Chiral Symmetry in Hadrons and Nuclei

The following sections are included:

• Contents
• Preface

A brief survey of results of studies of nuclear chirality in the mass 80 and 190 region at iThemba LABS is given, before looking at the case of ¹⁰⁶Ag in detail. Here, the crossing of a pair of candidate chiral bands is re-interpreted as the crossing of a prolate band by an aligned four-quasiparticle band.

We perform a calculation for three body scattering amplitude by using the fixed-center approximation to Faddeev Equations, taking the interaction between ρ and , ρ and K from the chiral unitary approach. We find peak in the modulus squared of the three-body scattering amplitude, indicating the existence of resonance which can be associated to ρ(1700).

Parton models predict several symmetries for the parton distribution functions of the nucleon, including flavour symmetry, charge symmetry, and quark-antiquark symmetry. We report calculations using the meson cloud model for the breaking of these symmetries.

Firstly the previous results of J/ψ hadronic and radiative decays are reported, based on the vector-vector molecular structure of some tensor resonance states and f₀(1710) which are generated dynamically from the interaction of pairs of more elementary hadrons, finding the results reasonably consistent with the experimental data available. Then some new results are further reported for ψ(nS) and ϒ(nS) decays, including the ψ(2S) decay into and radiative decay of ϒ(1S), ϒ(2S), ψ(nS) into . Agreement with experimental data is found, and some predictions are done for future experiments, hoping to set further tests on the molecular nature of these resonances.

We discuss how to use Morgan's pole counting rule to distinguish a molecular state from an ‘elementary’ particle. As two examples we focus on X(3872) and f₀(980) particles. A molecule may be generated from a meson loop bubble chain, and an ‘elementary’ particle is related to an explicit interaction field in the effective lagrangian and propagates with a Breit–Wigner propagator. For X(3872) it is found that the data favor the ‘elementary’ particle explanation. For f₀(3872) the study becomes much more difficult, since highly non-perturbative dynamics is involved. A unitarization model analysis suggests that f₀(980)'s property is quite exotic. Unlike other light scalars, it does not behave like a state, and could be interpreted as a molecule.

These proceedings summarize recent work on parity violation in proton-proton scattering in chiral effective field theory.

We study the Λ(1405), Λ(1670) and the isovector baryon resonances of Σ-type in the pseudo-Goldstone octet and the lightest baryon octet scattering. S-wave scattering is considered by employing unitary chiral perturbation theory. Through fitting various experimental data, such as cross sections, πΣ event distributions, atomic kaon hydrogen data, etc., we determine the free parameters, which are then used in the discussion of the baryon spectroscopy and the scattering lengths.

We treat explicitly Δ (1232) isobar degrees of freedom using bare nucleonnucleon interaction, which can be the origin of the three-body forces via the pion exchange. We adopt the Argonne delta model potential (AV28) and study the explicit role of Δ in light nuclei. It is surprising that the additional Δ states generate strong tensor correlations from the transitions between N and Δ states, and change various matrix elements from the results with only the nucleon space.

Recent experimental observations of many unconventional hadronic states stimulate an interest in the structure of hadrons. While various internal configurations have been proposed, it is a subtle problem to identify the structure of hadron resonances in a model independent manner. Here we discuss the composite/elementary nature of hadrons using the field renormalization constant Z. In particular, we show that the magnitude of the effective range parameter r_e is related to the structure of s-wave near-threshold resonances.

We investigate thermodynamics of hadrons using the Gaussian functional method (GFM) at finite temperature. Since the interaction among mesons is very large, we take into account fluctuations of mesons around their mean field values using the GFM. We obtain the ground state energy by solving the Schrödinger equation. The meson masses are obtained using the energy minimization condition. The resulting mass of pion is not zero even in the spontaneous chiral symmetry broken phase due to the non-perturbative effect. We consider then the bound state of mesons using the Bethe-Salpeter equation and show that the Nambu-Goldstone theorem is recovered. We investigate further the behavior of the meson masses and the mean filed value as functions of temperature for the cases of chiral limit and explicit chiral symmetry breaking.

Level structure of with the Δ particle in p orbit is investigated within the framework of the antisymmetrized molecular dynamics. It is found that there rotational bands appear by adding Δ in p orbit due to the triaxial deformation of the host nucleus ²⁴Mg.

The X(3872) is a charmonium-like hadron with a mass close to the threshold. It was first observed in 2003 by the Belle Collaboration and confirmed shortly after by the CDF collaboration. The quantum numbers were recently determined by the LHCb experiment to be J^PC = 1⁺⁺³. Yet, the nature of the X(3872) is not fully understood. In future, lattice QCD calculations should be able to obtain observables and are expected to contribute to a better understanding of the X…

Hyperfine structure of ground-state nucleons is studied by checking the isospin breaking effect due to the non-zero differences of mass and electromagnetic interaction between the up and down quarks. It is shown using chiral nonlinear quark model that the isospin breaking corrections to the baryon mass are of the order of one percent relatively to hadronic energies. The computed mass splittings due to the hyperfine strong and the electromagnetic corrections are in good agreement with the recent data of the baryon mass splitings.

We obtain the full U group chiral Lagrangian to the order p⁶ order, and check the existing results. We find one more linear relation in p⁴ order at U group, and some more linear relations in p⁶ order at SU group with tensor sources.

This manuscript sheds light on the puzzle created by the finding of two resonances with same quantum numbers and very similar mass but which possess very different decay properties. One of them, f₀(1790), has been found in the J/Ψ → φπ⁺π⁻ process while the other, f₀(1800), in J/Ψ → γωφ. As we shall discuss in this manuscript, our studies show that these two states are distinct to each other but only one of them is a new state, while the other one is the manifestation of the known f₀(1710). We also provide an explanation for the different decay properties of these states.

Comprehensive understanding of the structure and reactions of light nuclei poses theoretical and computational challenges. Still, a number of ab initio approaches have been developed to calculate the properties of atomic nuclei using fundamental interactions among nucleons. Among them, we work with the ab initio no core full configuration (NCFC) method and ab initio no core Gamow Shell Model (GSM). We first review these approaches and present some recent results.

The effect of strength of each interaction on the nuclear shape phase and their transitional patterns are studied in the SD-pair shell model with a Hamiltonian composed of the single-particle energy term, monopole-pairing, quadrupole-pairing and quadrupole-quadrupole interaction for identical nucleon system. It is shown that with quandrupole-pairing interaction and quadrupole-quadrupole interaction strengths set to be 0, the nuclear phase transition from single-particle motion to collective motion can be produced by changing the monopole pairing interaction. With fixed monopole-pairing interaction and quadrupole-pairing interactional strength set to be 0, the like-vibration-rotation shape phase transitional pattern can be produced by changing the quadrupole-quadrupole interaction from 0 to .

We investigate the three-body systems of and , by taking the fixed center approximation to Faddeev equations. We find a clear and stable resonance structure around 1490 MeV in the scattering amplitude for the system, which is not sensitive to the renormalization parameters. This resonance is associated to the η(1475). We get only an enhancement effect of the threshold in the amplitude.

Recently observed heavy quark exotic XYZ mesons stimulated heated discussions about their structures. In the molecule picture, we discuss the spin of the heavy quark pair in an S-wave meson-antimeson state, whose value is either 1 or 0. We find two rules that the spin is only 1 in the heavy quark limit. From the conservation of the spin, one may analyze the charmonium products from strong decays. The selection rules give constraints on the products.

As the latest effort to search for deeply-bound -nuclear states, E15 experiment has been carried out at K1.8 branch beam line (K1.8BR) at J-PARC. ³He(K⁻, N) reaction was employed to search for the simplest -nuclear bound state, K⁻-pp. In this proceeding, preliminary results of ³He(K⁻, n) spectra obtained in the first physics-run will be presented.

In this talk I show the results we find for the invariant mass distribution associated to the reaction , which has been studied by the BESIII collaboration and claims of a new J^P = 1⁺ state, called Z_c(4025), have been made. As I will show, while the interpretation of the BESIII collaboration for the signal found is plausible, there are others which are equally possible, like a J^P = 2⁺ resonance or a bound state or simply a pure D-wave background. Thus, the arguments to claim a new state around 4025 MeV in the invariant mass distribution get weaker.

I discuss the fine-tuning of the nuclear forces and in the formation of nuclei in the production of the elements in the Big Bang and in stars.

The interaction between pseudoscalar and/or vector mesons can be studied using hidden gauge Lagrangians. In this framework, the interaction between charmed mesons has been studied. Furthermore, doubly charmed states are also predicted. These new states are near the D^*D^* and thresholds, and have spin-parity J^P = 1⁺. We evaluate the decay widths of these states, named as R_cc(3970) and S_cc(3970) (with strangeness), and obtain 44 MeV for the nonstrangeness, and 24 MeV for the doubly charm-strange state. Essentially, the decay modes are DD_(s)π and DD_(s)γ, being the D_π and D_γ emitted by one of the D^* meson which forms the molecule.

In the framework of two flavor quark-meson model we study the effect of mixing between effective quarkonium and tetraquark fields on chiral phase transition. Depending on the values of different parameters we explore different scenarios. The common feature among all of them is that the transition for quarkonium and tetraquark happening at the same temperature for all densities. We find a sufficiently strong negative cubic self interaction coupling constant of the tetraquark field can drive the chiral phase transition to first order even at zero quark chemical potential.

Nuclear emulsion was used to search for double-Λ hypernuclei for a half century. We have nine events showing sequential decay of two units of Λ hyperon in nucleus, however our knowledge of Λ-Λ interaction is still poor, so far. Based on knowhow given by the past emulsion experiments, the E07 experiment at J-PARC is expected to present the events in ~10² and ~10³ with Hybrid-emulsion and Overall-scanning method, respectively.

We report here our results on how to obtain the Regge trajectory of a resonance from its pole in a scattering process by imposing analytic constraints in the complex angular momentum plane. The method, suited for resonances that dominate an elastic scattering amplitude, has been applied to the ρ (770) and the f₀(500) resonances. Whereas for the former we obtain a linear Regge trajectory, characteristic of ordinary quark-antiquark states, for the latter we find a non-linear trajectory with a much smaller slope at the resonance mass. This provides a strong indication of the non-ordinary nature of the sigma meson.

Recent studies of (hyperonic) nuclear forces based on lattice QCD are presented. An energy independent non-local potential can be obtained from Nambu-Bethe-Salpeter wave function which is measured from the lattice QCD calculation with a set of interpolating fields of baryons, where a time-dependent Schrödinger equation in imaginary time is employed so as to avoid the exact ground state saturation in the numerical computation. The central and the tensor potentials of ΛN and ΣN with isospin I = 2/3 channels are presented as specific numerical examples. We also present an attempt to study the fournucleon bound state problem using the lattice nuclear potential with stochastic variational method.

Heavy quarks play special roles in the hadron spectroscopy. Some distinct features of heavy quark dynamics and their significance in the P-wave baryons with a single heavy quark are discussed. We also explore a new color configuration in exotic tetra-quark mesons with two heavy quarks. Finally, possibility of bound states of a charmed baryon with a nucleon and nuclei are examined.

In this talk I report on the recent developments in the subject of dynamically generated resonances. In particular I discuss the and reactions, with a peculiar behavior around the K^*0Λ threshold, due to a 1/2⁻ resonance around 2035 MeV. Similarly, I discuss a BES experiment, decay, which provides evidence for a new h₁ resonance around 1830 MeV that was predicted from the vector-vector interaction. A short discussion is then made about recent advances in the charm and beauty sectors.

The effective field theory formulation of nuclear forces is able to provide a systematic and model independent description of nuclear physics, where all processes involving nucleons and pions can be described in terms of the same set of couplings, the theoretical errors are known in advance and the connection with QCD is present. These features are a consequence of renormalization group invariance, which in turn determines the power counting of the theory. Here we present a brief outline of how to determine the power counting of nuclear effective field theory, what does it looks like and what are the predictions for the two-nucleon sector at lowest orders.

I will briefly review in this talk the most significant developments in light scalars spectroscopy that have occurred since the last edition of this Conference, although I will comment on the updates of the mass and width of different light scalar mesons in the latest edition of the Particle Data Tables, I will be mostly focusing on the major revision of the f₀(500) meson, also known as σ meson. I will explain how this major update has been driven both by new data and rigorous dispersive analyses.

In this paper we summarize results for baryonic contact terms derived within SU(3) chiral effective field theory. The four-baryon contact terms, necessary for the description of the hyperon-nucleon interaction, include SU(3) symmetric and explicit chiral symmetry breaking terms. They also include four-baryon contact terms involving pseudoscalar mesons, which become important for three-body forces. Furthermore we derive the leading order six-baryon contact terms in the non-relativistic limit and study their contribution to the ΛNN three-body contact interaction. These results could play an important role in studies of hypernuclei or hyperons in nuclear matter.

We report an analysis of the octet baryon masses using the covariant baryon chiral perturbation theory up to next-to-next-to-next-to-leading order with and without the virtual decuplet contributions. Particular attention is paid to the finite-volume corrections and the finite lattice spacing effects on the baryon masses. A reasonable description of all the publicly available n_f = 2 + 1 lattice QCD data is achieved. Utilyzing the Feynman-Hellmann theorem, we determine the nucleon sigma terms as σ_πN = 55(1)(4) Mev and σ_sN = 27(27)(4) MeV.

In this talk, we briefly review our ongoing collaboration to precisely determine the low-energy πN scattering amplitude by means of Roy–Steiner equations. After giving a brief overview of this system of dispersive equations and their application to πN scattering, we proceed to solve for the lower partial waves of the s-channel (πN → πN) and the t-channel sub-problems.

This report reviewed the recently discovered Z_c(3900) at around 3.9 GeV/c² in the π±J/ψ mass spectrum by the Belle and BESIII collaborations simultaneously. Belle collaboration observed it in the process e⁺e⁻ → π⁺π⁻ J/ψ within the Y (4260) signal region with a 967 fb⁻¹ data sample using initial-stateradiation technology. BESIII collaboration discovered it in the same process at a fixed center-of-mass energy of 4.260 GeV using a 525 pb⁻¹ data sample. The measured resonance masses and widths from Belle and BESIII measurements are consistent with each other within the errors. The Z_c(3900) can be interpreted as a new charged charmonium-like state.

The interaction potentials between vector mesons and baryon octet are calculated explicitly with a summation of t−, s−, u− channel diagrams and a contact term originating from the tensor interaction. Altogether, 17 resonances are generated dynamically in different channels of strangeness zero by solving the relativistic Lippman-Schwinger equations in the S-wave approximation of partial wave analysis, and their masses, decay widths, isospins and spins are determined. Some resonances are well fitted with their counterparts listed in the newest review of Particle Data Group(PDG), while others might stimulate the experimental observation in these energy regions in the future.

How massive the hybrid stars could be is discussed by a “3-window model” proposed from a new strategy to construct the equation of state with hadron-quark transition. It is found that hybrid stars have a strong potentiality to generate a large mass compatible with two-solar-mass neutron star observations.

Gamma-ray spectroscopy following the β decay is an effective tool for exploring low-lying yrast and non-yrast states, which provide key structure information such as the shape transitions/coexistence and the single-particle levels. For the study of rare isotopes, especially when the nucleus of interest lies at the boundaries of availability for spectroscopic studies, isomeric decays are likely to be a more useful means than β decays to populate lower-lying levels. The identification of such characteristic isomers will pin down currently controversial subjects including the evolution of shell structures. The combined β- and isomeric-decay measurements at the RI Beam Factory (RIBF), which has the capability of providing the world's strongest RI beams, are at the forefront of exploration of exotic nuclei far from the stability line…

Using a coupled channel unitary approach, combining the heavy quark spin symmetry and the dynamics of the local hidden gauge, we investigate the meson-meson interaction with hidden beauty. We obtain several new states of isospin I = 0: six bound states, and weakly bound six more possible states which depend on the influence of the coupled channel effects.

To understand the nature of the low-lying negative parity Λ resonances, we carried out a combined study of the reaction K⁻p → Λη at low energies and their strong decays with a chiral quark model. It is found that the low-lying negative parity Λ resonances, such as Λ(1670), Λ(1405), Λ(1520) and Λ(1690), are most likely mixed states between different configurations.

The possible existence of and BNN states is discussed. They are manifestly exotic dibaryons whose bound states which are stable against a strong decay. As for the interactions, we consider the one pion exchange potential enhanced by the heavy quark spin symmetry. By solving the coupled-channel Schrödinger equations for the three-body systems, we find the bound states with J^P = 0⁻ and resonances with J^P = 1⁻ for I = 0. We also discuss the spin degeneracy of the P_QNN states in the heavy quark mass limit.

Since Weinberg's proposal two decades ago, chiral effective field theory in the NN sector has been developed and applied up to order O((Q/M_hi)⁴). In principle it could provide a model-independent description of nuclear force from QCD. However, in spite of its huge success, some open issues such as the renormalization group invariance and power counting, still remain to be solved. In this talk we refine the chiral effective field theory approach to the NN system based on a renormalization group analysis. Our results show that a truly model-independent description of NN system can be obtained by a new power counting which treats the subleading order corrections perturbatively.

Recent work unambiguously resolves the level of charge symmetry violation in moments of parton distributions using (2+1)-flavor lattice QCD. We introduce the methods used for that analysis by applying them to determine the strong contribution to the proton–neutron mass difference. We also summarize related work which reveals that the fraction of baryon spin which is carried by the quarks is in fact structure-dependent rather than universal across the baryon octet.

Progresses of the chirality in atomic nuclei are reviewed, in particular, the recently proposed collective Hamiltonian based on tilted axis cranking approach to describe chiral vibration and rotation modes, and the experimental achievements for chirality and multiple chiral doublets, i.e., in ¹⁰⁶Ag, ¹³³Ce, and ¹⁰³Rh. The first experimental evidences of multiple chiral doublet bands with distinct and identical configuration found in ¹³³Ce and ¹⁰³Rh are discussed in detail.