Partial Restoration Of Chiral Symmetry Research Articles

Spectral functions for D¯ and D¯0* mesons in nuclear matter with partial restoration of chiral symmetry

We investigate the in-medium masses of a $\bar{D} (0^-)$ meson and a $\bar{D}_0^* (0^+)$ meson and spectral functions for $\bar{D}$ and $\bar{D}_0^*$ meson channels in nuclear matter. These mesons are introduced as chiral partner in the chiral symmetry broken vacuum, hence they are useful to explore the partial restoration of the broken chiral symmetry in nuclear matter. We consider the linear sigma model to describe the chiral symmetry breaking. Our study shows that the loop corrections to $\bar{D}$ and $\bar{D}_0^*$ meson masses provide a smaller mass splitting at finite density than that in vacuum, whose result indicates a tendency of the restoration of the chiral symmetry. We investigate also the spectral function for $\bar{D}_0^*$ meson channel, and find three peaks. The first peak which corresponds to the resonance of $\bar{D}_0^*$ meson is broadened by collisions with nucleons in medium, and the peak position shifts to lower mass due to the partial restoration of chiral symmetry as the density increases. The second peak is identified as a threshold enhancement which shows a remarkable enhancement as the density increase. The third peak is Landau damping. The obtained properties of $\bar{D}$ and $\bar{D}_0^*$ mesons in nuclear matter will provide useful information for experiments.

A novel probe of chiral restoration in nuclear medium

We propose measuring the mass shift and width broadening of the f1(1285) meson together with those of the ω from a nuclear target as a means to experimentally probe the partial restoration of chiral symmetry inside the nuclear matter. The relation between the order parameter of chiral symmetry and the difference in the correlation functions of the f1(1285) current and the ω current is discussed in the limit where the disconnected diagrams are neglected. A QCD sum rule analysis of the f1(1285) meson mass leads to about 100 MeV attraction in nuclear matter, which can be probed in future experiments.

In-medium properties of mesons

In the project B.4 , the modification of meson properties (mass, width) in a nuclear medium has been studied in photoproduction of mesons off nuclear targets. This work has been motivated by theoretical expectations of in-medium modifications of hadrons based on the conjecture of a partial restoration of chiral symmetry in a strongly interacting medium. It has been shown that these in-medium changes can be discussed in a compact form in terms of an optical potential describing the meson-nucleus interaction. Experimental approaches to determine the real and imaginary part of the meson-nucleus potential have been developed. The experiments have been performed with the Crystal Barrel/TAPS detector at the electron accelerator ELSA (Bonn) and the Crystal Ball/TAPS detector at MAMI (Mainz). Measuring the excitation function and momentum distribution for photo production of ω and η′ mesons, the real parts of the ω and η′ -nucleus potential, given by the in-medium mass shift, have been determined. For the η′ meson a lowering of the mass at normal nuclear matter density by -(39±7(stat)±15(syst)) MeV is observed, while for the ω meson a slightly smaller mass shift is found, however, with much larger uncertainties, not excluding a zero mass shift. The imaginary part of the potentials has been extracted from the measurement of the transparency ratio which compares the meson production cross section per nucleon within a nucleus to the production cross section off the free proton. For the η′ meson the imaginary part of the potential is found to be smaller than the real part. In case of the ω meson the opposite is observed. This makes the η′ meson a good candidate for the search for meson-nucleus bound states while no resolved ω mesic states can be expected. The results are compared with theoretical predictions. An outlook on future experiments is given.

Partial restoration of chiral symmetry in hot and dense neutron matter

We review efforts to describe the approach to chiral symmetry restoration in neutron matter from the low-energy realization of QCD, chiral effective field theory.

Mass of heavy-light mesons in a constituent quark picture with partially restored chiral symmetry

We probe effects of the partial chiral symmetry restoration to the mass of heavy-light mesons in a constituent quark model by changing the constituent quark mass of the light quark. Due to the competing effect between the quark mass and the linearly rising potential, whose contribution to the energy increases as the quark mass decreases, the heavy-light meson mass has a minimum value near the constituent quark mass typically used in the vacuum. Hence, the meson mass increases as one decreases the constituent quark mass consistent with recent QCD sum rule analyses, which show an increasing $D$ meson mass as the chiral order parameter decreases.

Continuum study of the QCD phase diagram through an OPE-modified gluon propagator

Within the Dyson-Schwinger equations (DSEs) framework, a gluon propagator model incorporating quark's feedback through operator product expansion (OPE) is introduced to investigate the QCD phase diagram in the temperature--chemical-potential ($T-\mu$) plane. Partial restoration of chiral symmetry at zero temperature and finite temperature are both studied, suggesting a first order phase transition point on the $\mu$ axis and a critical end point at $(T_E,\mu_E)/T_c = (0.85,1.11)$, where $T_c$ is the pseudo-critical temperature. In addition, we find the pseudo-critical line can be well parameterized with the curvature parameter $\kappa$ and a consistent decrease in $\kappa$ with more of gluon propagator distributed to quark's feedback.

Phase diagram of the three-flavor color superconducting PNJL model

The phase diagram of a three-flavor Polyakov-loop Nambu-Jona-Lasinio model is analyzed for symmetric matter with a parametrization consistent with the 2 M⊙mass constraint from the pulsars PSR J1614-2230 and PSR J0348+0432. A coexistence of partial chiral symmetry restoration, diquark condensation (2SC phase) and the hadronic (confined) phase is conjectured that entails the existence of a quadruple point and is accessible by trajectories of constant entropy per baryon for heavy-ion collisions in the NICA/FAIR energy range.

Properties of the sigma meson at finite temperature

We study the changes of the mass and width of the sigma meson in the framework of the Linear Sigma Model at finite temperature, in the one-loop approximation. We have found that as the temperature increases, the mass of sigma shifts down. We have also analyzed the [Formula: see text]-spectral function and we observe an enhancement at the threshold which is a signature of partial restoration of chiral symmetry, also interpreted as a tendency to chiral phase transition. Additionally, we studied the width of the sigma, when the threshold enhancement takes place, for different values of the sigma mass. We found that there is a brief enlargement followed by an abrupt fall in the width as the temperature increases, which is also related with the restoration of chiral symmetry and an indication that the sigma is a bound state of two pions.

Baryon and chiral symmetry breaking in holographic QCD

We study the relationship between chiral symmetry breaking and baryons in holographic QCD. We construct a soliton with unit baryon charge in the presence of a nonzero mean value of the scalar bifundamental field, which is dual to the chiral condensate. We obtain a relation between the chiral condensate and the mass of the baryon and find in a clear-cut way that at large values of the condensate the holographic soliton is no longer located on the IR wall. Instead it is split into two halves, which are symmetrically located on the left and right flavor branes. On the other hand we find that the local value of the quark condensate is suppressed in the core of the soliton, which is evidence for a partial chiral symmetry restoration inside the baryon.

Partial restoration of chiral symmetry in the color flux tube

Using the quark eigenmodes computed on the lattice with the overlap-Dirac operator, we investigate the spatial distribution of the chiral condensate around static color sources corresponding to quark-antiquark and three-quark systems. A flux structure of chromo fields appears in the presence of such color charges. The magnitude of the chiral condensate is reduced inside the color flux, which implies partial restoration of chiral symmetry inside hadrons. Taking a static baryon source in a periodic box as a toy model of nuclear matter, we estimate the magnitude of the chiral symmetry restoration as a function of baryon matter density.

Momentum scale dependence of the net quark number fluctuations near chiral crossover

We investigate properties of the net baryon number fluctuations near chiral crossover in a hot and dense medium of strongly interacting quarks. The chirally invariant quark–antiquark interactions are modeled by an effective quark–meson Lagrangian. To preserve remnants of criticality in the |$O(4)$| universality class, we apply the functional renormalization group method to describe thermodynamics near chiral crossover. Our studies are focused on the influence of the momentum cuts on the critical behavior of different cumulants of the net quark number fluctuations. We use the momentum scale dependence of the flow equation to examine how the suppression of the momentum modes in the infrared and ultraviolet regimes modifies generic properties of fluctuations expected in the |$O(4)$| universality class. We show that the pion mass |$m_\pi$| is a natural soft momentum scale at which cumulants are saturated at their critical values, whereas for scales larger than |$2m_\pi$| the characteristic |$O(4)$| structure of the higher-order cumulants gets lost. These results indicate that when measuring fluctuations of the net baryon number in heavy ion collisions to search for a partial restoration of chiral symmetry or critical point, special care must be taken when introducing kinematical cuts on the fluctuation measurements.

Spectroscopy of η′-nucleus bound states at GSI and FAIR — very preliminary results and future prospects —

The possible existence of \eta'-nucleus bound states has been put forward through theoretical and experimental studies. It is strongly related to the \eta' mass at finite density, which is expected to be reduced because of the interplay between the $U_A(1)$ anomaly and partial restoration of chiral symmetry. The investigation of the C(p,d) reaction at GSI and FAIR, as well as an overview of the experimental program at GSI and future plans at FAIR are discussed.

The decay into 3 in asymmetric nuclear medium

We explore how the $\eta$-$\pi^0$ mixing angle and the $\eta$ meson decay into $\pi^{+}\pi^{-}\pi^0$ and 3$\pi^{0}$ are modified in the nuclear medium on the basis of the in-medium chiral effective theory with the isospin asymmetry $\alpha$ varied, where $\alpha\equiv \delta\rho/\rho$ with $\delta \rho=\rho_n-\rho_p$ and $\rho=\rho_n+\rho_p$. We find that the larger the isospin asymmetry $\delta \rho$ and smaller the total density $\rho$, the more enhanced the mixing angle. We show that the decay width in the nuclear medium has an additional density dependence which cannot be renormalized into that of the mixing angle: The additional term originates from the vertex proportional to a low energy constant $c_1$, which only comes into play in the nuclear medium but not in the free space. It turns out that the resultant density effect on the decay widths overwhelms that coming from the isospin asymmetry, and the higher the $\rho$, the more enhanced the decay widths; the width for the $\pi^{+}\pi^{-}\pi^0$ decay is enhanced with a factor two to three at the normal density $\rho_0$ with a minor increase due to $\delta \rho$, while that for the 3$\pi^0$ decay shows only a small increase of around 10 percent even at $\rho_0$. We mention the possible relevance of the partial restoration of chiral symmetry to the unexpected density effect on the decay widths in the nuclear medium.

Electromagnetic radiation in hot QCD matter: Rates, electric conductivity, flavor susceptibility, and diffusion

We discuss the general features of the electromagnetic radiation from a thermal hadronic gas as constrained by chiral symmetry. The medium effects on the electromagnetic spectral functions and the partial restoration of chiral symmetry are quantified in terms of the pion densities. The results are compared with the electromagnetic radiation from a strongly interacting quark-gluon plasma in terms of the leading gluon condensate operators. We use the spectral functions as constrained by the emission rates to estimate the electric conductivity, the light flavor susceptibility and diffusion constant across the transition from the correlated hadronic gas to a strongly interacting quark-gluon plasma.

Partial restoration of chiral symmetry in a confining string

We attempt to describe the interplay of confinement and chiral symmetry breaking in QCD by using the string model. We argue that in the quasi-abelian picture of confinement based on the condensation of magnetic monopoles and the dual Meissner effect, the worldsheet dynamics of the confining string can be effectively described by the $1+1$ dimensional massless electrodynamics, which is exactly soluble. The transverse plane distribution of the chromoelectric field stretched between the quark and antiquark sources can then be attributed to the fluctuations in the position of the string. The dependence of the chiral condensate in the string on the (chromo-)electric field can be evaluated analytically, and is determined by the chiral anomaly and the $\theta$-vacuum structure. Therefore, our picture allows to predict the distribution of the chiral condensate in the plane transverse to the axis connecting the quark and antiquark. This prediction is compared to the lattice QCD results; a good agreement is found.

Pion and Sigma Meson Dissociation in a Modified NJL Model at Finite Temperature

We investigate pion and sigma meson correlations in hot quark matter within a modified NJL model. Special emphasis is on the transformation of mesonic bound states to resonances (Mott dissociation) when due to the partial chiral symmetry restoration with increasing temperature the threshold of quark-antiquark continuum states drops below the meson mass at the corresponding Mott temperature. The description is based on evaluating the polarization functions for quark-antiquark (meson) correlations as a function of the temperature and the results can be represented by introducing modulus and phase of the complex propagator functions for the mesonic states. We study the effect of modelling confinement by introducing a low-momentum cutoff in loop integrals. We make the ansatz that this cutoff is identified with the dynamically generated quark mass gap and find an increase of the continuum threshold which makes the otherwise unbound sigma meson a bound state in the vacuum. We discuss the in-medium behavior of the mesonic phase shifts including the Mott effect and find accordance with the Levinson theorem.

ABC effect as a signal of chiral symmetry restoration in hadronic collisions

A new nonconventional mechanism for the basic 2{\pi}-fusion reaction pn --> d+({\pi}{\pi})_0 in the energy region T_p = 1.0-1.4 GeV is suggested. The mechanism is aimed at providing a consistent explanation for the comprehensive experimental studies of this reaction in exclusive setting done recently by the WASA-at-COSY Collaboration. The basic assumption of the model proposed is the production of the I(JP) = 0(3+) dibaryon resonance D03 in the pn collision. The interference of two decay channels of this resonance: D_03 --> d + {\sigma} --> d + ({\pi}{\pi})_0 and D_03 --> D_12 + {\pi} --> d + ({\pi}{\pi})_0 is shown to give a strong near-threshold enhancement in the {\pi}{\pi} invariant mass spectrum, which is well known as the ABC effect. The {\sigma}-meson parameters found to reproduce the ABC enhancement are in a general agreement with models which predict the chiral symmetry restoration at high excitation energy and/or high density of matter, although they are essentially less than those accepted for the free {\sigma} meson. So, this result might be considered as an indication of partial chiral symmetry restoration in dense and excited quark matter.

Spectroscopy of η′ Mesic Nuclei with (p, d) Reaction

We are going to perform an inclusive spectroscopy experiment of eta' mesic nuclei with the 12C(p,d) reaction to study in-medium properties of the eta' meson. In nuclear medium, the eta' meson mass may be reduced due to partial restoration of chiral symmetry. In case of sufficiently large mass reduction and small absorption width of eta' at normal nuclear density, peak structures of eta' mesic states in 11C will be observed near the eta' emission threshold even in an inclusive spectrum. The experiment will be carried out at GSI with proton beam supplied by SIS using FRS as a spectrometer. The detail of the experiment is described.

Formation of Deeply Bound Pionic Atoms in Sn Isotopes

We study the formation of deeply bound pionic atoms in the (d,3He) reaction theoretically. At different scattering angles, we find that the different subcomponents dominate the formation spectra because of the matching condition of the reaction. We also find that the pionic 1s state which is free from the residual interaction effects appears clearly in 117Sn(d, 3He) spectra. We conclude that the observation of the (d,3He) reaction for these new cases will provide more systematic and accurate information on the pionic bound states, and it will help to develop the study of the pion properties and the partial restoration of chiral symmetry in nuclei.

Dilepton Spectroscopy of QCD Matter at Collider Energies

Low-mass dilepton spectra as measured in high-energy heavy-ion collisions are a unique tool to obtain spectroscopic information about the strongly interacting medium produced in these reactions. Specifically, in-medium modifications of the vector spectral function, which is well known in the vacuum, can be deduced from the thermal radiation off the expanding QCD fireball. This, in particular, allows to investigate the fate of theρresonance in the dense medium and possibly infer from it signatures of the (partial) restoration of chiral symmetry, which is spontaneously broken in the QCD vacuum. After briefly reviewing calculations of thermal dilepton emission rates from hot QCD matter, utilizing effective hadronic theory, lattice QCD, or resummed perturbative QCD, we focus on applications to dilepton spectra at heavy-ion collider experiments at RHIC and LHC. This includes invariant-mass spectra at full RHIC energy with transverse-momentum dependencies and azimuthal asymmetries, as well as a systematic investigation of the excitation function down to fixed-target energies, thus making contact to previous precision measurements at the SPS. Furthermore, predictions for the energy frontier at the LHC are presented in both dielectron and dimuon channels.