Cold and dense matter may break rotational symmetry spontaneously and thus form an anisotropic phase in the interior of neutron stars. We consider the concrete example of an anisotropic chiral condensate in the form of a chiral density wave. Employing a nucleon-meson model and taking into account fermionic vacuum fluctuations, we improve and extend previous results by imposing the conditions of electric charge neutrality and electroweak equilibrium, by allowing for a more general form of the vector meson self-interactions, and by including properties of pure neutron matter into the fit of the model parameters. We find that the conditions inside neutron stars postpone the onset of the chiral density wave to larger densities compared to isospin-symmetric nuclear matter. While this still allows for the construction of stars with an anisotropic core, we find that the chiral density wave is energetically preferred only in a corner of the parameter space where matter is too soft to generate stars with realistic masses. Therefore, taking into account constraints from astrophysical data, our calculation predicts an isotropic neutron star core.
The role of chiral symmetry in nuclear physics is summarized. The topics treated are the chiral bag model for nucleon structure resulting from large $N_c$ QCD, the pion cloud in chiral perturbation theory for low-energy electroweak nuclear response functions, ``swelled hadrons" in nuclear matter, chiral symmetry restoration in terms of the Georgi vector limit and pseudo-Goldstone meson condensation in nuclear medium.
We discuss two topics concerning the application of chiral perturbation theory to nuclear physics: (1) the latest developments in the study of possible kaon condensation in dense baryonic systems; (2) nuclear responses to electro-weak probes.
I discuss the progress we have made on modifying Weinberg's prescription for chiral nuclear forces, using renormalization group invariance as the guideline. Some of the published results are presented.
A compressible liquid-drop approach adjusted to uniform matter many-body calculations based on chiral EFT interactions and to the experimental nuclear masses is used to investigate the neutron star crust properties. Eight chiral EFT hamiltonians and a representative phenomenological force (SLy4) are confronted. We show that some properties of the crust, e.g. clusters mass, charge, and asymmetry, are mostly determined by symmetric matter properties close to saturation density and are therefore mainly constrained by experimental nuclear masses, while other properties, e.g., energy per particle, …
Infinite sets of sum rules involving the excitations of infinite nuclear matter are derived using only completeness, the current algebra implicit in QCD, and relativistic covariance. The sum rules can be used for isospin-asymmetric nuclear matter, including neutron matter. They relate the chiral condensate and the isospin density to weighted sums over states with fixed velocity relative to the nuclear matter ground state.
We study inhomogeneous chiral phases in nuclear matter using a hadronic model with the parity doublet structure. With an extended ansatz for the dual chiral density wave off the chiral limit, we numerically determine the phase structure. A new type of dual chiral density wave where the condensate has nonvanishing space average is confirmed and it comes to occupy a wide range of low density region as the chiral invariant mass parameter is lowered.
I discuss in this lecture how to make a connection between effective chiral Lagrangians -- low-energy effective theory of QCD -- and Landau Fermi liquid theory extended by Migdal to nuclear matter. The practical purpose of such a connection is to provide a link between certain observables in relativistic heavy-ion processes and those in low-energy spectroscopy, giving a new insight into how chiral dynamics manifests itself in nuclear systems.
In this talk we present a description of nuclear binding in a chiral approach based on the existence of a chiral invariant scalar field associated with the generation of the masses through spontaneous chiral symmetry breaking. We discuss the emergence of such a field on the example of the NJL model. We also incorporate the effect of confinement at the level of the nucleon substructure to stabilize nuclear matter. In a particular quark-diquark model we illustrate the simutaneous influences of spontaneous chiral symmetry breaking and confinement on the nucleon mass and on the nuclear matter desc…
The link between non-linear chiral effective Lagrangians and the Walecka model description of bulk nuclear matter [1] is questioned. This fact is by itself due to the Mean Field Approximation (MFA) which in nuclear mater makes the picture of a nucleon-nucleon interaction based on scalar(vector) meson exchange, equivalent to the description of a nuclear matter based on attractive and repulsive contact interactions. We present a linear chiral model where this link between the Walecka model and an underlying to chiral symmetry realization still holds, due to MFA.
We discuss how the possible changes of hadron properties can be tested, associated with the chiral transition in nuclear medium; the hadrons discussed are the vector mesons,the $σ$ meson and the chiral partner of the nucleon. We emphasize that the proper quantity is the spectral function which describes the nuclear medium having a hadron; the analysis of electro-quasielastic reactions, for instance, has a relevance to the physics of CERES. The similarity is indicated between the physics discussed here with that of giant resonances. Experiments using nuclear targets are proposed to observe the …
Two aspects of the QCD phase diagrams are studied in the limit of a large number of colors: at zero temperature and nonzero density the (non)existence of nuclear matter, and at zero density and nonzero temperature the chiral phase transition.
Here we point out that the four-nucleon terms incorporate into lowest order non-linear chiral effective Lagrangians the same description of bulk nuclear matter contained in the Walecka model, that is generally considered satisfactory. We find this point worth noticing because, while the Walecka model is an entirely phenomenological renormalizable model, non-linear chiral Lagrangians have a deep basis in elementary particle physics, and, in this sense, are more fundamental.
Following Golterman and Shamir, we develop scale-chiral perturbation theory in the large $N_c$ and large $N_f$ Veneziano limit that incorporates both light-quark baryons and hidden local symmetric bosons and derive a leading-order scale symmetry Lagrangian applicable in nuclear physics. Some applications in the medium-free space and baryonic matter are discussed.
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.
The effective field theory of NN interactions in nuclear matter is considered. Due to the Pauli principle the effective NN amplitude is not affected by the shallow bound states. We show that the next-to-leading order terms in the chiral expansion of the effective NN potential can be interpreted as corrections so the expansion is systematic. The value of potential energy per particle is calculated and some issues concerning the chiral effective theory of nuclear matter are outlined.
We study the Dual Chiral Density Wave (DCDW) in nuclear matter using a hadronic model with the parity doublet structure. We first extend the ordinary DCDW ansatz so as to incorporate the effect of an explicit chiral symmetry breaking. Then via numerically evaluating and minimizing the effective potential, we determine the phase structure. We find, in addition to the ordinary DCDW phase where the space average of the chiral condensate vanishes, a new DCDW phase (sDCDW) with a nonvanishing space average depending on the value of the chiral invariant mass parameter.
The important role played by chiral symmetry and axial anomaly in QCD in nuclear physics is reviewed. Some recent topics on possible chiral restoration in hot and/or dense matter are picked up. We also discuss so called {\em effective} restoration of chiral anomaly hot and/or dense matter, as may be seen in a character change of $η'$ meson.
The thermal properties of cold dense nuclear matter are investigated with chiral perturbation theory. The evolution curves for the baryon number density, baryon number susceptibility, pressure and the equation of state are obtained. The chiral condensate is calculated and our result shows that when the baryon chemical potential goes beyond $1150 \mathrm{MeV}$, the absolute value of the quark condensate decreases rapidly, which indicates a tendency of chiral restoration.
The real part of the $K^{+}$ selfenergy for the interaction of the $K^{+}$ with the pion nuclear cloud is evaluated in lowest order of chiral perturbation theory and is found to be exactly zero in symmetric nuclear matter. This removes uncertainties in that quantity found in former phenomenological analyses and is supported by present experimental data on $K^{+}$ nucleus scattering.
Within an effective non-linear chiral model, we evaluate nuclear matter parameters exploiting the uncertainties in the nuclear saturation properties. The model is sternly constrained with minimal free parameters, which display the interlink between nuclear incompressibility ($K$), the nucleon effective mass ($m^{\star}$), the pion decay constant ($f_π$) and the $σ-$meson mass ($m_σ$). The best fit among the various parameter set is then extracted and employed to study the resulting Equation of state (EOS). Further, we also discuss the consequences of imposing constraints on nuclear EOS from He…
Chiral symmetry, first entering in nuclear physics in the 1970's for which Gerry Brown played a seminal role, has led to a stunningly successful framework for describing strongly-correlated nuclear dynamics both in finite and infinite systems. We review how the early germinal idea, conceived with the soft-pion theorems in the pre-QCD era, has evolved into a highly predictive theoretical framework for nuclear physics, aptly assessed by Steven Weinberg: "it (chiral effective field theory) allows one to show in a fairly convincing way that what they (nuclear physicists) have been doing all along.…
Chiral effective lagrangians may differ in their prediction of meson-nucleon scattering amplitudes off-meson-mass-shell, but must yield identical S-matrix elements. We argue that the effective meson mass in nuclear matter obtained from chiral effective lagrangians is also unique. Off-mass-shell amplitudes obtained using the PCAC choice of pion field must therefore not be viewed as fundamental constraints on the dynamics, the determination of the effective meson mass in nuclear matter or the possible existence of meson condensates in the ground state of nuclear matter. This hypothesis is borne …
We investigate how the masses of the singly heavy baryons undergo changes in nuclear matter, based on a medium-modified SU(3) chiral soliton model. Having explained the bulk properties of nuclear matter, we discuss the masses of the singly heavy baryons in nuclear matter. We generalize the vector-meson Lagrangian including the heavy-meson soliton interaction. The mass spectrum of the singly heavy baryon are obtained with the effects of explicit SU(3) symmetry breaking considered as a perturbation. The results show that the mass of the singly heavy baryon mass in nuclear medium is rather sensit…
Understanding the properties of atomic nuclei and nuclear dynamics from QCD remains a major challenge. Complementary to first attempts along these lines based on lattice QCD, an effective field theory approach has been developed in the past two decades and applied to a variety of nuclear bound states and reactions. I outline the foundations of this method, review selected applications and address some open challenges in this field.
We present a model for describing nuclear matter at finite density based on quarks interacting with chiral fields, sigma and pion. The chiral Lagrangian also includes a logarithmic potential, associated with the breaking of scale invariance. We provide results for the soliton in vacuum and at finite density, using the Wigner-Seitz approximation. We show that the model can reach higher densities respect to the Linear-sigma model, up to approximately 3 rho_0 for m_sigma=1200 MeV.
We calculate shell-model matrix elements of the axial-charge exchange current operators that have been obtained up to the next-to-leading order from heavy-fermion chiral perturbation theory. It is found that loop corrections to the soft one-pion-exchange contribution are small (around 10 \%) and have no significant dependence on the nuclear mass number or on the valence-nucleon orbits. These results render further support to the chiral-filtering conjecture.
Chiral perturbation theory supplemented by the Omnes function is employed to study the strength of the isoscalar central nuclear interaction, G_S, in the chiral limit vs the physical case. A very large modification is seen, i.e. eta_s = G_S ~ chiral /G_S ~ physical = 1.37 +- 0.10 . This large effect is seen to arise dominantly at low energy from the extra contributions made by massless pions at energies near the physical threshold where the physical spectral function must vanish kinematically. The slope away from the chiral limit, d_S, is also calculated and is correspondingly large. I also ex…
We consider an effective field theory of NN system in nuclear medium. The shallow bound states, which complicate the effective field theory analysis and lead to the large scattering length in the vacuum case do not exist in matter. We study whether the chiral expansion of the effective potential can be truncated in such situation. The cutoff regularization is used to render the solution of the Bethe-Goldstone equation finite. We show that the next-to-leading order terms in the chiral expansion of the effective NN potential can indeed be interpreted as corrections so that the truncation of the …
The effective chiral theory of the in-medium NN interactions is considered. The shallow bound states, which complicate the effective field theory analysis in vacuum do not exist in matter. We show that the next-to-leading order terms in the chiral expansion of the effective Lagrangian can be interpreted as corrections so that the expansion is systematic. The Low Energy Effective Constants of this Lagrangian are found to satisfy the concept of naturalness. The potential energy per particle is calculated. The problems and challenges in constructing the chiral theory of nuclear matter are outline…
We propose a novel way to formulate Chiral Perturbation Theory in a nuclear background, characterized by a static, non-uniform distribution of the baryon number that describes the finite nucleus. In the limiting case of a uniform distribution, the theory reduces to the well-known zero-temperature in-medium ChPT. The proposed approach is used to calculate the self-energy of the charged pion in the background of the heavy nucleus at O(p^5) in the chiral expansion, and to derive the leading terms of the pion-nucleus optical potential.
In-medium subthreshold KbarN scattering amplitudes calculated within a chirally motivated meson-baryon coupled-channel model are used self consistently to confront K^- atom data across the periodic table. Substantially deeper K^- nuclear potentials are obtained compared to the shallow potentials derived in some approaches from threshold amplitudes, with Re V_{chiral} = -(85+/-5) MeV at nuclear matter density. When KbarNN contributions are incorporated phenomenologically, a very deep K^- nuclear potential results, Re V_{chiral+phen.} = -(180+/-5) MeV, in agreement with density dependent potenti…
We shed light upon the eta' mass in nuclear matter in the context of partial restoration of chiral symmetry, pointing out that the U_{A}(1) anomaly effects causes the eta'-eta mass difference necessarily through the chiral symmetry breaking. As a consequence, it is expected that the eta' mass is reduced by order of 100 MeV in nuclear matter where partial restoration of chiral symmetry takes place. The discussion given here is based on Ref. [1].
Spontaneously broken chiral symmetry is an established property of low-energy quantum chromodynamics, but finding direct evidence for it from nuclear structure data is a difficult challenge. Indeed, phenomenologically successful energy-density functional approaches do not even have explicit pions. Are there smoking guns for chiral symmetry in nuclei?
We review a new generation of nuclear forces derived in chiral effective field theory using the recently proposed semilocal regularization method. We outline the conceptual foundations of nuclear chiral effective field theory, discuss all steps needed to compute nuclear observables starting from the effective chiral Lagrangian and consider selected applications in the two- and few-nucleon sectors. We highlight key challenges in developing high-precision tree-body forces, such as the need to maintain consistency between two- and many-body interactions and constraints placed by the chiral and ga…
These are personal recollections of how Gerry Brown's work and thinking influenced the development of the chiral effective Lagrangian based theory of nuclear forces.
Inspired by recent work on inhomogeneous chiral condensation in cold, dense quark matter within models featuring quark degrees of freedom, we investigate the chiral density-wave solution in nu- clear matter at zero temperature and nonvanishing baryon number density in the framework of the so-called extended linear sigma model (eLSM). The eLSM is an effective model for the strong interaction based on the global chiral symmetry of quantum chromodynamics (QCD). It contains scalar, pseudoscalar, vector, and axial-vector mesons as well as baryons. In the latter sector, the nucleon and its chiral pa…
We present a model for describing nuclear matter at finite density based on quarks interacting with chiral fields, σand πand with vector mesons introduced as massive gauge fields. The chiral Lagrangian includes a logarithmic potential, associated with the breaking of scale invariance. We provide results for the soliton in vacuum and at finite density, using the Wigner-Seitz approximation. We show that the model can reach higher densities respect to the linear-σmodel and that the introduction of vector mesons allows to obtain saturation. This result was never obtained before in similar approach…
We argue that the effective pion mass in nuclear matter obtained from chiral effective lagrangians is unique and does not depend on off-mass-shell extensions of the pion fields as e.g. the PCAC choice. The effective pion mass in isospin symmetric nuclear matter is predicted to increase slightly with increasing nuclear density, whereas the effective time-like pion decay constant and the magnitude of the density-dependent quark condensate decrease appreciably. The in-medium Gell-Mann-Oakes-Renner relation as well as other in-medium identities are studied in addition. Finally, several constraints…
We investigate modifications of mass and decay width of $N^*(1535)$ in nuclear matter in a chiral symmetric way. The nucleon and $N^*(1535)$ are introduced by a parity doublet model, and nuclear matter is constructed by one-loop diagrams of the nucleon and $N^*(1535)$. The decay width of $N^*(1535)$ is studied respecting chiral symmetry. Our calculations show that the partial width of $Γ_{N^*\to Nπ}$ is slightly broadened by a collisional broadening, and that of $Γ_{N^*\to Nη}$ is drastically suppressed at density. As a result, the total decay width $Γ_{\rm tot}$ gets small at density. These m…
It is shown that an enhancement in the spectral function near 2$m_π$ threshold in the I=J=0 channel is a good signal of the partial restoration of chiral symmetry in nuclear medium. Several experiments are discussed to detect the enhancement, which uses hadron-nucleus and photo-nucleus reactions.
A survey is given on selected topics concerning the role of spontaneous chiral symmetry breaking in low-energy QCD, and its dynamical implications for nuclear systems. This includes aspects of chiral thermodynamics (the temperature and density dependence of the chiral condensate). It also includes an update on the theory of low-energy (s-wave) pion-nuclear interactions relevant for deeply-bound states of pionic atoms and the quest for possible fingerprints of chiral symmetry restoration in nuclear systems.
Spectral enhancement near the 2m_π threshold in the I=J=0 channel in nuclei is shown to be a distinct signal of the partial restoration of chiral symmetry. The relevance of this phenomenon with the possible detection of 2π^{0} and 2γin hadron-nucleus and photo-nucleus reactions is discussed.
Chiral effective field theory has established itself as the method of choice to study nuclear forces and low-energy nuclear dynamics. I review the status and prospects of this approach and discuss ongoing efforts to advance the precision frontier for ab initio description of few-nucleon systems. Special emphasis is put on the precise determination of the two-nucleon force at fifth order in the chiral expansion, role of the chiral symmetry, the convergence pattern of the chiral expansion and the quantification of the theoretical uncertainties. The discussed topics are essential for ongoing stud…
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.
We consider a chiral baryon-meson model for nucleons and their parity partners in mirror assignment interacting with pions, sigma and omega mesons to describe the liquid-gas transition of nuclear matter together with chiral symmetry restoration in the high density phase. Within the mean-field approximation the model is known to provide a phenomenologically successful description of the nuclear-matter transition. Here, we go beyond this approximation and include mesonic fluctuations by means of the functional renormalization group. While these fluctuations do not lead to major qualitative chang…
A simple relation between the effective parameters of chiral Lagrangians in medium as predicted by BR scaling and Landau Fermi liquid parameters is derived. This provides a link between an effective theory of QCD at mean-field level and many-body theory of nuclear matter. It connects in particular the scaling vector-meson mass probed by dileptons produced in heavy-ion collisions (e.g., CERES of CERN-SPS) to the scaling nucleon-mass relevant for low-energy spectroscopic properties, e.g., the nuclear gyromagnetic ratios $δg_l$ and the effective axial-vector constant $g_A^\star$.
We derive a nonlocal effective Lagrangian for the chiral magnetic effect. An electric field is generated by winding number fluctuations of the nonabelian gauge field in the presence of a strong magnetic field. We estimate the magnitude of charge asymmetry fluctuations with respect to the reaction plane induced by the chiral magnetic effect in relativistic heavy ion collisions to be less than $10^{-6}$, several orders of magnitude smaller than the signal observed in the STAR experiment.
We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant one-body contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two- and three-nucleon contributions to the charge and current operators and pseudoscalar operators…
Spectral functions of the pseudoscalar $D$ meson in the nuclear medium are analyzed using QCD sum rules and the maximum entropy method. This approach enables us to extract the spectral functions without any phenomenological assumption, and thus to visualize in-medium modification of the spectral functions directly. It is found that the reduction of the chiral condensates of dimension 3 and 5 causes the masses of both $D^+$ and $D^-$ mesons to grow gradually at finite density. Additionally, we construct charge-conjugate-projected sum rules and find a $D^+$-$D^-$ mass splitting of about -15 MeV …
We introduce an effective chiral Lagrangian with a dilaton responsible for the trace anomaly in QCD. As the "dilaton limit" is taken, which drives a system to near chiral restoration density, a linear sigma model emerges from the highly non-linear structure. A striking prediction is that the vector-meson--nucleon interaction gets strongly suppressed when the dilaton limit is approached. Its phenomenological implications for the thermodynamics of dense baryonic matter are briefly discussed.
In these proceedings, we discuss the current status of nuclear bound state predictions based on chiral nuclear interactions. Results of ordinary $s$- and $p$-shell nuclei and light hypernuclei are shown.
