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/or b_1 parameter in U has density dependence.
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.
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.
The pion form factor calculation in the ``point-form'' of relativistic quantum mechanics is re-considered. Particular attention is given to the relation between the momentum of the system and the momentum transfer as well as to the quark current.
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.
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.
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 calculate isospin breaking in pion-nucleon scattering in the threshold region in the framework of covariant baryon chiral perturbation theory. All effects due to quark mass differences as well as real and virtual photons are consistently included. As an application, we discuss the energy dependence of the triangle relation that connects elastic scattering on the proton pi+- p --> pi+- p with the charge exchange reaction pi- p --> pi0 n.
We re-examine one-pion exchange as a possible binding mechanism in the X(3872) charmonium-like state and argue it to be not sufficiently binding for this purpose. We conclude therefore that other short-range dynamics are responsible for the X formation.
We provide a detailed discussion of the low-energy proton-deuteron system in pionless effective field theory, considering both the spin-quartet and doublet S-wave channels. Extending and amending our previous work on the subject, we calculate the 3He-3H binding energy difference both perturbatively (using properly normalized trinucleon wave functions) and non-perturbatively by resumming all O(alpha) Coulomb diagrams in the doublet channel. Our nonperturbative result agrees well with a calculation that involves the full off-shell Coulomb T-matrix. Carefully examining the cutoff-dependence in th…
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 re-investigate Adler's PCAC relation in the presence of an external electromagnetic field within the framework of QCD coupled to external fields. We discuss pion electroproduction within a tree-level approximation to chiral perturbation theory and explicitly verify a chiral Ward identity referred to as the Adler-Gilman relation. We critically examine soft-momentum techniques and point out how inadmissable approximations may lead to results incompatible with chiral symmetry. As a result we confirm that threshold pion electroproduction is indeed a tool to obtain information on the axial form …
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 finit…
We use a recently improved density-matrix expansion to calculate the nuclear energy density functional in the framework of in-medium chiral perturbation theory. Our calculation treats systematically the effects from $1π$-exchange, iterated $1π$-exchange, and irreducible $2π$-exchange with intermediate $Δ$-isobar excitations, including Pauli-blocking corrections up to three-loop order. We find that the effective nucleon mass $M^*(ρ)$ entering the energy density functional is identical to the one of Fermi-liquid theory when employing the improved density-matrix expansion. The strength $F_\nabla(…
The posibility of large charge and isospin fluctuations in high-energy heavy ion-collisions is studied within the framework of the nonlinear $σ$-model with quark degrees of freedom. The multipion exchange potential between two quarks is derived. It is shown that the soft chiral pion bremsstralung leads to anomalously large fluctuations in the ratio of neutral to charged pions, predicted by the formation of a disoriented chiral condensate (DCC). The factorization property of the scattering amplitude in the impact parameter space of the leading two-nucleon system is used to study semiclassical p…
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 use a Nambu-Jona Lasinio type model to investigate the phase diagram of dense quark matter under neutron star conditions in mean field approximation. The model contains selfconsistently determined quark masses and allows for diquark condensation in the scalar as well as in the pseudoscalar channel. The latter gives rise to the possibility of K^0 condensation in the CFL phase. In agreement with earlier studies we find that this CFLK^0 phase covers large regions of the phase diagram and that the predominant part of this phase is fully gapped. We show, however, that there exists a region at ve…
The Fubini-Furlan-Rossetti sum rule for pion photoproduction on the nucleon is evaluated by dispersion relations at constant t, and the corrections to the sum rule due to the finite pion mass are calculated. Near threshold these corrections turn out to be large due to pion-loop effects, whereas the sum rule value is closely approached if the dispersion integrals are evaluated for sub-threshold kinematics. This extension to the unphysical region provides a unique framework to determine the low-energy constants of chiral perturbation theory by global properties of the excitation spectrum.
The isoscalar single-pion production exhibits a broad bump in the energy dependence of the total cross section, which does not correspond to the usual opening of the $N^*(1440)$ production channel with subsequent pion decay. In arxiv:2102.05575 it was interpreted as a narrow Breit-Wigner structure, which leads in a sequential single-pion production process to a possible explanation of the $d^*(2380)$ resonance. We demonstrate that such an attempt fails already, when confronted with the data base for isoscalar single-pion production. We investigate whether the observed bump structure rather poi…
We discuss partial restoration of chiral symmetry in nuclear medium, which is realized as an effective reduction of the quark condensate in nuclear medium. We derive the in-medium Weinberg-Tomozawa relation. We also give a brief calculation of the in-medium quark condensate based on chiral perturbation theory. We conclude that the density dependence of the quark condensate beyond the linear density comes from the vertex correction of the chiral field insertion and nucleon correlations.
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-medium chiral perturbation theory is used to calculate the density dependence of the quark condensate $<\bar qq>$. The corrections beyond the linear density approximation are obtained by differentiating the interaction contributions to the energy per particle of isospin-symmetric nuclear matter with respect to the pion mass. Our calculation treats systematically the effects from one-pion exchange (with $m_π$-dependent vertex corrections), iterated $1π$-exchange, and irreducible $2π$-exchange including intermediate $Δ(1232)$-isobar excitations, with Pauli-blocking corrections up to three-loo…
As a result of a new improved fit to old bubble chamber data of the dominant axial C_5^A nucleon-to-Delta form factor, and due to the relevance of this form factor for neutrino induced coherent pion production, we re-evaluate our model predictions in Phys. Rev. D79, 013002 (2009) for different observables of the latter reaction. Central values for the total cross sections increase by 20% to 30%, while differential cross sections do not change their shape appreciably. Furthermore, we also compute the uncertainties on total, differential and flux averaged cross sections induced by the errors in …
We propose a new, renormalizable approach to nucleon-nucleon scattering in chiral effective field theory based on the manifestly Lorentz invariant form of the effective Lagrangian without employing the heavy-baryon expansion. For the pion-less case and for the formulation based on perturbative pions, the new approach reproduces the known results obtained by Kaplan, Savage and Wise. Contrary to the standard formulation utilizing the heavy-baryon expansion, the nonperturbatively resummed one-pion exchange potential can be renormalized by absorbing all ultraviolet divergences into the leading S-w…
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 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.
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…
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…
Exploiting operator relations in QCD, we derive a novel and model-independent formula relating the in-medium quark condensate <bar-q q>* to the decay constant F*_t and the wave function renormalization constant Z* of the pion in the nuclear medium. Evaluating Z* at low density from the iso-scalar pion-nucleon scattering data, it is concluded that the enhanced repulsion of the s-wave isovector pion-nucleusinteraction observed in the deeply bound pionic atoms implies directly the reduction of the in-medium quark condensate. The knowlege of the in-medium pion mass is not necessary to reach this c…
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 …
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…
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 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…
Understanding single pion production reactions on free nucleons is the first step towards a correct description of these processes in nuclei, which are important for signal and background contributions in current and near future accelerator neutrino oscillation experiments. In this work, we reanalyze our previous studies of neutrino-induced one-pion production on nucleons for outgoing $πN$ invariant masses below 1.4 GeV. Our motivation is to get a better description of the $ν_μn\toμ^- nπ^+$ cross section, for which current theoretical models give values significantly below data. This channel i…
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…
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.
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…
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…
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 q…
Disoriented chiral condensate can produce novel fluctuations of kaons as well as pions. Robust statistical observables can be used to extract the novel fluctuations from background contributions in K-short and K-charged correlation measurements in nuclear collisions. To illustrate how this can be done, I present new event-generator computations of these observables.
I sketch how long wavelength modes of the pion field can be amplified during the QCD phase transition. If nature had been kinder, and had made the pion mass significantly less than the critical temperature for the transition, then this phenomenon would have characterized the transition in thermal equilibrium. Instead, these long wavelength oscillations of the orientation of the chiral condensate can only arise out of equilibrium. There is a simple non-equilibrium mechanism, plausibly operational during heavy ion collisions, which naturally amplifies these oscillations. The characteristic signa…
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…
The pseudoscalar projection of the pion's Poincare'-covariant Bethe-Salpeter amplitude onto the light-front may be understood to provide the probability distribution of the chiral condensate within the pion. Unlike the parton distribution amplitudes usually considered and as befitting a collective effect, this condensate distribution receives contributions from all Fock space components of the pion's light-front wave-function. We compute this condensate distribution using the Dyson-Schwinger equation (DSE) framework and show the result to be a model-independent feature of quantum chromodynamic…
We study the Bose-Einstein condensation of a finite size pion gas subject to the influence of a magnetic field. We find the expressions for the critical chemical potential and temperature for the onset of condensation. We show that for values of the external magnetic flux larger than the elemental flux, the critical temperature is larger than the one obtained by considering only finite size effects. We use experimentally reported values of pion source sizes and multiplicities at LHC energies to show that if the magnetic flux, produced initially in peripheral heavy-ion collision, is at least pa…
We analyze s-wave pion-nucleon scattering in a unitarized chiral effective Lagrangian including all dimension two contact terms. We find that both the S11(1535) and the S11(1650) are dynamically generated, but the S31(1620) is not. We further discuss the structure of these dynamically generated resonances.
The indications of a possible pion condensation at the LHC are summarized. The condensation is predicted by the non-equilibrium hadronization model for 2.76 TeV Pb+Pb collisions at the LHC. The model solves the proton/pion puzzle and reproduces the low $p_T$ enhancement of the pion spectra, as well as the spectra of protons and antiprotons, charged kaons, $K^0_S$, $K^*(892)^0$ and $ϕ(1020)$. The obtained parameters allow to estimate the amount of pion condensate on the level of 5\% from the total number of pions at the LHC. The condensate is located at $p_T<250$ MeV.
The local-duality formulation of QCD sum rules allows for the prediction of hadronic form factors without knowledge of the subtle details of their structure. With the aid of this formalism, we take a fresh look at the behaviours of the charged-pion elastic form factor and of the form factors entering in the transitions of the ground-state neutral unflavoured pseudoscalar mesons pi^0, eta, eta' to one real and one virtual photon within a broad range of momentum transfers Q^2. The uncertainties induced by the approximations inherent to this local-duality approach are estimated by studying, in pa…
The lifetime of a disoriented chiral condensate formed within a heat bath of pions is calculated assuming temperatures and densities attainable at present and future heavy-ion colliders. A generalization of the reduction formula to include coherent states allows us to derive a formula for the decay rate. We predict the half-life to be between 4 and 7 fm/c, depending on the assumed pion density. We also calculate the lifetime in the presence of higher resonances and baryons, which shortens the lifetime by at most 20%.
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 derive the pseudoscalar condensate induced by anomaly and vorticity from the Wigner function for massive fermions in homogeneous electromagnetic fields. It has an anomaly term and a force-vorticity coupling term. As a mass effect, the pseudoscalar condensate is linearly proportional to the fermion mass in small mass expansion. By a generalization to two-flavor and three-flavor cases, the neutral pion and eta meson condensates are calculated from the Wigner function and have anomaly parts as well as force-vorticity parts, in which the anomaly part of the neutral pion condensate is consistent…
We consider a chemical freeze-out mechanism which is based on a strong medium dependence of the rates for inelastic flavor-equilibrating collisions based on the delocalization of hadronic wave functions and growing hadronic radii when approaching the chiral restoration. We investigate the role of mesonic (pion) and baryonic (nucleon) fluctuations for melting the chiral condensate in the phase diagram in the (T,mu)-plane. We apply the PNJL model beyond mean-field and present an effective generalization of the chiral perturbation theory result which accounts for the medium dependence of the pion…
