Making use of the recently developed chiral power counting for the physics of nuclear matter [1,2], we evaluate the in-medium chiral quark condensate up to next-to-leading order for both symmetric nuclear matter and neutron matter. Our calculation includes the full in-medium iteration of the leading order local and one-pion exchange nucleon-nucleon interactions. Interestingly, we find a cancellation between the contributions stemming from the quark mass dependence of the nucleon mass appearing in the in-medium nucleon-nucleon interactions. Only the contributions originating from the explicit quark mass dependence of the pion mass survive. This cancellation is the reason of previous observations concerning the dominant role of the long-range pion contributions and the suppression of short-range nucleon-nucleon interactions. We find that the linear density contribution to the in-medium chiral quark condensate is only slightly modified for pure neutron matter by the nucleon-nucleon interactions. For symmetric nuclear matter the in-medium corrections are larger, although smaller compared to other approaches due to the full iteration of the lowest order nucleon-nucleon tree-level amplitudes. Our calculation satisfies the Hellmann-Feynman theorem to the order worked out. Also we address the problem of calculating the leading in-medium corrections to the pion decay constant. We find that there are no extra in-medium corrections that violate the Gell-Mann-Oakes-Renner relation up to next-to-leading order.
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 …
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.
With the isovector coupling constants adjusted to reproduce the physical pion mass and lattice QCD results in baryon-free quark matter, we have carried out rigourous calculations for the pion condensate in the 3-flavor Nambu-Jona-Lasinio model, and studied the 3-dimensional QCD phase diagram. With the increasing isospin chemical potential $μ_I$, we have observed two nonzero solutions of the pion condensate at finite baryon chemical potentials $μ_B$, representing respectively the pion superfluid phase and the Sarma phase, and their appearance and disappearance correspond to a second-order (firs…
We discuss a dynamical mechanism of pion production from disoriented chiral condensates (DCC). It leads to an explosive production of pions via the parametric amplification mechanism, which is similar to the reheating mechanism in inflationary cosmology. Classically, it is related with the instability in the solutions of the Mathieu equation and we explore the quantum aspects of the mechanism. We show that nonlinearlities and back reactions can be ignorable for sufficiently long time under the small amplitude approximations of background $σ$ oscillations, which may be appropriate for the late …
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…
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.
The CMS experiment at the Large Hadron Collider has recently presented data on the average transverse momentum of protons, kaons and pions as a function of particle multiplicity. We relate the particle multiplicity to saturation momentum using recently published computations of the interaction radius determined from the theory of the Color Glass Condensate. We show that the pp and the pA experimental data scale in terms of these saturation momenta. Computing transverse momentum spectra for identified particles using Boltzmann-type distributions and relating different associated multiplicities …
We study the production of photons through the non-equilibrium relaxation of a disoriented chiral condensate. We propose that to search for non-equilibrium photons in the direct photon measurements of heavy-ion collisions can be a potential test of the formation of disoriented chiral condensates.
The probability distribution of neutral pion fraction from independent domains of disoriented chiral condensate is characterized. The signal for the condensate is clear for a small number of domains but is greatly reduced for more than three.
We investigate the pressure of the pion, which should be equal to zero to ensure the stability of the pion, within the framework of the chiral quark model beyond the chiral limit. The pressure of the pion turns out to vanish nontrivially by the Gell-Mann-Oakes-Renner relation within the present framework. It implies that the stability of the pion might be deeply rooted in spontaneous chiral symmetry breaking. We also discuss physical quantities relevant to the energy-momentum tensor operator.
We study the effect of the chiral phase transition on pion production in hot hadronic matter. The phase of restored chiral symmetry is characterized by the appearance of the scalar $σ$-meson as a chiral partner of the pion as well as by the degeneracy of the vector and axial-vector mesons. We find rapid thermal and chemical equilibration of these degrees of freedom in the symmetric phase. Provided that the chiral transition temperature is not considerably high, the presence of a chirally symmetric phase will result in $\sim 1.6$ times more thermal pions in the final state.
We show that chiral symmetry is responsible for large cancellations in the two-pion exchange nucleon-nucleon interaction, which are similar to those occuring in free pion-nucleon scattering.
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.
The influence of the magnetic field on the pion superfluidity and the phase structure is analyzed in the framework of the two-flavor Nambu--Jona-Lasinio(NJL) model. To do this, we first derive the thermodynamic potential from the Lagrangian density of the NJL model in the mean field approximation. Using this thermodynamic potential, we get the gap equation of the chiral condensate and the pion condensate. The effect of external magnetic field on the pion condensate is not simple promotion or suppression, which we will discuss in detail in the paper. It is shown that the tricritical point on th…
A new tool which combines chiral perturbation theory and unitarity in coupled channels is applied with success to the study of the meson-meson interaction, extending the theoretical predictions up to sqrt{s} = 1.2 GeV, hence improving considerably the convergence radius of conventional chiral perturbation theory. The method is applied to obtain the meson-meson phase shifts and inelasticities as well as the isoscalar pion-pion scattering amplitude inside a nuclear medium.
The existence of a Goldstone boson is demonstrated in chiral random matrix theory. After determining the effective coupling and calculating the scalar and pseudoscalar propagators, a random phase approximation summation reveals the massless pion and massive sigma modes expected whenever chiral symmetry is spontaneously broken.
It is shown that the spin polarized condensate appears in quark matter at high baryon density and low temperature due to the tensor-type four-point interaction in the Nambu-Jona-Lasinio-type model as a low energy effective theory of quantum chromodynamics. It is indicated within this low energy effective model that the chiral symmetry is broken again by the spin polarized condensate as increasing the quark number density, while the chiral symmetry restoration occurs in which the chiral condensate disappears at a certain density.
We study the phase diagram of the Nambu-Jona-Lasinio model in the external magnetic field within the mean-field approximation, taking into account the inhomogeneous chiral condensate. It is shown that there appears a new type of the chiral condensate, endowed with two features of real kink crystal and dual chiral density wave, in the magnetic field. We also show that there are first order phase transitions between different inhomogeneous phases in the presence of magnetic field.
A calculational scheme is developed to evaluate chiral corrections to properties of composite baryons with composite pions. The composite baryons and pions are bound states derived from a microscopic chiral quark model. The model is amenable to standard many-body techniques such as the BCS and RPA formalisms. An effective chiral model involving only hadronic degrees of freedom is derived from the macroscopic quark model by projection onto hadron states. Chiral loops are calculated using the effective hadronic Hamiltonian. A simple microscopic confining interaction is used to illustrate the der…
In order to study partial restoration of the chiral symmetry at finite density, we investigate the density corrections of the chiral condensate up to next-leading order of density expansion using the chiral Ward identity and an in-medium chiral perturbation theory. In our study, we assume that all the in-vacuum quantities for the pion, the nucleon and the pi N interaction are determined and focus on density expansion of the in-medium physical quantities. We perform diagrammatic analysis of the correlation functions which provide the in-medium chiral condensate. This density expansion scheme sh…
We investigate the effect of composite pions on the behaviour of the chiral condensate at finite temperature within the Polyakov-loop improved NJL model. To this end we treat quark-antiquark correlations in the pion channel (bound states and scattering continuum) within a Beth-Uhlenbeck approach that uses medium-dependent phase shifts. A striking medium effect is the Mott transition which occurs when the binding energy vanishes and the discrete pion bound state merges the continuum. This transition is triggered by the lowering of the continuum edge due to the chiral restoration transition. Thi…
We consider an ``oriented'' chiral condensate produced in the squeezed states of the effective field theory with time- and space-dependent pion mass parameter. We discuss the general properties of the solution, identifying condensate modes and determining the resulting pion distributions. The implementation of the dynamics in the form of sudden perturbation allows us to look for exact solutions. In the region of condensation, the dramatic increase in pion production and charge fluctuations are demonstrated.
In a series of articles it was recently claimed that the quantum chromodynamic (QCD) condensates are not the properties of the vacuum but of the hadrons and are confined inside them. We point out that this claim is incompatible with the chiral Lagrangian and Bose-Einstein statistics of the Goldstone bosons (pions) in chiral limit and conclude that the quark condensate must be the property of the QCD vacuum.
The vector form factor of the pion is calculated in the framework of chiral effective field theory with vector mesons included as dynamical degrees of freedom. To construct an effective field theory with a consistent power counting, the complex-mass scheme is applied.
The phase diagram of dense quark matter with chiral imbalance is considered with the conditions of electric neutrality and $β$-equilibrium. It has been shown recently that chiral imbalance can generate charged pion condensation in dense quark matter, so it was interesting to verify that this phenomenon takes place in realistic physical scenarios such as electrically neutral matter in $β$-equilibrium, because a window of pion condensation at dense quark matter phase diagram (without chiral imbalance) predicted earlier was closed by the consideration of these conditions at the physical current q…
We review the relationship between the pion decay constant $f_π$, the chiral symmetry restoration temperature $T_c$ and the phenomenology of low energy chiral symmetry breaking in view of the recent confirmation of the existence of a sigma meson with a mass of 600-700 MeV.
A small test/experiment has been performed at the Fermilab Collider to measure charged particle and photon multiplicities in the forward direction, $η\approx 4.1$. The primary goal is to search for disoriented chiral condensate (DCC). The experiment and analysis methods are described, and preliminary results of the DCC search are presented.
We extend our previous analysis of the unitarized pion-nucleon scattering amplitude including up to fourth order terms in Heavy Baryon Chiral Perturbation Theory. We pay special attention to the stability of the generated Delta(1232 resonance, the convergence problems and the power counting of the chiral parameters.
The environment generated in the mid-rapidity region of a high-energy nuclear collision endows the pionic degrees of freedom with a time-dependent effective mass. Its specific evolution provides a mechanism for the production of back-to-back charge-conjugate pairs of soft pions which may present an observable signal of the non-equilibrium dynamics of the chiral order parameter.
The decay of disoriented chiral condensates into soft pions is considered within the context of a linear sigma model. Unlike earlier analytic studies, which focused on the production of pions as the sigma field rolled down toward its new equilibrium value, here we focus on the amplification of long-wavelength pion modes due to parametric resonance as the sigma field oscillates around the minimum of its potential. This process can create larger domains of pion fluctuations than the usual spinodal decomposition process, and hence may provide a viable experimental signature for chiral symmetry br…
The effects of chiral imbalance and external magnetic field on pion superfluidity and color superconductivity are investigated in extended Nambu--Jona-Lasinio models. We take Schwinger approach to treat the interaction between charged pion condensate and magnetic field at finite isospin density and include simultaneously the chiral imbalance and magnetic field at finite baryon density. For the superfluidity, the chiral imbalance and magnetic field lead to catalysis and inverse catalysis effects, respectively. For the superconductivity, the chiral imbalance enhances the critical baryon density,…
Recent attempts to detect the pion polarizability via analysis of $γγ\rightarrowππ$ measurements are examined. The connection between calculations based on dispersion relations and on chiral perturbation theory is established by matching the low energy chiral amplitude with that given by a full dispersive treatment. Using the values for the polarizability required by chiral symmetry, predicted and experimental cross sections are shown to be in agreement.
We study pion--nucleon scattering with a chiral lagrangian of pions, nucleons, and $Δ$-isobars. The scattering amplitude is evaluated to one-loop $Q^3$ order, where $Q$ is a generic small momentum, using a new approach which is equivalent to heavy baryon chiral perturbation theory. We obtain a good fit to the experimental phase shifts for pion center-of-mass kinetic energies up to 100 MeV. A sigma term greater than 45 MeV is favored, but the value is not well determined.
We show that the variance in the number of charged pions (in a suitable range of momentum space) provides a signature for the observation of a disoriented chiral condensate (D$χ$C). The signal should be observable even if multiple domains of D$χ$C form provided the average number of pions per domain is significantly large than unity. The variance of the number charged pions alone provides a signal which can be used even if the number of neutral pions cannot be measured in a given detector. If the neutrals can be measured, however, the fluctuations in the total number of pions provides a signat…
In this work we study the thermodynamic properties of the pion gas starting from the realistic elastic scattering phase-shifts obtained from Chiral Perturbation Theory and using the virial expansion. In particular we study the state equation and the behavior of the quark condensate as a function of the temperature and the density.
We compute the light-cone momentum distributions of pions in the nucleon in chiral effective theory using both pseudovector and pseudoscalar pion-nucleon couplings. For the pseudovector coupling we identify δ-function contributions associated with end-point singularities arising from the pion-nucleon rainbow diagrams, as well as from pion bubble and tadpole diagrams which are not present in the pseudoscalar model. Gauge invariance is demonstrated, to all orders in the pion mass, with the inclusion of Kroll-Ruderman couplings involving operator insertions at the πNN vertex. The results pave the…
The Green-function approach has been extended to the moderate baryon density region in the framework of an extended Nambu--Jona-Lasinio model, and the thermodynamic potential with both chiral and diquark condensates has been evaluated by using the massive quark propagator. The phase structure along the chemical potential direction has been investigated and the strong competition between the chiral and diquark condensate has been analyzed by investigating the influence of the diquark condensate on the sharp Fermi surface. The influence of the diquark condensate on the quark properties has been …
We investigate the time evolution of a system of quarks interacting with sigma 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 c…
Two- and three-pion correlations are investigated in cases when disoriented chiral condensate (DCC) occurs. A chaoticity and weight factor are used as measures of two- and three-pion correlations, and the various models for DCC are investigated. Some models are found to yield the chaoticity and weight factor in a reasonable agreement with recent experimental data.
Near threshold neutral pion electroproduction on the deuteron is studied in the framework of baryon chiral perturbation theory at next-to-leading order in the chiral expansion. We develop the multipole decomposition for pion production off spin-1 particles appropriate for the threshold region. The existing data at photon virtuality k^2 = -0.1 GeV^2 can be described satisfactorily. Furthermore, the prediction for the S-wave multipole E_d at the photon point is in good agreement with the data.
The partial restoration of chiral symmetry in nuclear medium is investigated in a model independent way by exploiting operator relations in QCD. An exact sum rule is derived for the quark condensate valid for all density. This sum rule is simplified at low density to a new relation with the in-medium quark condensate <bar{q}q>*, in-medium pion decay constant F_{pi}^t and in-medium pion wave-function renormalization Z_{pi}*. Calculating Z_{pi}*at low density from the iso-scalar pion-nucleon scattering data and relating F_{pi}^t to the isovector pion-nucleus scattering length b_1^*, it is conclu…
We study the changes produced by the deuteron on the QCD quark condensate by means the Feynman-Hellmann theorem and find that the pion mass dependence of the pion-nucleon coupling could play an important role. We also discuss the relation between the many body effect of the condensate and the meson exchange currents, as seen by photons and pions. For pion probes, the many-body term in the physical amplitude differs significantly from that of soft pions, the one linked to the condensate. Thus no information about the many-body term of the condensate can be extracted from the pion-deuteron scatt…
Enhancement of omega and antiomega baryon production in Pb+Pb collisions at a c.m. energy of 17 A GeV can be explained by the formation of many small disoriented chiral condensate regions. This explanation implies that neutral and charged kaons as well as pions must exhibit novel isospin fluctuations. We compute the distribution of the fraction of neutral pions and kaons from such regions. We then propose robust statistical observables that can be used to extract the novel fluctuations from background contributions in pion and kaon measurements at RHIC and LHC.
We suggest two methods for the detection of the formation of disoriented chiral condensates in heavy ion collisions. We show that the variance in the number of charged pions (in a suitable range of momentum space) provides a signature for the observation of a disoriented chiral condensate. The signal should be observable even if multiple domains of D$χ$C form provided the average number of pions per domain is significantly larger than unity. The variance of the number charged pions alone provides a signal which can be used even if the number of neutral pions cannot be measured in a given detec…
There has been a discrepancy between values of the pion-nucleon sigma term extracted by two different methods for many years. Analysis of recent high precision pion-nucleon data has widened the gap between the two determinations. It is argued that the two extractions correspond to different quantities and that the difference between them can be understood and calculated.
The factorial moments of the pion multiplicity distributions are calculated with HIJING and UrQMD and found to be independent of the pT range included, in contrast to recent simulations with the linear sigma model which leads to large enhancements for pions with transverse kinetic energies below 200 MeV. This supports the use of the ratio of the factorial moments of low and high pT pions as a signal of ``new'' physics at low momentum scales, such as the formation of disoriented chiral condensates.
We show that an event-by-event fluctuation of the ratio of neutral pions or resulting photons to charged pions can be used as an effective probe for the formation of disoriented chiral condensates. The fact that the neutral pion fraction produced in case of disoriented chiral condensate formation has a characteristic extended non gaussian shape, is shown to be the key factor which forms the basis of the present analysis.
By exploiting the fact that the chiral condensate is related to the derivative of the free-energy density with respect to the bare quark mass we calculate the temperature dependence of the condensate ratio $\ave{\bar qq}_T/\ave{\bar qq}_0$ from an iteracting pion gas. When using the Weinberg Lagrangian at the Hartree level we find a depression of the condensate with temperature. For $T < 100$ MeV the results are in good agreement with chiral perturbation theory in the three loop approximation. Near $T_c$, however, there are marked differences due to non-perturbative nature of our approach.
We examine possibilities of pion condensation with zero momentum (s-wave condensation) in neutron stars by using the pion-nucleus optical potential U and the relativistic mean field (RMF) models. We use low-density phenomenological optical potentials parameterized to fit deeply bound pionic atoms or pion-nucleus elastic scatterings. Proton fraction (Y_p) and electron chemical potential (mu_e) in neutron star matter are evaluated in RMF models. We find that the s-wave pion condensation hardly takes place in neutron stars and especially has no chance if hyperons appear in neutron star matter and…
The probability distribution in $R$, the proportion of neutral pions to all pions emitted in heavy ion collisions in certain kinematic regions, has been suggested as a signal of a disoriented chiral condensate (D$χ$C). Here we note that the signature can be greatly enhanced by making suitable cuts in the data. In particular, we consider reducing the data set such that the $k$ pions with lowest $p_T$ are all neutral. We find that, given such cuts, $<R >$ can be substantially different from 1/3. For example, for a single D$χ$C domain without contamination due to incoherently emitted pions, $<R>$…
We investigate low-energy fluctuations in the real kink crystal phase of dense quark matter within the Nambu--Jona-Lasinio model. The modulated chiral condensate breaks both the translational symmetry and chiral symmetry spontaneously, which leads to the appearance of phonons and pions that are dominant degrees of freedom in the infrared. Using the Ginzburg-Landau expansion near the Lifshitz point, we derive elastic free energies for phonons and pions in dependence on the temperature and chemical potential. We show that the one-dimensional modulation is destroyed by thermal fluctuations of pho…
We calculate the chiral condensate in neutron matter at zero temperature based on nuclear forces derived within chiral effective field theory. Two-, three- and four-nucleon interactions are included consistently to next-to-next-to-next-to-leading order (N3LO) of the chiral expansion. We find that the interaction contributions lead to a modest increase of the condensate, thus impeding the restoration of chiral symmetry in dense matter and making a chiral phase transition in neutron-rich matter unlikely for densities that are not significantly higher than nuclear saturation density.
A general expression is discussed for pion probability distributions coming from relativistic heavy ion collisions. The general expression contains as limits: 1) The disoriented chiral condensate (DCC), 2) the negative binomial distribution and Pearson type III distribution, 3) a binomial or Gaussian result, 4) and a Poisson distribution. This general expression approximates other distributions such as a signal to noise laser distribution. Similarities and differences of the DCC distribution with these other distribution are studied. A connection with the theory of disordered systems will be d…
We study the quark-gluon mixed condensate g<\bar{q} σG q> using the SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level. We perform the first but accurate measurement of the thermal effects on the mixed condensate in lattice QCD at β= 6.0 with 16^3 * Nt (Nt=16,12,10,8,6,4), β= 6.1 with 20^3 * Nt (Nt=20,12,10,8,6), and β= 6.2 with 24^3 * Nt (Nt=24,16,12,10,8). At each temperature, the lattice calculation is carried out with high statistics using more than 100 gauge configurations. In particular, about 1000 gauge configurations are used near the critical temperature T_c. The…
We consider the chiral condensate in the baryonic dense medium using the generalized Sakai-Sugimoto model. It is defined as the vacuum expectation value of open Wilson line that is proposed to be calculated by use of the area of world-sheet instanton. We evaluate it in confined as well as deconfined phase. In both phases, the chiral condensate has a minimum as a function of baryon density. In the deconfined phase, taking into account the chiral symmetry restoration, we classify the behavior of chiral condensate into three types. One can set the parameter of the theory such that the results, in…
The recently proposed hard-pion chiral perturbation theory predicts that the leading chiral logarithms factorize with respect to the energy dependence in the chiral limit. This claim has been successfully tested in the pion form factors up to two loops in chiral perturbation theory. In the present paper we explain this factorization property at two loops and even show that it is valid to all orders for a subclass of diagrams. We also demonstrate that factorization is violated starting at three loops.
The thermal and nonthermal pion production by sigma decay and its relation with chiral symmetry restoration in a hot and dense matter are investigated. The nonthermal decay into pions of sigma mesons which are popularly produced in chiral symmetric phase leads to a low-momentum pion enhancement as a possible signature of chiral phase transition at finite temperature and density.
The relation between the chiral quark condensate in QCD sum rules and chiral perturbation theory is clarified with the help of a low-energy theorem for the scalar and pseudoscalar correlation functions. It is found that the quark condensate should be identified with the non-normal-ordered vacuum expectation value of quark-antiquark fields. Utilising results on flavour SU(3) breaking of the quark condensate from QCD sum rules, the unphysical low-energy constant H_2^r in the chiral Lagrangian, as well as next-to-leading order corrections to the Gell-Mann-Oakes-Renner relation are estimated.
