Partial Restoration Of Chiral Symmetry Research Articles

Exploring quantum entanglement in chiral symmetry partial restoration with 1+1 string model

Within the confining color flux tube picture, we assess the color electric field generated by quark-antiquark pairs within the framework of the Schwinger model and estimate its impact on the chiral condensate. We observe differences in the distribution of the color flux tube generated by quark-antiquark pairs at different separation distances, leading to discrepancies in the partial restoration of chiral symmetry. Furthermore, we suggest incorporating the color magnetic field in the calculation of chiral condensate, leading to quantum entanglement effects, and proceed to compute the entanglement entropy. We observe that the entanglement entropy increases with the distance of the color source (the separation distance between quark and anti-quark), and the magnitude of the color electric field and chiral condensate restoration after spatial integration also increases with the distance of the color source. Then, we try to provide a qualitative explanation for the existence of these phenomena.

The V-QCD baryon: numerical solution and baryon spectrum

The single baryon solution of V-QCD is numerically computed. The spectrum of spin and isospin modes is also computed by quantizing the light fluctuations around the baryon. It is shown that there is a partial restoration of chiral symmetry at the baryon center.

Strong decays of singly heavy baryons from a chiral effective theory of diquarks

A chiral effective theory of scalar and vector diquarks is formulated, which is based on $SU(3)_R\times SU(3)_L$ chiral symmetry and includes interactions between scalar and vector diquarks with one or two mesons. We find that the diquark interaction term with two mesons breaks the $U(1)_A$ and flavor $SU(3)$ symmetries. To determine the coupling constants of the interaction Lagrangians, we investigate one-pion emission decays of singly heavy baryons $Qqq$ ($Q=c, b$ and $q=u,d,s$), where baryons are regarded as diquark--heavy-quark two-body systems. Using this model, we present predictions of the unobserved decay widths of singly heavy baryons. We also study the change of masses and strong decay widths of singly heavy baryons under partial restoration of chiral symmetry.

Commissioning of the electron identification system for Dilepton measurement in pA collisions at J-PARC

Hadron mass spectra are expected to be modified in nuclear matter due to a partial restoration of chiral symmetry. We perform the J-PARC E16 experiment to measure the spectral modification of vector mesons in nuclei. We detect electron–positron pairs from decays of ϕ mesons, produced in 30 GeV pA reactions. It is a key for our experiment to separate electrons from huge hadronic backgrounds. To identify electrons, we developed two-stage detectors comprising hadron blind detectors (HBDs) and lead-glass electromagnetic calorimeters (LGs). These detectors were constructed and installed at the J-PARC high-momentum beamline in 2020, and commissioning runs were performed in 2020 and 2021. The HBDs and the LGs were stably operated at a high counting rate generated in 10-MHz pA interaction at targets, and successfully detected electrons. In the preliminary results, the pion rejection powers were found to be 97.6 ± 0.6% and 91.2 ± 0.7% for the HBD and LG, respectively, which are consistent with the design performance, at the operation thresholds. Further evaluation of electron efficiency is ongoing.

Chiral symmetry restoration and Δ matter formation in neutron stars

We analyze the effects of chiral symmetry restoration in hadronic matter, including the lowest-lying baryonic resonance $\Delta$ based on the parity doublet model. We study the role of $\Delta$ and its chiral partner on the equation of state (EoS) of dense matter under neutron star (NS) conditions of $\beta$-equilibrium and charge neutrality. We find that the softening of the EoS driven by the early onset of $\Delta$ matter due to partial restoration of chiral symmetry allows accommodating the modern multi-messenger astrophysical constraints on the mass, radius, and tidal deformability. The softening above the saturation density is accompanied by subsequent stiffening at high densities. We also find that the matter composition in the NS cores may be different upon variations of the repulsive interactions of $\Delta$ baryons in hadronic matter.

Reconciling Multi-messenger Constraints with Chiral Symmetry Restoration

Abstract We analyze the recent astrophysical constraints in the context of a hadronic equation of state (EoS) in which the baryonic matter is subject to chiral symmetry restoration. We show that with such EoS it is possible to reconcile the modern constraints on the neutron star (NS) mass, radius, and tidal deformability (TD). We find that the softening of the EoS, required by the TD constraint of a canonical 1.4 M ⊙ NS, followed by a subsequent stiffening, required by the 2 M ⊙ constraint, is driven by the appearance of Δ matter due to partial restoration of chiral symmetry. Consequently, a purely hadronic EoS that accounts for the fundamental properties of quantum chromodynamics linked to the dynamical emergence of parity doubling with degenerate masses of nucleons and Δ resonances can be fully consistent with multi-messenger data. Therefore, with the present constraints on the EoS, the conclusion about the existence of quark matter in the stellar core may still be premature.

Experimental Evidence for an Attractive p-ϕ Interaction.

This Letter presents the first experimental evidence of the attractive strong interaction between a proton and a ϕ meson. The result is obtained from two-particle correlations of combined p-ϕ⊕ p[over ¯]-ϕ pairs measured in high-multiplicity pp collisions at sqrt[s]=13 TeV by the ALICE Collaboration. The spin-averaged scattering length and effective range of the p-ϕ interaction are extracted from the fully corrected correlation function employing the Lednický-Lyuboshits approach. In particular, the imaginary part of the scattering length vanishes within uncertainties, indicating that inelastic processes do not play a prominent role for the p-ϕ interaction. These data demonstrate that the interaction is dominated by elastic p-ϕ scattering. Furthermore, an analysis employing phenomenological Gaussian- and Yukawa-type potentials is conducted. Under the assumption of the latter, the N-ϕ coupling constant is found to be g_{N-ϕ}=0.14±0.03(stat)±0.02(syst). This work provides valuable experimental input to accomplish a self-consistent description of the N-ϕ interaction, which is particularly relevant for the more fundamental studies on partial restoration of chiral symmetry in nuclear medium.

A Universal Binding Mechanism in Molecular Covalent Bonding and Nucleon-Nucleon Interaction

In the hydrogen molecular ion, the kinetic energy lowering of the electron is associated with its delocalization due to electron exchange between the two protons of the molecule. This decrease in the kinetic energy of the exchanged electron in the hydrogen molecular ion and the decrease in the dynamical mass of the two exchanged pions in the nucleon-nucleon interaction are at the origin of the attraction mechanism in the molecular covalent bonding and in the nuclear interaction. Based on this unitary approach of the attraction mechanism, the formulas of molecular potential and central nucleon-nucleon potential were derived. The decrease in the mass of the exchanged pions in the nucleon-nucleon bound state, actually means the decrease in the mass of the nucleons. This nucleon mass decrease could be a manifestation of the partial chiral symmetry restoration in nuclear matter.

Comparative study of proton and positive kaon interactions with carbon: hint of new physics like partial restoration of chiral symmetry in nuclei

Concerning the scattering of K+ - mesons on nuclei, the explicit discrepancy between experimental data and optical model calculations is a longstanding problem and none of the conventional medium effect corrections improves significantly the agreement with the data. In this paper the cross sections for the reactions K++12C at incident momenta of the kaon Plab < 800 MeV/c are calculated on the basis of Glauber’s high-energy approximation. The noneikonal corrections, Fermi motion effect and both Pauli and dynamic short-range correlations were incorporated in the Glauber approach for nuclear collisions. The influence of all these corrections on the calculation of the cross sections for the interactions of kaon with nucleus is discussed. The full calculations is compared to available data. The corrections seem to fail in reproducing the experimental data. Our results is compared to optical model calculations. We show that both our model and optical model fails to give a satisfactory description of K+-nuclei cross sections. Different attempts to remove this discrepancy with the in-medium effects taken into account are discussed.

Naive versus mirror assignment at finite density: correlator mixing and chiral symmetry restoration

Chiral symmetry imposes some constraints on hadron correlation functions in dense media. These constraints imply a certain general structure of the two- and three-point correlation functions of chiral partners and lead to the effect of mixing arising from the interaction of the long-ranged nuclear pions with corresponding interpolating currents. It reflects the phenomena of partial restoration of chiral symmetry. We consider several possible pairs of chiral partners for both mesons and nucleons and analyse their mixing patterns. We explored both naive and mirror assignments for the chiral partner of nucleons.

$K^{+}$ –nucleus elastic scattering revisited from the perspective of partial restoration of chiral symmetry

$K^{+}$ –nucleus elastic scattering revisited from the perspective of partial restoration of chiral symmetry

Production of exotic tetraquarks QQq¯q¯ in heavy-ion collisions at the LHC

We investigate the production of exotic tetraquarks, $QQ\bar{q}\bar{q} \equiv T_{QQ}$ ($Q=c$ or $b$ and $q=u$ or $d$), in relativistic heavy-ion collisions using the quark coalescence model. The $T_{QQ}$ yield is given by the overlap of the density matrix of the constituents in the emission source with the Wigner function of the produced tetraquark. The tetraquark wave function is obtained from exact solutions of the four-body problem using realistic constituent models. The production yields are typically one order of magnitude smaller than previous estimations based on simplified wave functions for the tetraquarks. We also evaluate the consequences of the partial restoration of chiral symmetry at the hadronization temperature on the coalescence probability. Such effects, in addition to increasing the stability of the tetraquarks, lead to an enhancement of the production yields, pointing towards an excellent discovery potential in forthcoming experiments. We discuss further consequences of our findings for the search of exotic tetraquarks in central Pb+Pb collisions at the LHC.

Structure of $\eta^{\prime}$ mesonic nuclei in a relativistic mean field theory

The structure and the energy spectrum of the $\eta^{\prime}$ mesonic nuclei are investigated in a relativistic mean field theory. One expects a substantial attraction for the $\eta^{\prime}$ meson in finite nuclei due to the partial restoration of chiral symmetry in the nuclear medium. Such a hadronic scale interaction for the $\eta^{\prime}$ mesonic nuclei may provide modification of the nuclear structure. The relativistic mean field theory is a self-contained model for finite nuclei which provides the saturation property within the model, and is good to investigate the structure change of the nucleus induced by the $\eta^{\prime}$ meson. Using the local density approximation for the mean fields, we solve the equations of motion for the nucleons and the $\eta^{\prime}$ meson self-consistently, and obtain the nuclear density distribution and the $\eta^{\prime}$ energy spectrum for the $\eta^{\prime}$ mesonic nuclei. We take $^{12}$C, $^{16}$O and $^{40}$Ca for the target nuclei. We find several bound states of the $\eta^{\prime}$ meson for these nuclei thanks to the attraction for $\eta^{\prime}$ in nuclei. We also find a sufficient change of the nuclear structure especially for the $1s$ bound state of $\eta^{\prime}$. This implies that the production of the $1s$ bound state in nuclear reaction may be suppressed.

Axial anomaly and hadronic properties in a nuclear medium

We investigate meson and nucleon dynamics at finite baryon density and temperature by coupling the nucleon field and the omega meson to the three-flavor linear sigma model and calculate hadronic properties around the nuclear liquid-gas transition. We apply the functional renormalization group method, and find that mesonic fluctuations increase the strength of the coefficient of the $U_A(1)$ breaking determinant operator as a function of the chiral condensate. As a consequence, we find that the actual value of the anomaly increases discontinuously at the first order nuclear liquid-gas transition. We calculate how mesonic masses and partial restoration of chiral symmetry are modified due to such an effect.

Catalysis of partial chiral symmetry restoration by Δ matter

We study the phase structure of dense hadronic matter including $\Delta(1232)$ as well as N(939) based on the parity partner structure, where the baryons have their chiral partners with a certain amount of chiral invariant masses. We show that, in symmetric matter, $\Delta$ enters into matter in the density region of about one to four times of normal nuclear matter density, $\rho_B \sim 1 - 4\rho_0$. The onset density of $\Delta$ matter depends on the chiral invariant mass of $\Delta$, $m_{\Delta0}$: The lager $m_{\Delta0}$, the bigger the onset density. The $\Delta$ matter of $\rho_B \sim 1 - 4\rho_0$ is unstable due to the existence of $\Delta$, and the stable $\Delta$-nucleon matter is realized at about $\rho_B \sim 4\rho_0$, i.e., the phase transition from nuclear matter to $\Delta$-nucleon matter is of first order for small $m_{\Delta0}$, and it is of second order for large $m_{\Delta0}$. We find that, associated with the phase transition, the chiral condensate changes very rapidly, i.e., the chiral symmetry restoration is accelerated by \Delta matter. As a result of the accelerations, there appear $N^*$(1535) and $\Delta$(1700), which are the chiral partners to N(939) and ${\Delta}$(1232), in high density matter, signaling the partial chiral symmetry restoration. Furthermore, we find that complete chiral symmetry restoration itself is delayed by $\Delta$ matter. We also calculate the effective masses, pressure and symmetry energy to study how the transition to $\Delta$ matter affects such physical quantities. We observe that the physical quantities change drastically at the transition density.

Examination of N*(1535) as a probe to observe the partial restoration of chiral symmetry in nuclear matter

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 $\Gamma_{N^*\to N\pi}$ is slightly broadened by a collisional broadening, and that of $\Gamma_{N^*\to N\eta}$ is drastically suppressed at density. As a result, the total decay width $\Gamma_{\rm tot}$ gets small at density. These modifications, especially the drastic narrowing of partial width of $\Gamma_{N^*\to N\eta}$, together with the dropping of mass of $N^*(1535)$ provide experiments for observing the partial restoration of chiral symmetry in nuclear matter by means of $N^*(1535)$ resonance with useful information.

Relation between the mass modification of heavy–light mesons and the chiral symmetry structure in dense matter

We point out that the study of the density dependences of the masses of heavy-light mesons give some clues to the chiral symmetry structure in nuclear matter. We include the omega meson effect as well as the sigma meson effect at mean field level on the density dependence of the masses of heavy-light mesons with chiral partner structure. It is found that the omega meson affects the masses of the heavy-light mesons and their antiparticles in the opposite way, while it affects the masses of chiral partners in the same way. This is because the omega meson is sensitive to the baryon number of the light degrees included in the heavy-light mesons. We also show that the mass difference between chiral partners is proportional to the mean field of sigma, reflecting the partial restoration of chiral symmetry in the nuclear matter. In addition to the general illustration of the density dependence of the heavy-light meson masses, we consider two concrete models for nuclear matter, the parity doublet model and skyrmion crystal model in the sense of mean field approximation.

K +–nucleus elastic scattering revisited from the perspective of partial restoration of chiral symmetry

The $K^{+}$ meson properties in the nuclear medium are investigated by considering the wavefunction renormalization as a first step to reveal the in-medium properties of the $K^{+}$ meson in the context of partial restoration of chiral symmetry. The $K^{+}N$ elastic scattering amplitude is constructed using chiral perturbation theory up to the next-to-leading order. Using the constructed amplitude, we calculate the wavefunction renormalization in the Thomas-Fermi approximation. We obtained a good description of the $K^{+}N$ elastic scattering amplitude. The obtained wavefunction renormalization factor suggests the 2 to 6% enhancement of the $K^{+}N$ interaction at the saturation density. We conclude that the wavefunction renormalization could be one of the important medium effects for the $K^{+}$ meson.

Partial restoration of chiral symmetry in cold nuclear matter: the ϕ-meson case

The work presented at this workshop is divided into two parts. In the first part, the mass and decay width of the ϕ-meson in cold nuclear matter are computed in an effective Lagrangian approach. The medium dependence of these properties are obtained by evaluating kaon-antikaon loop contributions to the ϕ-meson self-energy, employing medium-modified kaon masses calculated using the quark-meson coupling model. The loop integral is regularized with a dipole form factor, and the sensitivity of the results to the choice of cutoff mass in the form factor is investigated. At normal nuclear matter density, we find a downward shift of the ϕ mass by a few percent, while the decay width is enhanced by an order of magnitude. Our results support the literature which suggest that one should observe a small downward mass shift and a large broadening of the decay width. In the second part, we present ϕ-meson-nucleus bound state energies and absorption widths for four selected nuclei, calculated by solving the KleinGordon equation with complex optical potentials. The attractive potential for the ϕ-meson in the nuclear medium originates from the in-medium enhanced loop in the ϕ-meson self-energy. The results suggest that the ϕ-meson should form bound states with all the nuclei considered. However, the identification of the signal for these predicted bound states will need careful investigation because of their sizable absorption widths.

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.