Applying the Hellmann-Feynman theorem to a charged pion gas, the quark and gluon condensates at low isospin density are determined by precise pion properties. At intermediate density around $ f_π^2m_π$, from both the estimation for the dilute pion gas and the calculation with Nambu--Jona-Lasinio model, the quark condensate is strongly and monotonously suppressed, while the gluon condensate is enhanced and can be larger than its vacuum value. This unusual behavior of the gluon condensate is universal for Bose condensed matter of mesons. Our results can be tested by lattice calculations at finite isospin density.
The effects of mode-mode and isospin-isospin correlations on nonequilibrium chiral dynamics are investigated by using the method of the time dependent variational approach with squeezed states as trial states. Our numerical simulations show that large domains of the disoriented chiral condensate (DCC) are formed due to the combined effect of the mode-mode and isospin-isospin correlations. Moreover, it is found that, when the mode-mode correlation is included, the DCC domain formation is accompanied by the amplification of the quantum fluctuation, which implies the squeezing of the state. Howev…
We compute the density dependence of the quark condensate and how it changes under the influence of isospin-asymmetric nuclear matter. This is achieved by the calculation of the relevant Feynman diagrams using in-medium chiral perturbation theory. We find that the absolute value of the quark condensate decreases in nuclear matter by around 35% at normal nuclear density, in agreement with previous model-independent calculations. We also present an quantitative estimation of the difference of up- and down quark in-medium condensates.
We study the isospin singlet pairing in asymmetric nuclear matter with nonzero total momentum of the condensate Cooper pairs. The quasiparticle excitation spectrum is fourfold split compared to the usual BCS spectrum of the symmetric, homogeneous matter. A twofold splitting of the spectrum into separate branches is due to the finite momentum of the condensate, the isospin asymmetry, or the finite quasiparticle lifetime. The coupling of the isospin singlet and triplet paired states leads to further twofold splitting of each of these branches. We solve the gap equation numerically in the isospin…
We study gluon condensate in a pion superfluid, through calculating the equation of state of the system in the Nambu-Jona-Lasinio model. While in mean field approximation the growing pion condensate leads to an increasing gluon condensate, meson fluctuations reduce the gluon condensate and the broken scalar symmetry can be smoothly restored at finite isospin density.
It is possible that isospin violating dynamical effects are amplified due to coherence if a disoriented chiral condensate (or other source of a coherent pion state) is formed in a heavy ion collison. It is shown explicitly that altering the isospin of the coherent state by order of one unit can change the number of $π^0$'s in the condensate by some finite fraction of the total number. A possible signature of such amplified isospin violating effects is that the ratio of neutral to total low $p_T$ pions averaged over many events may differ markedly from 1/3. Such a signal would not be washed out…
We study the influence of the isospin asymmetry on the phase structure of strongly interacting quark matter near the tricritical point (TCP) using a generalized Ginzburg-Landau approach. The effect has proven to be so drastic, not only bringing about the shift of the location of TCP, but resulting in a rich fine structure at the vicinity of TCP. In particular, we find that an arbitrary small perturbation due to isospin density lifts the degeneracy of TCP making it split into four independent multicritical points. Accordingly, the homogeneous pion condensate and its solitonic counterpart come t…
In this paper, we consider two-flavor QCD at zero temperature and finite isospin chemical potential ($μ_I$) 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.
We consider a mechanism to create the $η- η'$ mass difference by the gluon anomaly in a squeezed vacuum. We find that the mass shift of the $η_0$ governing this mass difference is determined by the magnetic part of the gluon condensate. For the squeezed vacuum this magnetic part coincides with the total gluon condensate, so that we get a relation between the gluon condensate and the mass shift of the $η_0$ as a function of the strong coupling constant $α_s$. The values of the gluon condensate obtained through this relation are compared with the value by Shifman, Vainshtein and Zakharov and the…
We investigate the rotation effects on the mesonic condensation in isospin matter . Using the two-flavor NJL effective model with a global rotation, we demonstrate two important effects of the rotation on its phase structure: a rotational suppression of the scalar-channel condensates, in particular the pion condensation region; and a rotational enhancement of the rho condensation region with vector-channel condensate. A new phase diagram for isospin matter under rotation is mapped out on the $ω-μ_I$ plane where three distinctive phases, corresponding to $σ$, $π$, $ρ$ dominated regions respecti…
We investigate the thermal behaviour of gluon and chiral condensates within an effective Lagrangian of pseudoscalar mesons coupled to a scalar glueball. This Lagrangian mimics the scale and chiral symmetries of QCD. (Submitted to Z. Phys. C)
We make a complete dynamical study of Isotopic spin conservation effects on the multiplicity distributions of both hard and soft pions emitted in a quark gluon plasma undergoing a non-equilibrium phase transition.
Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this report we present a selection of new reaction observables in dissipative collisions particularly sensitive to the symmetry term of the nuclear Equation of State (Iso-EoS). We will first discuss the Isospin Equilibration Dynamics. At low energies this manifests via the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation with the symmetry term acting as a restoring force. At higher beam energies Iso-EoS effects will be see…
We describe some detailed numerical simulations of Disoriented Chiral Condensates (DCCs), using the chiral lagrangian as a controlled long-wavelength description. We focus on the possibility of multiple, independently coherent domains, and investigate the degree to which the DCC signal is attenuated. As an intermediate step in our analysis we compute the expected number of detector events in each isospin and momentum channel for a given asymptotic classical field configuration. We find that for sufficiently large initial field strengths, the non-linear interactions between domains become impor…
A recent chiral perturbation theory calculation of the in-medium quark condensate $<\bar q q>$ is extended to the isospin-asymmetric case of pure neutron matter. In contrast to the behavior in isospin-symmetric nuclear matter we find only small deviations from the linear density approximation. This feature originates primarily from the reduced weight factors (e.g. 1/6 for the dominant contributions) of the $2π$-exchange mechanisms in pure neutron matter. Our result suggests therefore that the tendencies for chiral symmetry restoration are actually favored in systems with large neutron excess (…
We consider two-flavor chiral perturbation theory ($χ$PT) at finite isospin chemical potential $μ_I$ and finite temperature $T$. We calculate the effective potential and the quark and pion condensates as functions of $T$ and $μ_I$ to next-to-leading order in the low-energy expansion in the presence of a pionic source. We map out the phase diagram in the $μ_I$--$T$ plane. Numerically, we find that the transition to the pion-condensed phase is second order in the region of validity of $χ$PT, which is in agreement with model calculations and lattice simulations. Finally, we calculate the pressure…
We examine the validity of the notion of the coherent state for pions and the quantum scattering effect in the final state of pion emission. When the number of particles is large, the effect caused by the small but finite mass difference between the neutral and charged pions can add up substantially in the quantum evolution of an initially coherent state. As a result, the states with quite different numbers of neutral or charged pions are essentially incoherent. The importance of the quantum scattering in the final-state isospin charge distribution of a disoriented chiral condensate (DCC) is i…
A calculation of the thermal quark propagator is presented taking the gluon condensate above the critical temperature into account. The quark dispersion relation following from this propagator is derived.
The gluon condensate as a function of temperature and baryon density in a nucleon medium is obtained from an effective dilaton Lagrangian. It is shown that, at a normal nuclear density of nucleons, n_0 = 0.17 fm^{-3} the gluon condensate decreases by about 10%.
We present a calculation of the thermal quark propagator taking the gluon condensate above the critical temperature into account. The quark dispersion relation following from this propagator, describing two massive modes, is discussed.
We study the influence of the isospin asymmetry on the phase structure of strongly interacting quark matter near the critical point (CP) using a Ginzburg-Landau approach. The effect is found to be drastic, not only bringing about the shift of the location of the CP, but resulting in a rich phase structure in the vicinity of the CP. In particular, new tricritical and triple points emerge as soon as the isospin density becomes finite. Moreover, we find the CP being washed out from the phase diagram due to the stabilization of a homogeneous charged pion condensate when the isospin chemical potent…
An expression for the photon condensate in quantum electrodynamics is presented and generalized to deduce a simple relation between the gluon condensate and the running coupling constant of quantum chromodynamics (QCD). Ambiguities in defining the condensates are discussed. The values of the gluon condensate from some Ansätze for the running coupling in the literature are compared with the value determined from QCD sum rules.
A calculation of the thermal quark propagator is presented taking the gluon condensate above the critical temperature into account. The quark dispersion relation and the dilepton production following from this propagator are derived.
We investigate the mesonic condensation in isospin matter under rotation. Using the two-flavor NJL effective model under the presence of global rotation, we demonstrate two important effects of the rotation on its phase structure: a rotational suppression of the scalar-channel condensates, in particular the pion condensation region; and a rotational enhancement of the rho condensation region with vector-channel condensate. A new phase diagram for isospin matter under rotation is mapped out on the $ω-μ_I$ plane where three distinctive phases, corresponding to $σ$, $π$, $ρ$ dominated regions res…
We investigate the phase structure of homogeneous and inhomogeneous neutron-proton condensate in isospin asymmetric nuclear matter. At extremely low nuclear density the condensed matter is in homogeneous phase at any temperature, while in general case it is in Larkin-Ovchinnikov-Fulde -Ferrell phase at low temperature. In comparison with the homogeneous superfluid, the inhomogeneous superfluid can survive at higher nuclear density and higher isospin asymmetry.
We evaluate the quark-photon vertex non-perturbatively taking into account the gluon condensate at finite temperature. This vertex is related to the previously derived effective quark propagator by a QED like Ward-Takahashi identity. The importance of the effective vertex for the dilepton production rate from a quark-gluon plasma is stressed.
The relation between the large mass of the $η'$ and the structure of the gluon vacuum via the $U_A(1)$ anomaly is discussed. A squeezed gluon vacuum is considered as an alternative to existing models. Considering Witten's formula for the $η_0$ mass we show that the contact term can give a sizable contribution and relate it to the physical gluon condensate. The values of the gluon condensate obtained through this relation are compared with the value by Shifman, Vainshtein and Zakharov and the recent update values by Narison.
Using the quark-meson coupling (QMC) model, we study the density dependence of the quark and gluon condensates in nuclear matter. We show that the change of the quark condensate is mainly driven by the scalar field in the medium and that the reduction of the quark condensate is suppressed at high density, even in the mean-field approximation. The gluon condensate decreases by 4 - 6 % at nuclear saturation density. We also give a simple relationship between the change of the quark condensate and that of a hadron mass in the medium.
A calculation of the thermal quark propagator is presented taking the gluon condensate above the critical temperature into account. The quark dispersion relation following from this propagator is derived.
The study of light pseudoscalar quark-antiquark bound states in the Dyson-Schwinger approach with the effective QCD coupling enhanced by the interplay of the dimension 2 gluon condensate <A^2> and dimension 4 gluon condensate <F^2>, is extended to the eta-eta' complex. We include the effects of the gluon axial anomaly into the Dyson-Schwinger approach to mesons. The calculated masses, mixing and two-photon decay widths of eta and eta' mesons are in agreement with experiment. Also, in a model-independent way, we give the modification of the Gell-Mann--Okubo and Schwinger nonet relations due to …
We exhibit the method for obtaining non perturbative quark and gluonic vacuum condensates from a model truncation of QCD. The truncation allows for a phenomenological description of the quark-quark interaction in a framework which maintains all global symmetries of QCD and allows an 1/N_c expansion. Within this approach the functional integration over the gluon fields can be performed and therefore any gluonic vacuum observable can be expressed in terms of a quark operator and the gluon propagator. As a special case we calculate the mixed quark gluon condensate. We investigate how the value de…
It is known now that chiral symmetry restoration requires the meson-nucleon coupling to be density dependent in nuclear-matter mean-field models. We further show that quite generally, the quark and gluon condensates in medium are related to the trace of energy-momentum tensor of nuclear matter and in these models the incompressibility, K, must be less than thrice the chemical potential, $μ$. In the critical density $ρ_c$, the gluon condensate is only reduced by $20\%$ indicating a larger effective nucleon mass.
The extraction of meson-baryon scattering parameters from lattice QCD is complicated by the necessity, in some channels, of including annihilation diagrams. We consider a strategy to avoid the need for these extremely costly and noisy contributions. The strategy is based on simulations with an isospin chemical potential which, contrary to a baryon chemical potential, has no sign problem. When the isospin chemical potential is larger than a critical value, a charged pion condensate forms. Baryons propagating in the pion condensate will have their masses modified by pion-baryon scattering parame…
We derive the set of kinetic equations that control the evolution of gluons in the presence of a condensate. We show that the dominant singularities remain logarithmic when the scattering involves particles in the condensate. This allows us to define a consistent small angle approximation.
We investigate the thermodynamics of two-flavor quark matter in presence of nonzero isospin chemical potential and external magnetic field. It is known that at sufficiently high isospin chemical potential, charged pions undergo Bose-Einstein condensation (BEC). The condensate behaves as a superconductor, exhibiting Meissner effect in weak external magnetic fields. Stronger fields stress the superconducting state, turning it first into an Abrikosov lattice of vortices, and eventually destroying the condensate altogether. On the other hand, for sufficiently strong magnetic fields and low-to-mode…
We consider here the vacuum structure in QCD with both quark and gluon condensates and a variational ansatz for the ground state. The method is nonperturbative using only equal time algebra for the field operators. We then find that a constrained energy minimisation of the Hamiltonian leads to a QCD vacuum with both quark and gluon condensates for $α_s > α_c=0.62$. Pion decay constant and the charge radius of the pion seem to fix the QCD coupling constant $α_s$ as 1.28. The approach opens up possibilities of relating the mysterious vacuum structure with common place hadronic properties.
We consider here quark matter equation of state including strange quarks and taking into account a nontrivial vacuum structure for QCD with gluon condensates. The parameters of condendsate function are determined from minimisation of the thermodynamic potential. The scale parameter of the gluon condensates is fixed from the SVZ parameter in the context of QCD sum rules at zero temperature and zero baryon density. The equation of state for strange matter at zero temperature as derived is used to study quark star structure using Tolman Oppenheimer Volkoff equations. Stable solutions for quark st…
The contribution of Lorentz non-scalar operators to finite temperature correlation functions is discussed. Using the local duality approach for the one-pion matrix element of a product of two vector currents, the temperature dependence of the average gluonic stress tensor is estimated in the chiral limit to be $\langle{\bf E}^2 +{\bf B}^2\rangle_{T}=\frac{π^2}{10}bT^4$. At a normalization point $μ=0.5$ GeV we obtain $b\approx 1.1$. Together with the known temperature dependence of the Lorentz scalar gluon condensate we are able to infer $\langle{\bf E}^2\rangle_T$ and $\langle{\bf B}^2\rangle_…
Within a self-consistent proper-time Renormalization Group (RG) approach we investigate an effective QCD trace anomaly realization with dilatons and determine the finite-temperature behavior of the gluon condensate. Fixing the effective model at vanishing temperature to the glueball mass and the bag constant a possible gluonic phase transition is explored in detail. Within the RG framework the full non-truncated dilaton potential analysis is compared with a truncated potential version.
Using the SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level, we study the quark-gluon mixed condensate g<\bar{q} sigma G q>, which is another chiral order parameter. For each current quark mass of m_q=21, 36, 52 MeV, we generate 100 gauge configurations in the 16^4 lattice with β= 6.0, and perform the measurement of the mixed condensate at 16 points in each gauge configuration. Using the 1600 data for each m_q, we find the ratio between the mixed condensate and the quark condensate, m_0^2 = g<\bar{q} sigma G q>/ <\bar{q}q> \simeq 2.5 GeV^2 at the lattice scale in the chi…
It is shown that in the large-N_c limit radial Regge trajectories give rise in a natural way to the presence of the dimension-2 gluon condensate, <A^2>, in meson correlators. We match these models to QCD and provide estimates for <A^2> in terms of other physical quantities. In particular, in the simplest strictly linear radial Regge model with equal residues <A^2> is proportional to the pion decay constant squared. However, the linear model fails a consistency condition based on matching the short- and long-distance string tensions, nor reproduces the phenomenological values of the gluon conde…
We study the quark-gluon mixed condensate g<\bar{q} sigma G q>, which is another chiral order parameter, using the SU(3)c lattice QCD with the Kogut-Susskind(KS) fermion at the quenched level. We generate 100 gauge configurations on the 16^4 lattice with β= 6.0, and measure the mixed condensate at 16 points in each gauge configuration for each current-quark mass of m_q=21, 36, 52 MeV. From the 1600 data for each m_q, we find the ratio between the mixed condensate and the quark condensate, m_0^2 = g<\bar{q} sigma G q> / <\bar{q}q> \simeq 2.5 GeV^2 at the lattice scale of 1/a \simeq 2 GeV in the…
We show that the quark condensates for the two light up and down flavors can have significantly different values in the hadronic phase at nonzero temperature, baryon and isospin chemical potentials. We quantify this difference using a simple model.
We present the first study of the thermal effects on the quark-gluon mixed condensate g<\bar{q} σG q>, which is another chiral order parameter, in SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level. Using the lattices at β=6.0, 6.1, 6.2 in high statistics, we calculate the mixed condensate as well as the quark condensate in the chiral limit for the temperature 0MeV <= T <= 500MeV. Except for the sharp decrease of both the condensates around T_c \simeq 280MeV, the thermal effects are found to be weak below T_c. We also find that the ratio m_0^2 = g<\bar{q} σG q>/ <\bar{q}q…
We study the quark-gluon mixed condensate g<\bar{q} sigma G q>, which is another chiral order parameter, in SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level. Using 100 gauge configurations on the 16^4 lattice with β= 6.0, we measure the mixed condensate at 16 points in each gauge configuration for each current-quark mass of m_q=21, 36, 52 MeV. From the 1600 data for each m_q, we find the ratio between the mixed condensate and the quark condensate, m_0^2 = g<\bar{q} sigma G q> / <\bar{q}q> \simeq 2.5 GeV^2 at the lattice scale of 1/a \simeq 2 GeV in the chiral limit. The…
Estimates of Lee-Yang zeros and a possible critical point on the pion condensate boundary in the QCD isospin phase diagram using an unbiased exponential resummation on the lattice
The density, spin and isospin correlation functions in nuclear matter with a neutron-proton ($np$) condensate are calculated to study the possible signatures of the BEC-BCS crossover in the low-density region. It is shown that the criterion of the crossover (Phys. Rev. Lett. {\bf 95}, 090402 (2005)), consisting in the change of the sign of the density correlation function at low momentum transfer, fails to describe correctly the density-driven BEC-BCS transition at finite isospin asymmetry or finite temperature. As an unambiguous signature of the BEC-BCS transition, there can be used the prese…
