We report the chiral quark model approach for the study of baryon resonances in meson photoproduction and meson-nucleon scattering processes. Focussing on the $πN$ and $K N$ scatterings, we show that the cross sections near threshold can be well accounted for by the chiral quark model with only few parameters. The $S$-wave dominance in both $π^- p\to ηn$ and $K^- p\to Σ^0π^0$ can be well understood in the quark model framework. In particular, the quark model provides a constraint on the relative signs for resonance coupling form factors, which seems to be consistent with results from isobaric models.
We discuss the masses of the ground state baryon octet and the nucleon sigma terms in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory. In order to obtain a consistent power counting for renormalized diagrams the extended on-mass-shell renormalization scheme is applied.
We calculate hyperon-nucleon and hyperon-hyperon interactions at next-to-leading order in SU(3) baryon chiral perturbation theory extending earlier work by the Bonn-Juelich group. The constructed potentials in momentum space include all one- and two-meson exchange terms generated by the SU(3) chiral Lagrangian. Effects from intermediate decuplet baryons are considered as well. These chiral baryon-baryon potentials, together with appropriate contact terms, provide a new basis for systematic studies of hyperon-nucleon scattering and light hypernuclei.
I report on recent progress in the description of baryon-baryon systems within chiral effective field theory. In particular, I discuss results for the strangeness S=-3 to -4 baryon-baryon systems, obtained to leading order.
The full QCD chiral symmetry algebra has predictive consequences at low energies. I discuss the ground-state chiral multiplet involving the light baryons and emphasize the special role of the Roper resonance.
We have constructed the leading order strangeness S=-1,-2 baryon-baryon potential in a chiral effective field theory approach. The chiral potential consists of one-pseudoscalar-meson exchanges and non-derivative four-baryon contact terms. The potential, derived using SU(3) symmetry constraints, contains six independent low-energy coefficients. We have solved a regularized Lippmann-Schwinger equation and achieved a good description of the available scattering data. Furthermore a correctly bound hypertriton has been obtained.
We derive the leading order strangeness S=-2 baryon-baryon interactions in chiral effective field theory. The potential consists of contact terms without derivatives and of one-pseudoscalar-meson exchanges. The contact terms and the couplings of the pseudoscalar mesons to the baryons are related via SU(3) flavor symmetry to the S=-1 hyperon-nucleon channels. We show that the chiral effective field theory predictions with natural values for the low-energy constants agree with the experimental information in the S=-2 sector.
We construct the most general chiral effective Lagrangian for baryon-baryon contact interactions in flavor SU(3) up to order q^2 using a covariant power counting. A subset of these contact terms contributes to the baryon-baryon potential in chiral effective field theory. The Lorentz invariant effective Lagrangian is constructed to fulfill the invariance under charge conjugation, parity transformation, Hermitian conjugation and the local chiral symmetry group SU(3)_L x SU(3)_R. Goldstone bosons and external fields are included as well, thus providing additional four-baryon contact vertices invo…
We discuss baryon resonances which are dynamically generated in hadron dynamics based on chiral coupled channels approach. With the dynamical description of the baryon resonance, we discuss the origin of the resonance pole, finding that for the description of N(1535) some other components than meson and baryon are necessary. Since the chiral unitary model provides a microscopic description in terms of constituent hadrons, it is straightforward to calculate transition amplitudes and form factors of resonances without introducing further parameters. Finally we briefly discuss few-body nuclear ka…
Interactions of two baryons are considered in large $N_C$ chiral perturbation theory and compared to the interactions derived from the Skyrme model. Special attention is given to a torus-like configuration known to be present in the Skyrme model.
We report on the recent studies of leading order baryon-baryon interactions in covariant baryon chiral perturbation theory. In the strangeness $S=0$ sector, one can achieve a rather good description of the Nijmegen $np$ phase shifts with angular momenta $J\leq 1$, particularly the $^1S_0$ and $^3P_0$ partial waves, comparable with the next-to-leading order (NLO) heavy baryon approach. In the strangeness $S=-1$ hyperon-nucleon sector, the best fit of the 36 scattering data is similar to the sophisticated phenomenological models and the NLO heavy baryon approach.
Results from an ongoing study of baryon-baryon systems with strangeness S=-1 and -2 within chiral effective field theory are reported. The investigations are based on the scheme proposed by Weinberg which has been applied rather successfully to the nucleon-nucleon interaction in the past. Results for the hyperon-nucleon and hyperon-hyperon interactions obtained to leading order are reviewed. Specifically, the issue of extrapolating the binding energy of the H-dibaryon, extracted from recent lattice QCD simulations, to the physical point is addressed. Furthermore, first results for the hyperon-…
The leading order strangeness S=-3 and -4 baryon-baryon interactions are analyzed within chiral effective field theory. The chiral potentials consist of contact terms without derivatives and of one-pseudoscalar-meson exchanges. Assuming SU(3) flavor symmetry those contact terms and the couplings of the pseudoscalar mesons to the baryons are related to the corresponding quantities of the S=-1 hyperon-nucleon channels. Specifically, the values of the pertinent five low-energy constants related to the contact terms are already fixed from our preceeding study of the Lambda-N and Sigma-N systems an…
Leading three-baryon forces are derived within SU(3) chiral effective field theory. Three classes of irreducible diagrams contribute: three-baryon contact terms, one-meson exchange and two-meson exchange diagrams. We provide the minimal non-relativistic terms of the chiral Lagrangian, that contribute to these diagrams. SU(3) relations are given for the strangeness S=0 and -1 sectors. In the strangeness-zero sector we recover the well-known three-nucleon forces from chiral effective field theory. Explicit expressions for the lambda-nucleon-nucleon chiral potential in isospin space are presented…
We have constructed the leading order strangeness S=-1,-2 baryon-baryon potential in a chiral effective field theory approach. The chiral potential consists of one-pseudoscalar-meson exchanges and non-derivative four-baryon contact terms. The potential, derived using SU(3)_f symmetry constraints, contains six independent low-energy coefficients. We have solved a regularized Lippmann-Schwinger equation and achieved a good description of the available scattering data. Furthermore a correctly bound hypertriton has been obtained.
A formalism for treating the scattering of decuplet baryons in chiral effective field theory is developed. The minimal Lagrangian and potentials in leading-order SU(3) chiral effective field theory for the interactions of octet baryons ($B$) and decuplet baryons ($D$) for the transitions $BB\to BB$, $BB\leftrightarrow DB$, $DB\to DB$, $BB\leftrightarrow DD$, $DB\leftrightarrow DD$, and $DD\to DD$ are provided. As an application of the formalism we compare with results from lattice QCD simulations for $ΩΩ$ and $NΩ$ scattering. Implications of our results pertinent to the quest for dibaryons are…
We study the phase diagram of a generalized chiral SU(3)-flavor model in mean-field approximation. In particular, the influence of the baryon resonances, and their couplings to the scalar and vector fields, on the characteristics of the chiral phase transition as a function of temperature and baryon-chemical potential is investigated. Present and future finite-density lattice calculations might constrain the couplings of the fields to the baryons. The results are compared to recent lattice QCD calculations and it is shown that it is non-trivial to obtain, simultaneously, stable cold nuclear ma…
We calculate the complete $T$ matrices of the elastic nucleon-nucleon scattering up to third order in SU(3) heavy baryon chiral perturbation theory. The phase shifts with orbital angular momentum $L\geq 2$ and the mixing angles with $J\geq 2$ are evaluated by using low-energy constants that were extracted from the meson-baryon analysis. It turns out that our prediction is consistent with the empirical phase shifts and mixing angles data, and also the results from SU(2) heavy baryon chiral perturbation theory. The errors from the low-energy constants are analyzed in detail. Our calculation prov…
It is shown that the principal pattern in baryon spectroscopy, which is associated with the flavor-spin dependent hyperfine interaction, is due to the spontaneous breaking of chiral symmetry in QCD and persists in the chiral limit. All corrections, which are associated with a finite quark (Goldstone boson) mass are suppressed by the factor $(μ/Λ_χ$)^2 and higher.
In this proceeding 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 …
I review the present status of three flavor baryon chiral perturbation theory in the heavy fermion formalism. It is argued that precise calculations have to include all terms quadratic in the quark masses. As examples, I consider the chiral expansion of the octet baryon masses, the baryon magnetic moments and kaon photoproduction off nucleons.
We have systematically investigated the magnetic moments and magnetic form factors of the decuplet baryons to the next-to-next-leading order in the framework of the heavy baryon chiral perturbation theory. Our calculation includes the contributions from both the intermediate decuplet and octet baryon states in the loops. We also calculate the charge and magnetic dipole form factors of the decuplet baryons. Our results may be useful to the chiral extrapolation of the lattice simulations of the decuplet electromagnetic properties.
We report on a systematic study of the ground-state octet baryon masses in the covariant baryon chiral perturbation theory with the extended-on-mass-shell renormalization scheme up to next-to-next-to-next-to-leading order, taking into account the contributions of the virtual decuplet baryons. A reasonable description of the lattice results is achieved by fitting simultaneously all the publicly available $n_f = 2+1$ lattice QCD data. It confirms that the various lattice simulations are consistent with each other. We stress that a self-consistent treatment of finite-volume corrections is importa…
We review recent progress in the understanding of low-energy baryon structure by means of chiral perturbation theory. In particular, we discuss the application of this formalism to the description of various properties such as the baryon-octet magnetic moments, the electromagnetic structure of decuplet resonances and the hyperon vector coupling $f_1(0)$. Moreover, we present the results on the chiral extrapolation of recent lattice QCD results on the lowest-lying baryon masses and we predict the corresponding baryonic sigma-terms.
The mass spectrum of the lowest lying octet baryons is calculated to next-to-next-to-leading order in heavy baryon chiral perturbation theory and partially quenched heavy baryon chiral perturbation theory. We work in the isospin limit and treat the decuplet baryons as dynamical fields. These results are necessary for extrapolating QCD and partially quenched QCD lattice simulations of the octet baryon masses.
The thermal properties of cold dense nuclear matter are investigated with chiral perturbation theory. The evolution curves for the baryon number density, baryon number susceptibility, pressure and the equation of state are obtained. The chiral condensate is calculated and our result shows that when the baryon chemical potential goes beyond $1150 \mathrm{MeV}$, the absolute value of the quark condensate decreases rapidly, which indicates a tendency of chiral restoration.
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 t…
We report on some recent developments in our understanding of the light-quark mass dependence and the SU(3) flavor symmetry breaking corrections to the magnetic moments of the ground-state baryons in a covariant formulation of baryon chiral perturbation theory, the so-called EOMS formulation. We show that this covariant ChPT exhibits some promising features compared to its heavy-baryon and infrared counterparts.
We consider a symmetry-preserving approach to the nucleon-nucleon scattering problem in the framework of the higher-derivative formulation of baryon chiral perturbation theory. Within this framework the leading-order amplitude is calculated by solving renormalizable equations and corrections are taken into account perturbatively.
The masses of the spin-3/2 baryons are calculated to next-to-next-to-leading order in heavy baryon chiral perturbation theory and partially quenched heavy baryon chiral perturbation theory. The calculation is performed for three light flavors in the isospin limit. These results are necessary for extrapolating QCD and partially quenched QCD lattice calculations of the decuplet baryon masses.
The relativistic chiral SU(3) Lagrangian is used to describe kaon-nucleon scattering imposing constraints from the pion-nucleon sector and the axial-vector coupling constants of the baryon octet states. We solve the covariant coupled-channel Bethe-Salpeter equation with the interaction kernel truncated at chiral order Q^3 where we include only those terms which are leading in the large N_c limit of QCD. The baryon decuplet states are an important explicit ingredient in our scheme, because together with the baryon octet states they form the large N_c baryon ground states of QCD. Part of our tec…
It is demonstrated that using a suitable renormalization condition one obtains a consistent power counting in manifestly Lorentz-invariant baryon chiral perturbation theory including vector mesons as explicit degrees of freedom.
The QCD sum-rule method has been widely used in studying various baryon properties. For a given problem, there are usually more than one sum rules and they do not work equally well. In this paper, we point out that chirality plays an important role in determining the reliability of a baryon sum rule. The contributions of positive- and negative-parity excited baryon states partially cancel each other in the chiral-odd sum rules, but add up in the chiral-even sum rules. As such, the chiral-odd sum rules are generally more reliable than the chiral-even sum rules. This allows one to identify the m…
We consider a renormalization scheme for relativistic baryon chiral perturbation theory which provides a simple and consistent power counting for renormalized diagrams. As an application we discuss the chiral expansion of the nucleon mass.
We have analyzed the chiral expansion of the baryon masses to second order in the quark masses, including strong isospin violation. The calculations are performed in Lorentz-invariant baryon chiral perturbation theory. Chiral extrapolation functions for three-flavor unquenched lattice simulations are derived. The matching to the two-flavor case and the sigma terms are also considered.
We have systematically investigated the decuplet (T) to octet (B) baryon ($T\rightarrow Bγ$) transition magnetic moments to the next-to-next-to-leading order and electric quadruple moments to the next-to-leading order in the framework of the heavy baryon chiral perturbation theory. Our calculation includes the contributions from both the intermediate decuplet and octet baryon states in the loops. Our results show reasonably good convergence of the chiral expansion and agreement with the experimental data. The analytical expressions may be useful to the chiral extrapolation of the lattice simul…
I review recent results in baryon chiral perturbation theory, in particular related to pion-nucleon scattering and first systematic attempts to go beyond next-to-leading order in the case of three flavors. New insight into the chiral expansion of the baryon masses and magnetic moments is presented.
The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symmetry in the lattice calculation of $πN σ$ term and strangeness. The third one is the role of chiral $U(1)$ anomaly in the anomalous Ward identity in evaluating the quark spin and the quark orbital angular momentum. Finally, the chiral effective theory for baryons is discussed.
We include in a systematic way the eta' in baryon chiral perturbation theory. The most general relativistic effective Lagrangian describing the interaction of the lowest lying baryon octet with the Goldstone boson octet and the eta' is presented up to linear order in the derivative expansion and its heavy baryon limit is obtained. As explicit examples, we calculate the baryon masses and the pi N sigma-term up to one-loop order in the heavy baryon formulation. A systematic expansion in the meson masses is possible, and appearing divergences are renormalized.
We have studied the chiral soliton model in a thermal vacuum. The soliton equations are solved at finite temperature and density. The temperature or density dependent soliton solutions are presented. The physical properties of baryons are derived from the soliton solutions at finite temperature and density. The temperature or density dependent variation of the baryon properties are discussed.
We study the reaction $π^\pm p \to π^\pm π^+ n$ and $π^- p \to π^0 π^0 n$ in heavy-baryon chiral perturbation theory of chiral order three from threshold up to pion laboratory kinetic energies of 400 MeV. We find that the contributions from amplitudes of chiral order three are large and play an essential role in reproducing the experimental data.
Integral equations for meson-baryon scattering amplitudes are obtained by utilizing time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of baryon chiral perturbation theory. Effective potentials are defined as sums of two-particle irreducible contributions of time-ordered diagrams and the scattering amplitudes are obtained as solutions of integral equations. Ultraviolet renormalizability is achieved by solving integral equations for the leading order amplitude and including higher order corrections perturbatively. As an application of the developed formalism, pion-n…
We extend our previous analysis of the unitarized pion-nucleon scattering amplitude including up to fourth order terms in Heavy Baryon Chiral Perturbation Theory. We pay special attention to the stability of the generated Delta(1232 resonance, the convergence problems and the power counting of the chiral parameters.
We construct the complete and minimal O(q^2) and O(q^3) three-flavour Lorentz invariant chiral meson-baryon Lagrangians for the first time in the literature. We compare with previous three-flavour studies reducing the number of independent monomials and adding new ones that were missing.
Chiral symmetry aspects for baryon properties are studied. After a brief discussion on general framework, we introduce two distinctive chiral group representations for baryons: the naive and mirror assignments. Using linear sigma models, nucleon properties are studied in both representations. Finally, we propose an experiment to distinguish the two assignments in the reactions of pion and eta productions.
Studies of the baryon-baryon interaction involving hyperons within chiral effective field theory, so far performed up to next-to-leading order (NLO) in the chiral expansion, have shown that for the strangeness $S=-1$ ($ΛN$, $ΣN$) and $S=-2$ ($ΛΛ$, $ΞN$) sectors a consistent and satisfactory description of the available scattering data and experimental constraints can be achieved based on the assumption of broken SU(3) flavor symmetry. We explore the possible extension of this approach at the NLO level to strangeness $S=-3$ and $S=-4$ baryon-baryon systems where empirical information is rather …
In the past, the axion-nucleon coupling has been calculated in the framework of SU(2) heavy baryon chiral perturbation theory up to third order in the chiral power counting. Here, we extend these earlier studies to the case of heavy baryon chiral perturbation theory with SU(3) flavor symmetry and derive the axion coupling to the full SU(3) baryon octet, showing that the axion also significantly couples to hyperons. As studies on dense nuclear matter suggest the possible existence of hyperons in stellar objects such as neutron stars, our results should have phenomenological implications related…
The structure of baryon resonance in coupled-channel meson-baryon scattering is studied from the viewpoint of chiral dynamics. The meson-baryon scattering amplitude can be successfully described together with the properties of the resonance in the scattering, by implementing the unitarity condition for the amplitude whose low energy structure is constrained by chiral theorem. Recently, there have been a major progress in the study of the structure of the resonance in chiral dynamics. We review the methods to clarify the structure of the resonance by focusing on the Lambda(1405) resonance.
Using the unified scheme for describing both quark spin and orbital angular momenta in the chiral quark model developed in the previous work, the magnetic moments of octet and decuplet baryons are calculated. The numerical result shows that the overall agreement with data is improved by including the orbital contributions.
We investigate the production of baryons and antibaryons in the central rapidity region of high energy nuclear collisions within the framework of the Skyrme model taking into account the effects of explicit chiral symmetry breaking. We argue that the formation of disordered chiral condensates may lead to enhanced baryon-antibaryon production at low transverse momentum.
Mass differences of the flavor octet and decuplet ground-state baryons are studied in the perturbative chiral quark model. We present a way to understand the nontrivial spin- and flavor dependent mass differences, where both pseudoscalar mesons and gluons play a significant role.
We analyze the electromagnetic form factors of the ground state baryon octet to fourth order in relativistic baryon chiral perturbation theory. Predictions for the Σ^- charge radius and the Λ-Σ^0 transition moment are found to be in excellent agreement with the available experimental information. Furthermore, the convergence behavior of the hyperon charge radii is shown to be more than satisfactory.
Reordering of the chiral perturbation series, proposed recently by Becher and Leutwyler in the framework of SU(2) baryonic ChPT, is applied to the SU(3) case. This results in improved convergence of the chiral expansion of static properties of the lowest lying baryon octet, which in most cases is quite impressive. Finite renormalization of coupling constants and the role it plays in the interpretation of effective field theories is discussed. Some future tests of the viability of the scheme are proposed too.
The complete renormalization of the weak Lagrangian to chiral order q^2 in heavy baryon chiral perturbation theory is performed using heat kernel techniques. The results are compared with divergences appearing in the calculation of Feynman graphs for the nonleptonic hyperon decay Lambda -> p pi^- and an estimate for the size of the counterterm contributions to the s-wave amplitudes in nonleptonic hyperon decays is given.
We cautiously review the treatment of pentaquark exotic baryons in chiral soliton models. We consider two examples and argue that any consistent and self-contained description must go beyond the mean field approximation that only considers the classical soliton and the canonical quantization of its (would-be) zero modes via collective coordinates.
Heavy baryon chiral perturbation theory is briefly reviewed, paying particular attention to the role of the spin 3/2 delta resonances. The concept of resonance saturation for the baryonic sector is critically discussed. Starting from a relativistic formulation of the pion-nucleon-delta system, the heavy baryon chiral lagrangian including spin 3/2 resonances is constructed by means of a 1/m-expansion. The effective theory obtained admits a systematic expansion in terms of soft momenta, the pion mass $M_π$ and the delta-nucleon mass difference $Δ$.
In these lectures, the status of baryon chiral perturbation theory is reviewed. Particular emphasis is put on the two--flavor sector and the physics related to electromagnetic probes. I discuss in some detail the structure of the effective Lagrangian at next--to--leading order, the meaning of low--energy theorems in Compton scattering and pion photoproduction and confront the chiral predictions with the existing data. Some remaining problems and challenges are outlined.
The self-energies of the full set of flavor SU(3) octet and decuplet baryons are computed within a relativistic chiral effective theory framework. The leading nonanalytic chiral behavior is derived for the octet and decuplet masses, and a finite-range regularization consistent with Lorentz and gauge invariance is applied to account for the finite size of the baryons. Using a four-dimensional dipole form factor, the relative importance of various meson-baryon loop contributions to the self-energies is studied numerically as a function of the dipole range parameter and meson mass, and comparison…
The complete renormalization of the generating functional for Green functions of quark currents between one--baryon states in three flavor heavy baryon chiral perturbation theory is performed to order q^3. As an example, we study the kaon loop induced divergences in neutral pion photoproduction off protons.
