Parity Doublet Structure Research Articles

Optical Trapping of a Polyatomic Molecule in an ℓ-Type Parity Doublet State.

We report optical trapping of a polyatomic molecule, calcium monohydroxide (CaOH). CaOH molecules from a magneto-optical trap are sub-Doppler laser cooled to 20(3) μK in free space and loaded into an optical dipole trap. We attain an in-trap molecule number density of 3(1)×10^{9} cm^{-3} at a temperature of 57(8) μK. Trapped CaOH molecules are optically pumped into an excited vibrational bending mode, whose ℓ-type parity doublet structure is a potential resource for a wide range of proposed quantum science applications with polyatomic molecules. We measure the spontaneous, radiative lifetime of this bending mode state to be ∼0.7 s.

Chiral Restoration of Nucleons in Neutron Star Matter: Studies Based on a Parity Doublet Model

We review the chiral variant and invariant components of nucleon masses and the consequence of their existence on the chiral restoration in extreme conditions, particularly in neutron star matter. We consider a model of linear realization of chiral symmetry with the nucleon parity doublet structure that permits the chiral invariant mass, m0, for positive and negative parity nucleons. The nuclear matter is constructed with the parity doublet nucleon model coupled to scalar fields σ, vector fields (ω,ρ), and mesons with strangeness through the U(1)A anomaly. In models with a large m0, the nucleon mass is insensitive to the medium, and the nuclear saturation properties can be reproduced without demanding strong couplings of the nucleons to the scalar fields σ and vector fields ω. We confront the resulting nuclear equations of state with nuclear constraints and neutron star observations and delineate the chiral invariant mass and effective interactions. To further examine the nuclear equations of state beyond the saturation density, we supplement quark models to set the boundary conditions from the high-density side. The quark models are constrained by the two-solar-mass conditions, and such constraints are transferred to nuclear models through the causality and thermodynamic stability conditions. We also calculate various condensates and the matter composition from nuclear to quark matter in a unified matter by constructing a generating functional that interpolates the nuclear and quark matter with external fields. Two types of chiral restoration are discussed: one due to the positive scalar charges of nucleons and the other triggered by the evolution of the Dirac sea. We found that the U(1)A anomaly softens equations of state from low to high density.

Parity doublet bands in Th223 within reflection-asymmetric triaxial particle rotor model

The recently updated parity doublet structures in $^{223}\mathrm{Th}$ are investigated by using the reflection-asymmetric triaxial particle rotor model. The calculated results well reproduce the available data of the energy spectra and the $B(E1)/B(E2)$ ratios for both medium spin region and the newly established higher spin region, as well as the average value of $B(M1)/B(E2)$ for spins $9/2\ensuremath{\hbar}$ and $11/2\ensuremath{\hbar}$ in the positive-parity band. The main components of the intrinsic wave functions are analyzed to investigate the intrinsic wave functions and their evolutions with spin. The parity doublet bands are mainly based on a single neutron configuration, in which the largest component of the intrinsic wave function is $\ensuremath{\nu}({g}_{9/2},{j}_{15/2})[\mathrm{\ensuremath{\Omega}}=5/2]$ and the second largest one is $\ensuremath{\nu}({g}_{9/2},{j}_{15/2})[\mathrm{\ensuremath{\Omega}}=3/2]$. The amplitude of the largest component decreases whereas the second largest one increases with increasing spin, and the signature splitting behavior for the parity doublet bands could be understood by the variation of these main components with spin.

An analytical description of the parity-doublet structure in an odd-A nucleus

In this paper, we discuss an analytical description of a parity-doublet structure for an odd-A nucleus. We use the controlled single particle (CSP) concept to present the analytical model. In a parity-doublet structure, those bands consisting of states with opposite positive and negative parity appear. At first glance, it seems complex to present an analytical description, but the CSP concept enables us to present an analytical description of such an event. The calculated results are compared to the experimental data of Pm151, and there is a good agreement with calculated and experimental results.

Quark-hadron crossover equations of state for neutron stars: Constraining the chiral invariant mass in a parity doublet model

We construct an equation of state (EOS) for neutron stars by interpolating hadronic EOS at low density and quark EOS at high density. A hadronic model based on the parity doublet structure is used for hadronic matter and a quark model of Nambu--Jona-Lasinio type is for quark matter. We assume crossover between hadronic matter and quark matter in the the color-flavor locked phase. The nucleon mass of the parity doublet model has a mass associated with the chiral symmetry breaking, and a chiral invariant mass $m_0$ which is insensitive to the chiral condensate. The value of $m_0$ affects the nuclear EOSs at low density, and has strong correlations with the radii of neutron stars. Using the constraint to the radius obtained by LIGO-Virgo and NICER, we find that $m_0$ is restricted as $600\,\mathrm{MeV}\lesssim m_0 \lesssim 900\,\mathrm{MeV}$.

Chiral partner structure of light nucleons in an extended parity doublet model

We study chiral partner structure of four light nucleons, $N(939)$, $N(1440)$, $N(1535)$ and $N(1650)$ using an effective chiral model based on the parity doublet structure. In our model we introduce four chiral representations, $({\bf 1},{\bf 2})$, $({\bf 2},{\bf 1})$, $({\bf 2},{\bf 3})$ and $({\bf 3},{\bf 2})$ under ${\rm SU}(2)_{\rm L} \otimes {\rm SU}(2)_{\rm R}$ symmetry. We determine the model parameters by fitting them to available experimental values of masses, widths and the axial charge of $N(939)$ together with the axial charges of $N(1535)$ and $N(1650)$ by lattice analyses. We find five groups of solutions: In a group the chiral partner to $N(939)$ is $N(1440)$ having small chiral invariant mass. In another group, the chiral partner is a mixture of $N(1535)$ and $N(1650)$ having a large chiral invariant mass. We claim that off-diagonal elements of axial-charge matrix can be used for distinguishing these groups. We also discuss changes of masses associated with chiral symmetry restoration, which could emerge in high density matter.

Novel dual chiral density wave in nuclear matter based on a parity doublet structure

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 with a nonvanishing space average depending on the value of the chiral invariant mass parameter.

Parity doublet structures in doubly-odd Fr216

Parity doublet structures are established in $^{216}\mathrm{Fr}$, which lies at the lower boundary of enhanced octupole collectivity in the trans-lead region. The newly identified levels are established as the simplex partner of a previously reported band leading to parity doublets with small ($\ensuremath{\sim}55$ keV) average energy splitting, a feature typical of nuclei with near-static octupole deformation. The observed levels do not follow a regular pattern of rotational bands, indicating low quadrupole collectivity. However, enhanced octupole correlations are evident from the small energy splitting and large B(E1)/B(E2) values. Staggering in E1 transition energies and B(E1)/B(E2) ratios is noted. The enhancement of octupole correlations in $^{216}\mathrm{Fr}$ is attributed to the availability of a neutron orbital with a K = 3/2 component.

Dual chiral density waves in nuclear matter

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.

Parity-doublet structure in the La9057147 nucleus

Excited states in $^{147}\mathrm{La}$, populated in spontaneous fission of $^{252}\mathrm{Cf}$, have been reinvestigated by means of $\ensuremath{\gamma}$-ray spectroscopy, using high-fold $\ensuremath{\gamma}$-ray coincidences measured with the Gammasphere array of Ge detectors. The 229.5-keV level, which has been assigned spin parity $9/{2}^{\ensuremath{-}}$ in a recent evaluation, is shown to have spin parity $11/{2}^{\ensuremath{-}}$. Consequently, the ground state has spin parity $5/{2}^{+}$. Excited levels in $^{147}\mathrm{La}$ have been arranged into a parity-doublet structure, showing that at medium excitation energy the $^{147}\mathrm{La}$ nucleus may have octupole deformation. The $B(E1)$ rates in $^{147}\mathrm{La}$, which are factor of four lower than in $^{145}\mathrm{La}$, suggest that the electric dipole moment in $^{147}\mathrm{La}$ is depressed by an extra mechanism, probably connected with the population of particular neutron orbitals.

Application of the hidden local symmetry in hadron physics

About two decades ago, Gerry Brown pushed me to study hadron physics using hadronic models based on the hidden local symmetry (HLS). Since then, I have been involving many works related to the HLS. In this contribution to Gerry’s memorial, I will summarize my recent analyses associated with the HLS. After a very brief summary of the HLS, I will show a way to determine parameters of the HLS model from holographic QCD models. This model provides a soliton solution which is identified with the nucleon. I will briefly introduce a model in which the solitons are put onto a crystal lattice for simulating nuclear matter. The results suggest existence of the chiral invariant mass of nucleon. I also briefly review my recent analyses on the nuclear matter by using a hadronic model including nucleon field together with the [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] mesons based on the parity doublet structure of nucleon combined with the HLS, in which the chiral invariant mass of the nucleon is naturally embedded. The result implies that studying effective masses of nucleons will give a clue for the chiral invariant mass. Finally, I will show our recent analysis on the medium modification of charmed meson masses using a chiral model based on the chiral doubling structure of charmed mesons. The result shows that the masses of the chiral partners of charmed mesons become closer in high density reflecting the particle chiral symmetry restoration in medium.

Characterization of octupole-type structures inTh221

A detailed level scheme for $^{221}\mathrm{Th}$ has been established in an experiment using the $^{18}\mathrm{O}+{}^{207}\mathrm{Pb}$ reaction at 96 MeV. The evaporation residues from this fissile system were selected with the HERCULES detector array and residue-gated $\ensuremath{\gamma}$ rays were measured with Gammasphere. Three band structures of interlinked, alternating-parity levels are observed, two of which are non-yrast. In addition, several high-lying excitations are found. The yrast band is seen up to spin-parity $37/{2}^{\ensuremath{-}}$ and $39/{2}^{+}$, beyond which a high-spin feeding transition is observed. The non-yrast sequences are interpreted as parity-doublet structures, based on a configuration similar to that of the yrast band in $^{223}\mathrm{Th}$ $(K=5/2)$. The key properties of even-odd nuclei in this mass region $[B(E1)/B(E2)$ and $B(M1)/B(E2)$ ratios, spin alignments, parity splittings] are reviewed.

Non-yrast spectra of odd-Anuclei in a model of coherent quadrupole-octupole motion

The model of coherent quadrupole and octupole motion is applied to describe non-yrast split parity-doublet spectra in odd-mass nuclei. The yrast levels are described as low-energy rotation-vibration modes coupled to the ground single-particle (s.p.) state, while the non-yrast parity-doublet structures are obtained as higher-energy rotation-vibration modes coupled to excited s.p. states. It is shown that the extended model scheme describes both the yrast and non-yrast quasi parity-doublet spectra and the related $B(E1)$ and $B(E2)$ transition rates in different regions of heavy odd-$A$ nuclei. The involvement of the reflection-asymmetric deformed shell model to describe the single-particle motion and the Coriolis interaction on a deeper level is discussed.

Coherent quadrupole-octupole modes and split parity-doublet spectra in odd-Anuclei

A collective model describing coherent quadrupole-octupole oscillations and rotations with a Coriolis coupling between the even-even core and the unpaired nucleon is applied to odd nuclei. The particle-core coupling provides a parity-doublet structure of the spectrum, whereas the quadrupole-octupole motion leads to a splitting of the doublet energy levels. The formalism successfully reproduces the split parity-doublet spectra and the attendant $B(E1)$ and $B(E2)$ transition probabilities in a wide range of odd-$A$ nuclei. It provides estimations for the influence of the Coriolis interaction on the collective motion and subsequently for the value of angular momentum projection $K$ on which the spectrum is built. The analysis of the energy splitting and $B(E1)$ transition probabilities between opposite parity counterparts suggests degenerate doublet structures at high angular momenta. The study provides information about the evolution of quadrupole-octupole collectivity in odd-mass nuclei.

Collective states of odd nuclei in a model with quadrupole-octupole degrees of freedom

We apply the collective axial quadrupole—octupole Hamiltonian to describe the rotation—vibration motion of odd nuclei with Coriolis coupling between the even-even core and the unpaired nucleon.We consider that the core oscillates coherently with respect to the quadrupole and octupole axialdeformation variables. The coupling between the core and the unpaired nucleon provides a split paritydoublet structure of the spectrum. The formalism successfully reproduces the parity-doublet splitting in a wide range of odd-A nuclei. It provides model estimations for the third angular-momentum projection K on the intrinsic symmetry axis and the related intrinsic nuclear structure.

Formula omitted] as the lowest mass pseudoscalar glueball and proton spin problem

We consider the parity doublet structure observed in high hadronic excitations within the instanton model for the QCD vacuum. In the conventional approach this doubling phenomenon is treated as a manifestation of the partial restoration of chiral or U(1)A symmetry. We demonstrate that the suppression of direct instanton contribution to the masses of excited hadrons leads to the partial U(1)A symmetry restoration in hadron spectrum. The origin of X(1835) resonance observed by BES Collaboration is studied upon the doublet structure. We argue also how X(1835) be interpreted as the lowest pseudoscalar glueball state, and derive its coupling constant to proton. It turns out that this coupling is large and negative. Demonstrated is how this large coupling affects the gluonic contribution to the proton spin.

N ∗ and Δ ∗ parity doublets in the baryon spectrum

The N and Δ excitation spectrum exhibits parity doublets, i.e. states of equal total angular momentum but with opposite parity being almost degenerate in mass. Among others, it has been suggested by L.Ya. Glozman that the parity-doublet structure may be due to effective chiral restoration.

DOES ONE OBSERVE CHIRAL SYMMETRY RESTORATION IN BARYON SPECTRUM?

It has recently been suggested that the parity doublet structure seen in the spectrum of highly excited baryons may be due to effective chiral symmetry restoration for these states. We review the recent developments in this field. We demonstrate with a simple quantum-mechanical example that it is a very natural property of quantum systems that a symmetry breaking effect which is important for the low-lying spectrum of the system, can become unimportant for the highly-lying states; the highly lying states reveal a multiplet structure of nearly degenerate states. Using the well-established concepts of quark–hadron duality, asymptotic freedom in QCD and validity of the operator product expansion in QCD, we show that the spectral densities obtained with the local currents that are connected to each other via chiral transformations, very high in the spectrum must coincide. Hence effects of spontaneous breaking of chiral symmetry in QCD vacuum that are crucially important for the low-lying spectra, become irrelevant for the highly-lying states. Then to the extent that identifiable hadronic resonances still exist in the continuum spectrum at high excitations, this implies that the highly excited hadrons must fall into multiplets associated with the representations of the chiral group. We demonstrate that this is indeed the case for meson spectra in the large Nc limit. All possible parity-chiral multiplets are classified for baryons and it is demonstrated that the existing data on highly excited N and Δ states at masses of 2 GeV and higher is consistent with approximate chiral symmetry restoration. However new experimental studies are needed to achieve any definitive conclusions.

Chiral multiplets versus parity doublets in highly excited baryons

It has recently been suggested that the parity doublet structure seen in the spectrum of highly excited baryons may be due to effective chiral restoration for these states. We argue how the idea of chiral symmetry restoration high in the spectrum is consistent with the concept of quark-hadron duality. If chiral symmetry is effectively restored for highly lying states, then the baryons should fall into representations of ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{R}$ that are compatible with the given parity of the states---the parity-chiral multiplets. We classify all possible parity-chiral multiplets: (i) $(1/2,0)\ensuremath{\bigoplus}(0,1/2)$ that contain parity doublet for nucleon spectrum, (ii) $(3/2,0)\ensuremath{\bigoplus}(0,3/2)$ consists of the parity doublet for delta spectrum, (iii) $(1/2,1)\ensuremath{\bigoplus}(1,1/2)$ contains one parity doublet in the nucleon spectrum and one parity doublet in the delta spectrum of the same spins that are degenerate in mass. Here we show that the available spectroscopic data for nonstrange baryons in the $\ensuremath{\sim}2 \mathrm{GeV}$ range are consistent with all possibilities, but the approximate degeneracy of parity doublets in nucleon and delta spectra support the latter possibility with excited baryons approximately falling into $(1/2,1)\ensuremath{\bigoplus}(1,1/2)$ representation of ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{R}$ with approximate degeneracy between positive and negative parity N and $\ensuremath{\Delta}$ resonances of the same spin.

SKYRMIONS, SPECTRAL FLOW AND PARITY DOUBLES

It is well-known that the winding number of the Skyrmion can be identified as the baryon number. We show in this paper that this result can also be established using the Atiyah–Singer index theorem and spectral flow arguments. We argue that this proof suggests that there are light quarks moving in the field of the Skyrmion. We then show that if these light degrees of freedom are averaged out, the low energy excitations of the Skyrmion are in fact spinorial. A natural consequence of our approach is the prediction of a [Formula: see text] state and its excitations in addition to the nucleon and delta. Using the recent numerical evidence for the existence of Skyrmions with discrete spatial symmetries, we further suggest that the the low energy spectrum of many light nuclei may possess a parity doublet structure arising from a subtle topological interaction between the slow Skyrmion and the fast quarks. We also present tentative experimental evidence supporting our arguments.