zeromomentum state forming a superfluid. Chiral perturbation theory provides a very powerful tool for studying this phase. However, the formalism that is usually employed in this context does not clarify various aspects of the condensation mechanism and makes the identification of the soft modes problematic. We reexamine the pion condensed phase using different approaches within the chiral perturbation theory framework. As a first step, we perform a low-density expansion of the chiral Lagrangian valid close to the onset of the Bose-Einstein condensation. We obtain an effective theory that can be mapped to a Gross-Pitaevskii Lagrangian in which, remarkably, all the coefficients depend on the isospin chemical potential. The lowdensity expansion becomes unreliable deep in the pion condensed phase. For this reason, we develop an alternative field expansion deriving a low-energy Lagrangian analog to that of quantum magnets. By integrating out the "radial" fluctuations we obtain a soft Lagrangian in terms of the Nambu-Goldstone bosons arising from the breaking of the pion number symmetry. Finally, we test the robustness of the second-order transition between the normal and the pion condensed phase when next-to-leading-order chiral corrections are included. We determine the range of parameters for turning the second-order phase transition into a first-order one, finding that the currently accepted values of these corrections are unlikely to change the order of the phase transition.
Chiral dynamics and pion properties at finite temperature and isospin chemical potential
2005
The thermal and density corrections, in terms of the isospin chemical potential mui\mui mui, to the mass of the pions, the decay constant and different condensates are studied in the framework of the SU(2) low energy effective chiral lagrangian at finite temperature in the two phases: The first phase ∣mui∣m|\mui|m∣mui∣m, being mmm the tree-level pion mass. As a function of
Nonequilibrium chiral perturbation theory and pion decay functions
Physics Letters B, 1999
We analyse the extension of Chiral Perturbation Theory to describe a meson gas out of thermal equilibrium. For that purpose, we let the pion decay constant be a time-dependent function and work within the Schwinger-Keldysh contour technique. A useful connection with curved space-time QFT allows to consistently renormalise the model, introducing two new low-energy constants in the chiral limit. We discuss the applicability of our approach within a Relativistic Heavy-Ion Collision environment. In particular, we investigate the formation of Disoriented Chiral Condensate domains in this model, via the parametric resonance mechanism.
Charged pion condensation in anti-parallel electromagnetic fields and nonzero isospin density *
Chinese Physics C, 2020
The formation of charged pion condensate in anti-parallel electromagnetic fields and in the presence of the isospin chemical potential is studied in the two-flavor Nambu–Jona-Lasinio model. The method of Schwinger proper time is extended to explore the quantities in the off-diagonal flavor space, i.e. the charged pion. In this framework, are treated as bound states of quarks and not as point-like charged particles. The isospin chemical potential plays the role of a trigger for charged pion condensation. We obtain the associated effective potential as a function of the strength of the electromagnetic fields and find that it contains a sextic term which possibly induces a weak first order phase transition. The dependence of pion condensation on model parameters is investigated.
Low momentum π-meson production from evolvable quark condensate
Physics of Particles and Nuclei, 2008
The pion production by sigma decay in hot and dense matter in the framework of the Nambu-Jona-Lasinio model [1] is investigated. The kinetic equation for joint evolution of pions and sigmas is constructed. The pion enhancement due to additional sigma creation via inertial mechanism is calculated.
Disoriented chiral condensate formation from a state with collective pion fields
Physical Review D, 1997
We investigate the time evolution of a system of quarks interacting with σ and pion fields starting from an initial configuration consisting of a tube of hot quark plasma undergoing a boost-invariant longitudinal expansion. We work within the framework of the linear sigma model using classical transport equations for the quarks coupled to the mean-field equations for the meson fields. In certain cases we find strong amplifications of any initial pion fields. For large-radius tubes, starting from quark densities that are very close to critical, we find that a disoriented chiral condensate can form in the centre of the tube. Eventually the collapse of the tube drives this state back to the true vacuum. This process converts the disoriented condensate, dominated by long-wavelength pion modes, into a coherent excitation of the pion field that includes significant components with transverse momenta of around 400 MeV. In contrast, for narrow tubes or larger initial temperatures, amplification occurs only via the pion-laser-like mechanism found previously for spherical systems. In addition, we find that explicit chiral symmetry breaking significantly suppresses the formation of disoriented condensates.
Pion transitions and models of chiral symmetry
Physical Review D, 1989
We describe a set of pion-decay and scattering amplitudes which are described by only two lowenergy parameters in the effective chiral Lagrangian of QCD. After a phenomenological analysis of the data, we demonstrate how the effective-Lagrangian framework correlates the many predictions of these reactions which have been made in the literature using a variety of models with chiral symmetry. A comparison with the data then also determines which model represents @CD. Not surprisingly, the winner is a form of vector dominance.
arXiv (Cornell University), 2017
By employing QCD inequalities, we discuss appearance of the pion condensate for both real and imaginary isospin chemical potentials. In our discussion, imaginary quark chemical potential is also taken into account. We show that the charged pion can condense for real isospin chemical potential, but not for imaginary one. Furthermore, we evaluate the expectation value of the neutral-pion field π 3 for imaginary isospin chemical potential by using framework of the twisted mass. As a result, it is found that π 3 becomes zero for the finite current-quark mass, whereas the expression of π 3 gives the Banks-Casher relation in the massless limit.
Pion Masses in Two-Flavor QCD with η Condensation
Physical Review Letters, 2014
We investigate some aspects of 2-flavor QCD with m u = m d at low-energy, using the leading order chiral perturbation theory including anomaly effects. While nothing special happens at m u = 0 for the fixed m d = 0, the neutral pion mass becomes zero at two critical values of m u , between which the neutral pion field condenses, leading to a spontaneously CP broken phase, the so-called Dashen phase. We also show that the "topological susceptibility" in the ChPT diverges at these two critical points. We briefly discuss a possibility that m u = 0 can be defined by the vanishing the "topological susceptibility. We finally analyze the case of m u = m d = m with θ = π, which is equivalent to m u = −m d = −m with θ = 0 by the chiral rotation. In this case, the η condensation occurs at small m, violating the CP symmetry spontaneously. Deep in the η condensation phase, three pions become Nambu-Goldstone bosons, but they show unorthodox behavior at small m that m 2 π = O(m 2 ), which, however, is shown to be consistent with the chiral Ward-Takahashi identities.