Pseudoscalar Meson Octet Research Articles

Interactions of the pseudoscalar meson octet and the baryon decuplet in the continuum and a finite volume

This study focuses on the interaction of the pseudoscalar meson octet and the baryon decuplet. In the continuum, it is observed that several JP=32-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^{P}=\\frac{3}{2}^-$$\\end{document} baryon resonances can be produced by the Weinberg-Tomozawa interaction in unitarized chiral perturbation theory, including the N(1875), Σ(1670)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma (1670)$$\\end{document}, Σ(1910)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma (1910)$$\\end{document}, Ξ(1820)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi (1820)$$\\end{document} and Ω(2012)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega (2012)$$\\end{document}. Among them, the Ξ(1820)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi (1820)$$\\end{document} and Σ(1670)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma (1670)$$\\end{document} may exhibit a potential two-pole structures. The unitarized chiral perturbation approach is then applied as the underlying theory to predict the energy levels of these systems in a finite volume. These energy levels are well described by the K-matrix parameterization constrained by flavor SU(3) symmetry. With the parameters from the best fits, the poles extracted from the K-matrix parameterization closely correspond to those derived from the underlying chiral effective field theory, as long as they are close to physical region and not significantly higher than the lowest relevant threshold.

Application of Bayesian statistics to the sector of decay constants in three-flavour chi PT

The sector of decay constants of the octet of light pseudoscalar mesons in the framework of ‘resummed’ SU(3) chiral perturbation theory is investigated. A theoretical prediction for the decay constant of eta -meson is compared to a range of available determinations. Compatibility of these determinations with the latest fits of the SU(3) low energy coupling constants is discussed. Using a Bayesian statistical approach, constraints on the low energy coupling constants L_4^r and L_5^r, as well as higher order remainders to the decay constants F_K and F_eta , are extracted from the most recent experimental and lattice QCD inputs for the values of the decay constants.

Axial-vector form factors of the baryon octet and chiral symmetry

We consider the axial-vector form factors of the baryon octet in flavor-SU(3) chiral perturbation theory. The baryon octet and decuplet and the pseudoscalar-meson octet are included as explicit degrees of freedom. We explore the use of on-shell meson and baryon masses in the one-loop contributions to the axial-vector form factors and focus on a consistent treatment in terms of chiral power counting. The convergence properties of such an approach are scrutinized. We discuss the potential for comparison to upcoming QCD lattice data.

Chiral symmetry breaking and chemical equilibrium in heavy-ion collisions

We examine the thermalization of an ensemble of the octet of pseudoscalar mesons, in the isospin symmetric limit, whose interactions are constrained through chiral symmetry, unitarity, and measurements. The reaction amplitudes generate all resonances up to masses of about 2 GeV, with twelve input parameters, namely f_pi, three masses, and eight low energy constants (LECs) of chiral perturbation theory. In linear response theory, we find that matter takes an extremely long time to thermalize. These long relaxation times are directly related to the fact that these mesons are pseudo-Goldstone bosons of chiral symmetry breaking. This result indicates that fireballs created with zero baryon number in heavy-ion collisions will drop out of chemical equilibrium once they enter the chiral symmetry broken phase.

Studying two-body nonleptonic weak decays of hyperons with topological diagram approach

Many decays of light baryons consisting of light u, d, s quarks have been measured, and these measurements will help us to understand the decay properties of light baryons. In this work, we study two-body nonleptonic weak decays of light baryon octets (T8) and baryon decuplets (T10) by the topological diagram approach (TDA) under the SU(3) flavor symmetry for the first time. We find that () the TDA and the SU(3) irreducible representation approach (IRA) match consistently in (P8 is the light pseudoscalar meson octet); (2) almost all relevant not-yet-measured may be predicted by using three experimental data of , and the upper limits of may be obtained from the experimental upper limit of by both the TDA and the IRA together, nevertheless, all new predicted branching ratios are too small to be reached in current experiments; (3) T8 → T8′P8 decays are quite complex in terms of the TDA, and we find that W-exchange diagrams give large and even dominant contributions by using relevant experimental data and the isospin relations.

Meson–baryon coupling constants of the SU(3) baryons with flavor SU(3) symmetry breaking

We investigate the strong coupling constants for the baryon octet–octet, decuplet–octet, and decuplet–decuplet vertices with pseudoscalar mesons within a general framework of the chiral quark-soliton model, taking into account the effects of flavor SU(3) symmetry breaking to linear order in the expansion of the strange current quark mass. All relevant dynamical parameters are fixed by using the experimental data on hyperon semileptonic decays and the singlet axial-vector constant of the nucleon. The results of the strong coupling constants for the baryon octet and the pseudoscalar meson octet are compared with those determined from the Jülich–Bonn potential and the Nijmegen extended soft-core potential for hyperon–nucleon scattering. The results of the strong decay widths of the baryon decuplet are in good agreement with the experimental data. The effects of SUf(3) symmetry breaking are sizable on the η′ coupling constants. We predict also the strong coupling constants for the Ω baryons.

The S- and P-Wave Low-Lying Baryons in the Chiral Quark Model

The $1S$, $2S$, $1P$ and $2P$ states of light baryons are investigated within the chiral quark model, paying particular attention to the well-known order reverse problem of $1P$ and $2S$ states. Besides a nonperturbative linear-screened confining interaction and a perturbative one-gluon exchange between quarks, we incorporate the Goldstone-boson exchanges taking into account not only the full octet of pseudoscalar mesons but also the scalar one. The scalar meson exchange potential simulates the higher order multi-pion exchange terms that appear in the chiral Lagrangian and its omission has been already admitted as a deficiency of the original model in describing, for instance, the $\rho-\omega$ splitting. The numerical approach to the three body bound state problem is the so-called Gau\ss ian expansion method, which is able to get a precision as good as Faddeev calculations. With a set of parameters fixed to different hadron and hadron-hadron observables, we find that the chiral potential could play an important role towards the issue on the mass order reverse problem. We extend our calculation to the $qqQ$ and $qQQ$ sectors (with $q$ representing a light $u$-, $d$-, or $s$-quark and $Q$ denoting the charm quark or the bottom one) in which many new states have been recently observed. Some tentative assignments are done attending to the agreement between theoretical and experimental masses; however, we admit that other sources of information are needed in order to make strong claims about the nature of these states.

Strangeness production in $p \bar{p}$ collision

We study strangeness production reactions in the framework of a Chiral Constituent Quark Model. The model includes the coupling with the SU(3) pseudoscalar meson octet due to the spontaneous chiral symmetry breaking. It also includes QCD perturbative effects through the coupling with the gluon field. In this way the two traditional mechanism of strangeness production, i.e., the kaon exchange and gluon annihilation, are introduce in the same framework. Two meson exchanges are parametrized through the exchange of scalar mesons, namely a sigma and a kappa exchange. The kappa exchange allows a better description of the polarization observables of the \(p\bar p \to \Lambda \bar \Lambda\) production reaction. Other strangeness production reaction in the isospin 1 sector are also studied.

Predictive AdS/QCD model for mass spectra of mesons with three flavors

The predictive soft-wall AdS/QCD model with a modified 5D metric at the infrared region is constructed to obtain a nontrivial dilaton solution for three flavor quarks $u$, $d$ and $s$. Such a model is shown to incorporate both the chiral symmetry breaking and linear confinement. After considering some high-order terms including the $\mathrm{U}(1{)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{R}$ chiral symmetry breaking term, we find that the resulting predictions for the SU(3) octet and singlet resonance states of pseudoscalar, scalar, vector and axial-vector mesons agree well with the experimentally confirmed resonance states. Contributions from the instanton effects given by the determinant term are also discussed. It is observed that the chiral symmetry breaking phenomena of $\mathrm{SU}(3{)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3{)}_{R}$ and $\mathrm{U}(1{)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1{)}_{R}$ can be well described in this model, while the SU(3) flavor symmetry breaking effect due to quark mass difference in the source term is not enough to explain all of the current experimental data.

Shell model formalism for all hypernuclei types: A guide to solving the nonmesonic weak decay puzzle

We extend to odd-odd core hypernuclei our independent particle shell model (IPSM) formalism developed previously for the evaluation of the ${\ensuremath{\Gamma}}_{\mathrm{NM}},{\ensuremath{\Gamma}}_{n/p}$, and ${a}_{\ensuremath{\Lambda}}$ hypernuclear weak decay observables. The present procedure reproduces the even-odd and even-even core results as particular cases. Adopting the standard strangeness-changing weak $\ensuremath{\Lambda}N\ensuremath{\rightarrow}\mathit{NN}$ transition potential with exchange of the complete pseudoscalar and vector meson octets ($\ensuremath{\pi},\ensuremath{\eta},K,\ensuremath{\rho},\ensuremath{\omega},{K}^{*}$) we get simple analytical expressions for all observables. Numerical values for ${}_{\ensuremath{\Lambda}}^{4}\mathrm{He},{}_{\ensuremath{\Lambda}}^{5}\mathrm{He},{}_{ \ensuremath{\Lambda}}^{11}\mathrm{B},{}_{ \ensuremath{\Lambda}}^{12}\mathrm{C},{}_{ \ensuremath{\Lambda}}^{16}\mathrm{O},{}_{ \ensuremath{\Lambda}}^{17}\mathrm{O}$, and ${}_{\ensuremath{\Lambda}}^{28}\mathrm{Si}$ hypernuclei are obtained and compared with available experimental data, putting special attention on the asymmetry parameter. We remark that, in the present form, the IPSM gives roughly the same value of ${a}_{\ensuremath{\Lambda}}$ for all hypernuclei in contradiction with experiments. We stress the necessity of introducing configuration mixing to go beyond the IPSM taking into account, in a more realistic way, nuclear structure effects. Moreover, one could to include more relevant degrees of freedom, even within the IPSM framework, like: (i) modifications of the exchange potential (two-pion, ${a}_{1}$ meson, $\ensuremath{\Delta}T=3/2$ terms of vector mesons, etc.), (ii) final state interactions accounting for the distortion of the plane waves of emitted nucleons, and (iii) two-nucleon induced decay, as possible ways to solve the puzzle.

Decuplet contribution to the meson–baryon scattering lengths

We calculate decuplet contributions to the s-wave pseudoscalar meson octet–baryon scattering lengths to the third order in heavy baryon chiral perturbation theory (HBχPT). Using experimental pion–nucleon and kaon–nucleon scattering lengths as inputs, we determine low-energy constants and predict other meson–baryon scattering lengths. Numerically we consider three cases: (1) the case with only baryon octet contributions; (2) with decuplet contributions and (3) in the large Nc limit. Hopefully, the analytical expressions and the predictions are helpful to future investigations of the meson–baryon scattering lengths.

Radiative decay of the [formula omitted

Electromagnetic properties provide information about the structure of strongly interacting systems and allow for independent tests of hadronic models. The radiative decay of the Δ ∗ ( 1700 ) is studied, which appears dynamically generated in a coupled channel approach from the rescattering of the ( 3 / 2 + ) decuplet of baryons with the ( 0 − ) octet of pseudoscalar mesons. The radiative decay is predicted from the well-known couplings of the photon to the mesons and baryons which constitute this resonance in the dynamical picture.

Recent developments in chiral dynamics of hadrons and hadrons in a nuclear medium

In this talk I present recent developments in chiral dynamics of hadrons and hadrons in a medium addressing the following points: interaction of the octet of pseudoscalar mesons with the octet of baryons of the nucleon, showing recent experimental evidence on the existence of two Λ(1405) states, the interaction of the octet of pseudoscalar mesons with the decuplet of baryons of the Δ, with particular emphasis on the Λ(1520) resonance, dynamically generated by this interaction. Then I review the interaction of kaons in a nuclear medium and briefly discuss the situation around the claims of deeply bound states in nuclei. The large renormalization of the Λ(1520) in the nuclear medium is shown as another example of successful application of the chiral unitary techniques.

Simple analytical expression for vector hypernuclear asymmetry in nonmesonic decay of $^5_Lambda$He and $^{12}_\Lambda$C

We present general explicit expressions for a shell-model calculationof the vector hypernuclear parameter in nonmesonic weak decay. We use a widely accepted effective coupling Hamiltonian involving theexchange of the complete pseudoscalar and vector meson octets(p, h, K, r, w, K*). In contrast to the approximated formula widely used in the literature,we correctly treat the contribution of transitions originated fromsingle-proton states beyond the s-shell. Exact and simple analytical expressions are obtained for the particularcases of $^5_Lambda$He and $^{12}_\Lambda$C, within theone-pion-exchange model. Numerical computations of the asymmetry parameter, $a_\Lambda$, are presented. Our results show a qualitative agreementwith other theoretical estimates but also acontradiction with recent experimental determinations. Our simple analytical formulas provide a guide in searchingthe origin of such discrepancies, andthey will be useful for helping to solve the hypernuclearweak decay puzzle.

Low lying axial-vector mesons as dynamically generated resonances

We make a theoretical study of the $s$-wave interaction of the nonet of vector mesons with the octet of pseudoscalar mesons starting from a chiral invariant Lagrangian and implementing unitarity in coupled channels. By looking for poles in the unphysical Riemann sheets of the unitarized scattering amplitudes, we get two octets and one singlet of axial-vector dynamically generated resonances. The poles found can be associated with most of the low lying axial-vector resonances quoted by the Particle Data Group: ${b}_{1}(1235)$, ${h}_{1}(1170)$, ${h}_{1}(1380)$, ${a}_{1}(1260)$, ${f}_{1}(1285)$, and two poles to the ${K}_{1}(1270)$ resonance. We evaluate the couplings of the resonances to the $VP$ states and the partial decay widths in order to reinforce the arguments in the discussion.

Finite volume effects for meson masses and decay constants

We present a detailed numerical study of finite volume effects for masses and decay constants of the octet of pseudoscalar mesons. For this analysis we use chiral perturbation theory and asymptotic formulae à la Lüscher and propose an extension of the latter beyond the leading exponential term. We argue that such a formula, which is exact at the one-loop level, gives the numerically dominant part at two loops and beyond. Finally, we discuss the possibility to determine low energy constants from the finite volume dependence of masses and decay constants.

Baryonic Resonances from Baryon Decuplet-Meson Octet Interactions and the Exotic Resonance [formula omitted], [formula omitted], [formula omitted

Using the lowest order chiral Lagrangian we study s -wave interactions of the baryon decuplet with the octet of pseudoscalar mesons. We find two bound states in the flavour SU (3) limit corresponding to the octet and decuplet representations. These are found to split into eight different trajectories in the complex plane when the SU (3) symmetry is broken gradually. Finally, we are able to provide a reasonable description for a good number of 4-star 3 2 − resonances listed by the Particle Data Group. In particular, the Ξ(1820), the Λ1520) and the Σ(1670) states are well reproduced. We predict a few other resonances and also evaluate the couplings of the observed resonances to the various channels from the residues at the poles of the scattering matrix from where partial decay widths into different channels can be evaluated.

BARYONIC RESONANCES FROM BARYON DECUPLET-MESON OCTET INTERACTION

The s-wave interactions of the baryon decuplet with the octet of pseudoscalar mesons is studied in a unitarized coupled channel approach. We obtain a fair agreement for mass and width of several [Formula: see text] resonances. In particular, the Ξ(1820), the Λ(1520) and the Σ(1670) states are well reproduced. Other resonances are predicted and also the couplings of the observed resonances to the various channels are evaluated.

Study of a possible S = + 1 dynamically generated baryonic resonance

Starting from the lowest order chiral Lagrangian for the interaction of the baryon decuplet with the octet of pseudoscalar mesons we find an attractive interaction in the $\Delta K$ channel with L=0 and I=1, while the interaction is repulsive for I=2. The attractive interaction leads to a pole in the second Riemann sheet of the complex plane and manifests itself in a large strength of the $\Delta K$ scattering amplitude close to the $\Delta K$ threshold, which is not the case for I=2. However, we also make a study of uncertainties in the model and conclude that the existence of this pole depends sensitively upon the input used and can disappear within reasonable variations of the input parameters. We take advantage to study the stability of the other poles obtained for the ${3/2}^-$ dynamically generated resonances of the model and conclude that they are stable and not contingent to reasonable changes in the input of the theory.

Baryonic resonances from baryon decuplet-meson octet interaction

We study S-wave interactions of the baryon decuplet with the octet of pseudoscalar mesons using the lowest order chiral Lagrangian. In the S = 1 sector, we find an attractive interaction in the ΔK channel with I = 1 while it is repulsive for I = 2 . The attractive interaction leads to a pole in the second Riemann sheet of the complex plane and is manifested as a large strength in the scattering amplitude close to the ΔK threshold, which is not the case for I = 2 . We use the unitarized coupled channel approach to also investigate all the other possible values of strangeness and isospin. We find two bound states in the SU ( 3 ) limit corresponding to the octet and decuplet representations. These are found to split into eight different trajectories in the complex plane when the SU ( 3 ) symmetry is broken gradually. Finally, we are able to provide a reasonable description for a good number of 4-star 3 2 − resonances listed by the Particle Data Group. In particular, the Ξ ( 1820 ) , the Λ ( 1520 ) and the Σ ( 1670 ) states are well reproduced. We predict a few other resonances and also evaluate the couplings of the observed resonances to the various channels from the residues at the poles of the scattering matrix from where partial decay widths into different channels can be evaluated.