Chiral Partners Research Articles

Quartet of spin-3/2baryons in the chiral multiplet(1,1/2)⊕(1/2,1)with mirror assignment

We study the possible existence of chiral partners in the spin-$\thalf$ sector of the baryon spectrum. We consider a quartet scheme where four spin-3/2 baryons, $P_{33}$, $D_{33}$, $D_{13}$ and $P_{13}$, group into higher-dimensional chiral multiplets $(1, \half)\oplus (\half,1)$ with a mirror assignment. With an effective $SU(2)_R\times SU(2)_L$ Lagrangian, we derive constraints imposed by chiral symmetry together with the mirror assignment on the masses and coupling constants of the quartet. Using the effective Lagrangian, we try to find a set of baryons suitable for the chiral quartet. It turns out that two cases reasonably agree with the mass pattern of the quartet: ($\Delta(1600)$, $\Delta(1940)$, $N(1520)$, $N(1720)$) and ($\Delta(1920)$, $\Delta(1940)$, $N(2080)$, $N(1900)$).

Some indication for a missing chiral partnerη4around 2 GeV

The high-lying mesons in the light quark sector previously obtained from the partial wave analysis of the proton-antiproton annihilation in flight at 1.9--2.4 GeV region at CERN reveal a very high degree of degeneracy. This degeneracy can be explained as due to an effective restoration of both $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$ and $U(1{)}_{A}$ symmetries combined with a principal quantum number $\ensuremath{\sim}n+J$. In this case there must be chiral partners for the highest spin states in the 2 and 2.3 GeV bands presently missing in the data. Here we reanalyze the Crystal Barrel data and show an indication for existence of the missing ${4}^{\ensuremath{-}+}$ state around 2 GeV. This result calls for further experimental search of the missing states both in the proton-antiproton annihilation and in the production reactions.

Vacuum phenomenology of the chiral partner of the nucleon in a linear sigma model with vector mesons

We investigate a linear sigma model with global chiral $U(2)_{R} \times U(2)_{L}$ symmetry. The mesonic degrees of freedom are the standard scalar and pseudoscalar mesons and the vector and axial-vector mesons. The baryonic degrees of freedom are the nucleon, $N$, and its chiral partner, $N^{*}$, which is usually identified with N(1535). The chiral partner is incorporated in the so-called mirror assignment, where the nucleon mass is not solely generated by the chiral condensate but also by a chirally invariant mass term, $m_{0}$. The presence of (axial-) vector fields modifies the expressions for the axial coupling constants of the nucleon, $g_{A}^{N}$, and its partner, $g_{A}^{N^{*}}$. Using experimental data for the decays $N^{*} \to N \pi$ and $a_{1} \to\pi\gamma$, as well as lattice results for $g_{A}^{N^{*}}$ we infer $m_{0}\sim500$ MeV, i.e., an appreciable amount of the nucleon mass originates from sources other than the chiral condensate. We test our model by evaluating the decay $N^{*} \to N \eta$ and the s-wave nucleon-pion scattering lengths $a_{0}^{(\pm)}$.

Enantioseparation in microfluidic channels

Since the pharmaceutical or biological activity of enantiomers may be significantly different for the two chiral partner molecules, the separation of a racemic mixture into its component enantiomers represents a challenge of immense practical relevance. Established chiral separation techniques rely on the presence of a chiral auxiliary substance. We propose an alternative separation scheme in a microfluidic device without employing such chiral selectors. Using computer simulations and analytical arguments, we reveal that enantiomers migrate with chirality-specific average velocities through a microfluidic channel, provided the driving force field breaks the mirror symmetry. This effect can be exploited for the sorting of chiral molecules. Its origin is attributed to the coupling between rotational and translational degrees of freedom in the molecule motion induced by the nonlinear force fields. Two “basic” types of enantiomers are considered, characterized by mirror-symmetric geometrical conformations and mirror-symmetric charge-distributions in solution.

Candidate chiral bands in 198Tl

High-spin states in Tl-198 were studied using the Au-197(alpha, 3n) reaction. The level scheme was considerably extended including two new bands and several non-yrast levels. One of the new bands is possibly a chiral partner to the yrast pi h(9/2) circle times vi(13/2)(-1) band. Two-quasiparticle-plus-triaxial-rotor model calculations suggest an aplanar orientation of the total angular momenta for these bands, thus supporting possible chirality.

Reaching degeneracy in two-quasiparticle chiral bands

The conditions for reaching degeneracy in chiral partner bands built on two-quasiparticle configurations are examined using the two-quasiparticle-plus-triaxial-rotor model. It is shown that in order for degeneracy to occur it is not sufficient to have an aplanar orientation of the total angular momentum, but the angular momenta of the two valence particles need to be completely aligned along the short and long nuclear axes. Such perfect alignment seems impossible to reach with realistic parameters within this model. These results suggest that two-quasiparticle chiral bands may be formed in suitable nuclei, but perfect degeneracy between the partner bands is unlikely to be found.

Meson masses and mixing angles in the2+1flavor Polyakov quark meson sigma model and symmetry restoration effects

The meson masses and mixing angles have been calculated for the scalar and pseudoscalar sector in the framework of the generalized $2+1$ flavor Polyakov loop augmented quark meson linear sigma model. We have given the results for two different forms of the effective Polyakov loop potential. The comparison of results with the existing calculations in the bare $2+1$ quark meson linear sigma model, shows that the restoration of chiral symmetry becomes sharper due to the influence of the Polyakov loop potential. We find that inclusion of the Polyakov loop in the quark meson linear sigma model together with the presence of axial anomaly, triggers an early and significant melting of the strange condensate. We have examined how the inclusion of the Polyakov loop qualitatively and quantitatively affects the convergence in the masses of the chiral partners in pseudoscalar ($\ensuremath{\pi}$, $\ensuremath{\eta}$, ${\ensuremath{\eta}}^{\ensuremath{'}}$, $K$) and scalar ($\ensuremath{\sigma}$, ${a}_{0}$, ${f}_{0}$, $\ensuremath{\kappa}$) meson nonets as the temperature is varied on the reduced temperature scale. The role of ${U}_{A}(1)$ anomaly in determining the isoscalar masses and mixing angles for the pseudoscalar ($\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$) and scalar ($\ensuremath{\sigma}$ and ${f}_{0}$) meson complex, has also been investigated in the Polyakov loop augmented quark meson linear sigma model. The interplay of chiral symmetry restoration effects and the setting up of ${U}_{A}(1)$ restoration trend has been discussed and analyzed in the framework of the presented model calculations.

Meson properties at finite temperature in a three flavor nonlocal chiral quark model with Polyakov loop

We study the finite temperature behavior of light scalar and pseudoscalar meson properties in the context of a three-flavor nonlocal chiral quark model. The model includes mixing with active strangeness degrees of freedom, and takes care of the effect of gauge interactions by coupling the quarks with the Polyakov loop. We analyze the chiral restoration and deconfinement transitions, as well as the temperature dependence of meson masses, mixing angles and decay constants. The critical temperature is found to be T_c = 202 MeV, in better agreement with lattice results than the value recently obtained in the local SU(3) PNJL model. It is seen that above T_c pseudoscalar meson masses get increased, becoming degenerate with the masses of their chiral partners. The temperatures at which this matching occurs depend on the strange quark composition of the corresponding mesons. The topological susceptibility shows a sharp decrease after the chiral transition, signalling the vanishing of the U(1)_A anomaly for large temperatures.

Asymmetric Cooperative Catalysis of Strong Brønsted Acid–Promoted Reactions Using Chiral Ureas

Cationic organic intermediates participate in a wide variety of useful synthetic transformations, but their high reactivity can render selectivity in competing pathways difficult to control. Here, we describe a strategy for inducing enantioselectivity in reactions of protio-iminium ions, wherein a chiral catalyst interacts with the highly reactive intermediate through a network of noncovalent interactions. This interaction leads to an attenuation of the reactivity of the iminium ion and allows high enantioselectivity in cycloadditions with electron-rich alkenes (the Povarov reaction). A detailed experimental and computational analysis of this catalyst system has revealed the precise nature of the catalyst-substrate interactions and the likely basis for enantioinduction.

Information on the structure of the rho meson from the pion form factor

The electromagnetic pion form factor is calculated in a Bethe-Salpeter approach which accounts for pion rescattering. In the scattering kernel the pion-pion contact interaction from lowest-order chiral perturbation theory is considered together with an optional vector meson in the $s$ channel. Correspondingly the virtual photon couples to a two-pion state and optionally to the vector meson. It is shown that for reasonable ranges of input parameters the experimentally observed pion form factor cannot be described by the iterated pion-pion contact interaction alone, i.e. without an elementary vector meson. The inclusion of an elementary vector meson allows for an excellent description. This completes a recent study (``Information on the structure of the ${a}_{1}$ from tau decay'') where it has been shown that the ${a}_{1}$ meson can be well understood as a rescattering process of the $\ensuremath{\rho}$ meson and the pion. Here it is demonstrated that within the same formalism the $\ensuremath{\rho}$ meson cannot be understood as a pion-pion rescattering process. This suggests that the chiral partners ${a}_{1}$ and $\ensuremath{\rho}$ are not only different in mass, but also different in nature.

Robust localized modes in bilayer graphene induced by an antisymmetric kink potential

When bilayer graphene is gated with a kink potential, pair particle localization occurs at the kink where a particle (electron) and its chiral partner (hole) are held in balance by electrostatic coupling. Zero-energy states (zero modes) are always present in pairs and occur at the same point in the dispersion graph, regardless of kink strength. The robust and binary nature of the kink-induced modes, which are topologically protected against disorder, and the ease with which a kink is created suggest applications in switching devices or information storage.

Observation of Three-Quasiparticle Doublet Bands in 123I: Possible Evidence of Chirality

A new band in the odd proton nucleus 123I is identified via in-beam γ-ray spectroscopy using the 14N+116Cd reaction. This band shows up as doublets with the previously assigned πg7/2 ⊗ (νh11/2)2 band. Possible configurations of the new band are discussed in the framework of the cranked shell model and the geometrical model. It is argued that the new band might be a chiral partner of the previously known πg7/2 ⊗ (νh11/2) band.

CHIRAL PARTNERS IN A CHIRALLY BROKEN WORLD

The isovector–vector and the isovector–axial-vector current are related by a chiral transformation. These currents can be called chiral partners at the fundamental level. In a world where chiral symmetry was not broken, the corresponding current-current correlators would show the same spectral information. In the real world chiral symmetry is spontaneously broken. A prominent peak — the ρ-meson — shows up in the vector spectrum (measured in e+e--collisions and τ-decays). On the other hand, in the axial-vector spectrum a broad bump appears — the a1-meson (also accessible in τ-decays). It is tempting to call ρ and a1 chiral partners at the hadronic level. Strong indications are brought forward that these "chiral partners" do not only differ in mass but even in their nature: The ρ-meson appears dominantly as a quark-antiquark state with small modifications from an attractive pion-pion interaction. The a1-meson, on the other hand, can be understood as a meson-molecule state mainly formed by the attractive interaction between pion and ρ-meson. A key issue here is that the meson-meson interactions are fixed by chiral symmetry breaking. It is demonstrated that one can understand the vector and the axial-vector spectrum very well within this interpretation. It is also shown that the opposite cases, namely ρ as a pion-pion molecule or a1 as a quark-antiquark state lead to less satisfying results. Finally speculations on possible in-medium changes of hadron properties are presented.

Chiral partners and their electromagnetic radiation (Ingredients for a systematic in-medium calculation)

It is argued that the chiral partners of the lowest-lying hadrons are hadronic molecules and not three-quark or quark–antiquark states, respectively. As an example the case of a 1 as the chiral partner of the ρ is discussed. Deconfinement–or as a precursor large in-medium widths for hadronic states–is proposed as a natural way to accommodate for the fact that at chiral restoration the respective in-medium spectra of chiral partners must become degenerate. Ingredients for a systematic and self-consistent in-medium calculation are presented with special emphasis on vector-meson dominance which emerges from a recently proposed systematic counting scheme for the mesonic sector including pseudoscalar and vector mesons as active degrees of freedom.

Neutron stars within the SU(2) parity doublet model

The equation of state of beta-stable and charge neutral nucleonic matter is computed within theSU(2) parity doublet model in mean-field and in the relativistic Hartree approximation. The mass of the chiral partner of the nucleon is assumed to be 1200MeV. The transition to the chiral restored phase turns out to be a smooth crossover in all the cases considered, taking place at a baryon density of just 2ρ0 . The mass-radius relations of compact stars are calculated to constrain the model parameters from the maximum mass limit of neutron stars. It is demonstrated that chiral symmetry starts to be restored, which in this model implies the appearance of the chiral partners of the nucleons, in the center of neutron stars. However, the analysis of the decay width of the assumed chiral partner of the nucleon poses limits on the validity of the present version of the model to describe vacuum properties.

LOW LYING SCALAR RESONANCES AND CHIRAL SYMMETRY

Current theoretical studies on the σ and κ resonances are reviewed. It is emphasized that all evidences accumulated so far are consistent with the picture that the σ meson is the chiral partner of the Nambu–Goldstone bosons in a linear realization of chiral symmetry.

πNandππNCouplings of theΔ(1232)and Its Chiral Partners

We investigate the interactions and chiral properties of the four spin-3/2 baryons N(-)(D13), N+(P13), Delta+(P33), and Delta(-)(D33) together with the nucleon. We construct the SU(2)R x SU(2)L invariant interactions between the spin-1/2 and spin-3/2 baryons with the aid of a new, specially developed spin and isospin projection technique for these baryon fields, where the chiral invariant interactions contain one- and two-pion couplings. We obtain simple relations for the coupling constants of the one- and two-pion spin-1/2-3/2 transitions terms. The relation for the one-pion interactions reasonably agrees with the experiments, which suggests that these spin-3/2 baryons are chiral partners.

Chiral properties of baryon interpolating fields

We study the chiral transformation properties of all possible local (non-derivative) interpolating field operators for baryons consisting of three quarks with two flavors, assuming good isospin symmetry. We derive and use the relations/identities among the baryon operators with identical quantum numbers that follow from the combined color, Dirac and isospin Fierz transformations. These relations reduce the number of independent baryon operators with any given spin and isospin. The Fierz identities also effectively restrict the allowed baryon chiral multiplets. It turns out that the non-derivative baryons’ chiral multiplets have the same dimensionality as their Lorentz representations. For the two independent nucleon operators the only permissible chiral multiplet is the fundamental one, $(\frac{1}{2},0)\oplus(0,\frac{1}{2})$ . For the Δ, admissible Lorentz representations are $(1,\frac{1}{2})\oplus(\frac{1}{2},1)$ and $(\frac{3}{2},0)\oplus(0,\frac{3}{2})$ . In the case of the $(1,\frac{1}{2})\oplus (\frac{1}{2},1)$ chiral multiplet, the $I(J)=\frac{3}{2}(\frac{3}{2})$ Δ field has one $I(J)=\frac{1}{2}(\frac{3}{2})$ chiral partner; otherwise it has none. We also consider the Abelian (U A(1)) chiral transformation properties of the fields and show that each baryon comes in two varieties: (1) with Abelian axial charge +3; and (2) with Abelian axial charge −1. In case of the nucleon these are the two Ioffe fields; in case of the Δ, the $(1,\frac{1}{2})\oplus(\frac{1}{2},1)$ multiplet has an Abelian axial charge −1 and the $(\frac{3}{2},0)\oplus(0,\frac{3}{2})$ multiplet has an Abelian axial charge +3.

Level crossing of particle–hole and mesonic modes in eta-mesonic nuclei

We study eta-meson properties in the infinite nuclear matter and in atomic nuclei with an emphasis on effects of the eta coupling to N ∗ ( 1535 ) -nucleon–hole modes. The N ∗ ( 1535 ) resonance, which dominates the low-energy eta-nucleon scattering, can be seen as a chiral partner of the nucleon. The change of the chiral mass gap between the N ∗ and the nucleon in a nuclear medium has an impact on the properties of the eta-nucleus system. If the N ∗ -nucleon mass gap decreases with a density increase (chiral symmetry restoration) the calculations show the existence of the resonance state at the energy about 60 MeV and two bound eta-nucleus states with the binding energies about − 80 MeV . These states can have strong effect on predicted cross sections of the 12C ( γ , p ) 11B reaction with eta-meson production.

Role of the axial vectora1-meson exchange in hypernuclear nonmesonic weak decays

In the meson-theoretical potential model for the study of the nonmesonic decay rates and asymmetries of hypernuclei, for the first time, the axial-vector ${a}_{1}$ meson (${J}^{\mathrm{PC}}={1}^{++},{m}_{{a}_{1}}=1230\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$) is introduced. The ${a}_{1}$ meson is the chiral partner of the \ensuremath{\rho} meson and has been treated in the meson-pair exchange framework as $\ensuremath{\rho}\ensuremath{\pi}/{a}_{1}$ and $\ensuremath{\sigma}\ensuremath{\pi}/{a}_{1}$. This is analogous to the treatment of \ensuremath{\rho} and \ensuremath{\sigma} exchange in our model. The ${a}_{1}$-meson exchange is found to give remarkable modifications of the parity-conserving decay potentials $({}^{1,3}S\ensuremath{\rightarrow}{}^{1,3}S$ and ${}^{3}{S}_{1}\ensuremath{\rightarrow}{}^{3}{D}_{1})$ at short range $r\ensuremath{\leqslant}1$ fm. As a result, the calculated intrinsic asymmetry parameter ${\ensuremath{\alpha}}_{\ensuremath{\Lambda}}$ for ${}_{\ensuremath{\Lambda}}^{5}\mathrm{He}$ becomes very small and positive in good agreement with the recent high-quality experimental data. The calculated small values of ${\ensuremath{\alpha}}_{\ensuremath{\Lambda}}$ are well compared with the data for ${}_{\ensuremath{\Lambda}}^{11}\mathrm{B}$ and ${}_{\ensuremath{\Lambda}}^{12}\mathrm{C}$ within error bars. The inclusion of the ${a}_{1}$ meson also improves the ${\ensuremath{\Gamma}}_{n}/{\ensuremath{\Gamma}}_{p}$ ratios and leads to a consistent explanation for the existing nonmesonic weak decay data of the light \ensuremath{\Lambda} hypernuclei $(A\ensuremath{\leqslant}12)$. The results calculated in the $\ensuremath{\pi}+2\ensuremath{\pi}/\ensuremath{\rho}+2\ensuremath{\pi}/\ensuremath{\sigma}+\ensuremath{\omega}+K+\ensuremath{\rho}\ensuremath{\pi}/{a}_{1}+\ensuremath{\sigma}\ensuremath{\pi}/{a}_{1}$ exchange interaction model are presented together with the estimates without ${a}_{1}$. Also, the derivation of the expression for the proton asymmetry is described in some detail to elucidate the calculation procedures and phase conventions.