Recent progress on the chiral unitary approach to meson meson and meson baryon interactions
E. Oset, J. A. Oller, J. R. Pelaez, A. Ramos, H. C. Chiang, F. Guerrero, S. Hirenzaki, T. S. H. Lee, E. Marco, J. C. Nacher, Y. Okumura, A. Parreno, H. Toki, M. Vicente-Vacas
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Contribution to the KEK Tanashi Symposium on Physics of Hadrons and Nuclei, Tokyo, December 1998, 10 pages, 3 postscript figures. To be published as a special issue of Nuclear Physics A
We report on recent progress on the chiral unitary approach, analogous to the effective range expansion in Quantum Mechanics, which is shown to have a much larger convergence radius than ordinary chiral perturbation theory, allowing one to reproduce data for meson meson interaction up to 1.2 GeV. Applications to physical processes so far unsuited for a standard chiral perturbative approach are presented. Results for the extension of these ideas to the meson baryon sector are discussed, together with applications to kaons in a nuclear medium and $K^-$ atoms.
If baryons couple only with $ω$-mesons, one found the baryon spectral function may be negative. We show this unacceptable result is caused by the $k_μk_ν$-terms in the $ω$-meson propagator. Their contribution may not vanish in approximate calculations which violate the baryon current conserves. A rule is suggested, by which the calculated baryon spectral function is well behaved.
We present an unquenched quark model calculation of the mass shifts of ground-state octet and decuplet baryons due to the coupling to the meson-baryon continuum. The $q\bar{q}$ pair-creation effects are taken explicitly into account through a microscopic, QCD-inspired, quark-antiquark pair- creation mechanism.
The Nijmegen soft-core model for the pseudoscalar-meson baryon interaction is derived, analogous to the Nijmegen NN and YN models. The interaction Hamiltonians are defined and the resulting amplitudes for one-meson-exchange and one-baryon-exchange in momentum space are given for the general mass case. The partial wave projection is carried through and explicit expressions for the momentum space partial wave meson-baryon potentials are presented.
We report four $Σ$'s and three $Λ$'s, in the 1500 - 1800 MeV region, as two meson - one baryon S-wave $(1/2)^+$ resonances. We solve Faddeev equations in the coupled channel approach. The invariant mass of one of the meson-baryon pairs and that of the three particles have been varied and peaks in the squared three body $T$-matrix have been found very close to the existing $S$ = -1, $J^P= 1/2^+$ low lying baryon resonances. The input two-body $t$-matrices for meson-meson and meson-baryon interaction have been calculated by solving the Bethe-Salpeter equation with the potentials obtained in the …
Phi meson production in pion-baryon and baryon-baryon interactions near the production threshold is studied in a boson-exchange model. Parameters in this model are either taken from the Bonn model for the nucleon-nucleon potential or determined from the measured phi meson decay width and the experimental data for the reactions $π^-p\arr ϕn$ and $pp\arr ppϕ$. The isospin-averaged cross sections for the reactions $πN\arr ϕN$, $πΔ\arr ϕN$, $NN\arr NNϕ$, which are needed in transport models to study phi meson production in heavy-ion collisions at subthreshold energies, have been evaluated. For the…
We study the four-body decays $J/ψ\to N {\bar N}$ {\it meson meson} using a chiral unitary approach to account for the meson meson final state interaction (FSI). The calculation of the $J/ψ\to N \bar N π^+ π^-$ process properly reproduces the experimental data after taking the FSI of mesons and the contribution of intermediate $ρ$ meson into account. The isoscalar resonances $σ$, $f_0(980)$ and the isovector resonance $a_0(980)$ are generated through the FSI of the mesons in the channels $J/ψ\to N \bar N π^0 π^0$ and $J/ψ\to N \bar N π^0 η$, respectively. We also calculate the two mesons invar…
A new version, v2.0, of the HIJING/BB Monte Carlo nuclear collision event generator is introduced in order to explore further the possible role of baryon junctions loops in the baryon/meson anomaly (2 $< p_{T} <$ 5 GeV/c) observed in 200A GeV Au+Au reactions at RHIC. We show that junction loops with an enhanced intrinsic $k_T\approx 1$ GeV/c transverse momentum kick may provide a partial explanation of the anomaly as well as other important baryon stopping observables.
We present a chiral-invariant meson-baryon Lagrangian which describes the interactions of the baryon octet with the lowest-mass meson nonets. The nonlinear realization of the chiral symmetry generates pair-meson interaction vertices. The corresponding pair-meson coupling constants can all be expressed in terms of the meson-nucleon-nucleon pseudovector, scalar, and vector coupling constants, and their corresponding $F/(F+D)$ ratios, and for which empirical estimates are given. We show that it is possible to construct an NN potential of reasonable quality satisfying these theoretical and empiric…
Phi meson-baryon cross sections, estimated within a one-boson-exchange model, serve as input for a calculation of the collision rates in hot hadronic matter. We find that the width of the ϕmeson is modified through collisions with baryons by 1-10 MeV at 160 MeV temperature depending on the baryon fugacity. Thermalization of the ϕin high energy heavy ion collisions is discussed.
The mass shifts of experimentally well-known baryons due to meson-baryon self-energy loops are calculated, and their impact on the observed splitting of the baryon spectrum is studied. Configuration-mixed wave functions adapted from a `relativized' model are used with the 3P0 model to provide predictions for the strength and analytical momentum dependence of the strong vertices. Intermediate states include all the lightest pseudoscalar and vector mesons and corresponding baryons required to provide a complete set of spin-flavor symmetry related baryon-meson states. The sum over intermediate-st…
We relate the fragmentation functions of partons into mesons and baryons in the framework of recombination of shower partons. The results are in reasonable agreement with the data. The implication is that the meson and baryon fragmentation functions are not independent when hadronization of the shower partons are taken into account. The conclusion therefore closes a conceptual gap in the system of fragmentation functions whose $Q^2$ evolution has been more extensively studied than their interrelationship.
This is the contribution to the proceedings of the MENU 2010 conference. The recent work of Ref. [7] is summarized. Elastic piN scattering and the reaction pi^+ p --> K^+ Sigma^+ are described simultaneously in a unitary coupled-channels approach which respects analyticity. SU(3) flavor symmetry is used to relate the t- and u- channel exchanges that drive the meson-baryon interaction in the different channels. Angular distributions, polarizations, and spin-rotation parameters are compared with available experimental data. The pole structure of the amplitudes is extracted from the analytic cont…
Resolving the $ϕ$-meson directed-flow puzzle by multi-step meson--baryon dynamics
GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI亥姆霍兹重离子研究中心）；Heidelberg University（海德堡大学）；Institut für Kernphysik, Max-von-Laue-Str. 1, 60438 Frankfurt, Germany（法兰克福核物理研究所）；Joint Institute for Nuclear Research（俄罗斯杜布纳联合核子研究所）；Nantes University（南特大学）；Frankfurt Institute for Advanced Studies（法兰克福高等研究院）；Helmholtz Research Academy Hessen for FAIR (HFHF)（黑森亥姆霍兹FAIR研究学院）；Johann Wolfgang Goethe University（约翰·沃尔夫冈·歌德法兰克福大学）；Central China Normal University（华中师范大学）；Chinese Academy of Sciences（中国科学院）
We calculate the effect of many-body interactions in nuclear matter on the spectral function of $ρ$ and $ω$ meson. In particular, we focus on the role played by baryon resonances in this context.
The renormalised form factors for pseudoscalar meson-baryon coupling are computed in chiral colour dielectric model. This has been done by rearranging the Lippmann-Schwinger series for the meson baryon scattering matrix so that it can be expressed as a baryon pole term with renormalized form factors and baryon masses and the rest of the terms which arise from the crossed diagrams. Thus we are able to obtain an integral equation for the renormalized meson-baryon form factors in terms of the bare form factors as well as an expression for the meson self energy. This integral equation is solved an…
We study baryon spectroscopy including the effects of pseudoscalar meson exchange and one gluon exchange potentials between quarks, governed by $α_s$. The non-perturbative, hyperspherical method calculations show that one can obtain a good description of the data by using a quark-meson coupling constant that is compatible with the measured pion-nucleon coupling constant, and a reasonably small value of $α_s$.
We extend the Fock-Tani formalism to include the meson-baryon interaction. The Fock-Tani formalism is a first principle method which allows the use of field theoretic methods for treating systems of composite particles. An application of this general result can be the $K^{+}N$ system which is now reconized as much more suitable system for the investigation of the short range nature of the hadronic repulsion.
After some short introductory remarks on particular issues on the vector mesons in nuclei, in this paper we present a short review of recent developments concerning the interaction of vector mesons with baryons and with nuclei from a modern perspective using the local hidden gauge formalism for the interaction of vector mesons. We present results for the vector baryon interaction and in particular for the resonances which appear as composite states, dynamically generated from the interaction of vector mesons with baryons, taking also the mixing of these states with pseudoscalars and baryons in…
It is shown that most of the models for analyzing meson-baryon reactions in the nucleon resonance region can be derived from a Hamiltonian formulation of the problem. An extension of the coupled-channel approach to include $ππN$ channel is briefly described and some preliminary results for the $N^*(1535)$ excitation are presented.
We present the results of the first calculations involving the interaction of vector mesons with baryons, by means of which one generates a large amount of dynamically generated resonances, many of which can be associated to known resonances, while others represent predictions for new states.
By means of a coupled channel non-perturbative unitary approach, it is possible to extend the strong constrains of Chiral Perturbation Theory to higher energies. In particular, it is possible to reproduce the lowest lying resonances in meson-meson scattering up to 1.2 GeV using the parameters of the O(p^2) and O(p^4) Chiral Lagrangian. The meson baryon sector can also be tackled along similar lines. We report on an update of these results showing some examples of photon induced reactions where the techniques have been recently applied.
We study s-wave meson-baryon scattering using the chiral unitary model. We consider $1/2^{-}$ baryon resonances as quasibound states of the low lying mesons ($π,K,η$) and baryons ($N,Λ,Σ,Ξ$). In previous works, the subtraction constants which appear in loop integrals were found to largely depend on the channels, and it was necessary to fit these constants to reproduce the data. In order to extend this model to all channels with fewer parameters, we introduce flavor SU(3) breaking interactions in the framework of chiral perturbation theory. It is found, however, that the observed SU(3) breaking…
We study the multiplicity fluctuation and correlation of identified mesons and baryons formed at the hadronization by the quark combination mechanism in the context of ultra-relativistic heavy-ion collisions. Based on the statistical method of free quark combination, we derive the two-hadron multiplicity correlations such as meson-meson and meson-baryon correlations, and take the effects of quark number fluctuation at hadronization into account by a Taylor expansion method. After including the decay contributions, we calculate the dynamical fluctuation observable $ν_{dyn}$ for $\text{K}π$, $pπ…
We have recently studied coupled channel interactions of vector and pseudoscalar mesons with octet baryons having total strangeness null and spin-parity $1/2^-$. We, thus, considered $πN$, $ηN$, $K Λ$, $K Σ$, $ρN$, $ωN$, $ϕN$, $K^* Λ$, and $K^*Σ$ with total isospin 1/2 and 3/2. The interactions between pseudoscalar mesons and baryons are obtained by using the Weinberg-Tomozawa theorem. For the case of vector mesons, we calculate $s$-, $t$-, $u$-exchange diagrams and a contact term. The subtraction constants, required to calculate the loop-function in the scattering equations, are constrained b…
A study of meson-baryon systems with total strangeness -1 is made within a framework based on the chiral and hidden local symmetries. These systems consist of octet baryons, pseudoscalar and vector mesons. The pseudoscalar meson-baryon (PB) dynamics has been earlier found determinant for the existence of some strangeness -1 resonances, for example, $Λ(1405)$, $Λ(1670)$, etc. The motivation of the present work is to study the effect of coupling the closed vector meson-baryon (VB) channels to these resonances. To do this, we obtain the $PB \rightarrow PB$ and $VB \rightarrow VB$ amplitudes from …
The most general spin structures of the spin-1/2 baryon and spinless meson production operator for both photon and nucleon induced reactions are derived from the partial-wave expansions of these reaction amplitudes. The present method provides the coefficients multiplying each spin operator in terms of the partial-wave matrix elements. The result should be useful in studies of these reactions based on partial-wave analyses, especially, when spin observables are considered.
We study the central part of Lambda N and Lambda Lambda potential by considering the correlated and uncorrelated two-meson exchange besides the omega exchange contribution. The correlated two-meson is evaluated in a chiral unitary approach. We find that a short range repulsion is generated by the correlated two-meson potential which also produces an attraction in the intermediate distance region. The uncorrelated two-meson exchange produces a sizeable attraction in all cases which is counterbalanced by omega exchange contribution.
Based on ideas that relate meson and baryon spectrum considering SUSY QM and light front holography, we propose a procedure to obtain LFWF for baryons starting from mesonic ones. We apply a procedure suggested for Gaussian ansatz used to study mesons.
Meson-baryon interactions are the fundamental building blocks to study the structures of baryon resonances and meson properties in few-body nuclear systems. We review the recent progress in the investigation of the meson-baryon interaction in the strangeness S=-1 sector and the structure of the Lambda(1405) resonance. In particular, we present an attempt to construct a realistic Kbar N-pi Sigma interaction in chiral SU(3) dynamics in response to the precise measurement of the kaonic hydrogen, and discuss the subthreshold extrapolation of the Kbar N interaction with the information of the pi Si…
A qualitative account of the meson-meson and meson-baryon interactions using chiral Lagrangians and the inverse amplitude method in coupled channels is done. The method, imposing exact unitarity, proves to be very useful tool to extend the information contained in the chiral Lagrangians at energies beyond the realm of applicability of chiral perturbation theory.
We report on recent nonperturbative techniques that combine the information of chiral Lagrangians (with and without resonances) with unitarity in coupled channels and other requirements of the S-matrix theory of the strong interactions. As a result, the region of applicability of such techniques is much larger than the one of Chiral Perturbation Theory allowing one to study also resonance physics. Applications to meson-meson and meson-baryon scattering, as well as to problems where pairs of mesons or a meson and a baryon appear in the initial or final state are shown. Implications in several n…
We study the S-wave interaction of mesons with baryons in the strangeness S=0 sector in a coupled channel unitary approach. The basic dynamics is drawn from the lowest order meson baryon chiral Lagrangians. Small modifications inspired by models with explicit vector meson exchange in the t-channel are also considered. In addition the pi pi N channel is included and shown to have an important repercussion in the results, particularly in the isospin 3/2 sector.
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.
In this paper, we consider an exotic baryon (pentaquark) as a bound state of two-particle systems composed of a baryon (nucleon) and a meson.We used a baryon - meson picture to reduce a complicated five-body problem to a simple two-body problems. The homogeneous Lippmann-Schwinger integral equation is solved in configuration space by using one pion exchange potential. We calculate the masses of pentaquarks $θ_{c}(uudd\bar{c})$, $θ_{b}(uudd\bar{b})$.
We extend the method of infrared regularization to spin-1 fields coupled to baryons. As an application, we discuss the axial form factor of the nucleon.
We develop a model for describing excited mesons decay into three mesons. The properties of the excited mesons can be extracted with this model. The model maintains the three-body unitarity that has been missed in previous data analyses based on the conventional isobar models. We study an importance of the three-body unitarity in extracting hadron properties from data. For this purpose, we use the unitary and isobar models to analyze the same pseudo data of gamma p -> pi+pi+pi-n, and extract the properties of excited mesons. We find a significant difference between the unitary and isobar model…
A new tool which combines chiral perturbation theory and unitarity in coupled channels is applied with success to the study of the meson-meson interaction, extending the theoretical predictions up to sqrt{s} = 1.2 GeV, hence improving considerably the convergence radius of conventional chiral perturbation theory. The method is applied to obtain the meson-meson phase shifts and inelasticities as well as the isoscalar pion-pion scattering amplitude inside a nuclear medium.
A meson-baryon interaction in the charm $+1$, strangeness $-2$ and isospin $0$ sector is built from a t-channel vector meson exchange model employing effective Lagrangians. The implementation of coupled-channel unitarization in the s-wave scattering amplitudes gives rise to two structures that have similar masses and widths to those of the $Ω_c(3050)^0$ and $Ω_c(3090)^0$ states recently observed by the LHCb collaboration. A meson-baryon molecular interpretation of these resonances would assign their spin-parity to be $J^P=1/2^-$.
We explore the possibility that some of the five narrow $Ω_c$ resonances recently observed at LHCb could correspond to pentaquark states, structured as meson-baryon bound states or molecules. The interaction of the low-lying pseudoscalar mesons with the ground-state baryons in the charm $+1$, strangeness $-2$ and isospin 0 sector is built from t-channel vector meson exchange, using effective Lagrangians. The resulting s-wave coupled-channel unitarized amplitudes show the presence of two structures with similar masses and widths to those of the observed $Ω_c(3050)^0$ and $Ω_c(3090)^0$. The iden…
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 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.
We examine flavor SU(3) breaking effects on meson-baryon scattering amplitudes in the chiral unitary model. It turns out that the SU(3) breaking, which appears in the leading quark mass term in the chiral expansion, can not explain the channel dependence of the subtraction parameters of the model, which are crucial to reproduce the observed scattering amplitudes and resonance properties.
We investigate the coupling of vector mesons with nucleons to nucleon resonances in an isospin-selective VMD approach and explore the in-medium properties of vector mesons.
The spatial dependence of static meson correlation functions at finite baryon density is studied in the Nambu -- Jona - Lasinio model. In contrast to the finite temperature case, we find that the correlation functions at finite density are not screened but exhibit long-range oscillations. The observed phenomenon is analogous to the Friedel oscillations in a degenerate electron gas.
A recent general analysis of light-baryon isospin splittings is updated and extended to charmed baryons. The measured $Σ_c$ and $Ξ_c$ splittings stand out as being difficult to understand in terms of two-body forces alone. We also discuss heavy-light mesons; though the framework here is necessarily less general, we nevertheless obtain some predictions that are not strongly model-dependent.
The validity of SU(4)-flavor symmetry relations of couplings of charmed $D$ mesons to light mesons and baryons is examined with the use of $^3{\rm P}_0$ quark-pair creation model and nonrelativistic quark model wave functions. We focus on the three-meson couplings $ππρ$, $KKρ$ and $DDρ$ and baryon-baryon-meson couplings $NNπ$, $NΛK$ and $NΛ_c D$. It is found that SU(4)-flavor symmetry is broken at the level of 30% in the $DDρ$ tree-meson couplings and 20% in the baryon-baryon-meson couplings. Consequences of these findings for DN cross sections and existence of bound states D-mesons in nuclei …
We present a microscopic derivation of the form factors of strong-interaction piNN and piNDelta vertices within a relativistic constituent quark model. The results are compared with form factors from phenomenological meson-baryon models and recent lattice QCD calculations. We give an analytical representation of the vertex form factors suitable for applications in further studies of hadron reactions.
We study $pK^-$ scattering in the energy range from threshold through the $Λ(1520)$ peak in UBChPT, taking into account $\mathcal{O}(q)$ vertices from meson-baryon contact interactions and $s$- and $u$-channel ground-state baryon exchange, $s$- and $u$-channel decuplet- and nonet-baryon exchange and $t$-channel vector-meson exchange, as well as $\mathcal{O}(q^2)$ flavor-breaking vertices. Detailed fits to data are presented, including a substantial body of differential cross-section data with meson momentum $q_\mathrm{lab} > 300$ MeV not considered in previous treatments.
We calculate decuplet contributions to the s-wave pseudoscalar meson octet-baryon scattering lengths to the third order in heavy baryon chiral perturbation theory (HB$χ$PT). 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 N_c limit. Hopefully, the analytical expressions and the predictions are helpful to future investigations of the meson-ba…
We summarize the current theoretical and experimental status of the spectral changes of vector mesons ($ρ$, $ω$, $ϕ$) at finite baryon density. Various approaches including QCD sum rules, effective theory of hadrons and bag models show decreasing of the vector meson masses in nuclear matter. Possibility to detect the mass shift through lepton pairs in $γ-A$, $p-A$ and $A-A$ reactions are also discussed.
We analyze experimental particle spectra and show that the Hagedorn temperature is significantly larger for mesons than for baryons. The effect can be explained within dual string models: excitations of three strings in the baryon produce ``faster'' combinatorics than a single string in the meson, hence lead to a more rapid growth of baryons than mesons. Predictions of other approaches for the gross features of particle spectra are also discussed.
We show that the Hagedorn temperature obtained from experimental spectra is larger for mesons than for baryons. Dual string models explain this behavior asymptotically.
We consider the meson and baryon production in the quark-gluon plasma as applied to the early Universe and ultrarelativistic heavy ion collisions in collider. The essential feature of our investigation is to take into account a potential barrier for quarks under meson and baryon production. We have used the Boltzmann equation to describe kinetic processes of quark fusion. We have derived analytic expressions for solutions of kinetic equations. This permits to find the dependence of reaction rate on a time, temperature, mass and charge of quarks as well as on a string tension connected with the…
In this work we extend our formalism to study meson-baryon interactions by including $s$- and $u$-channel diagrams for pseudoscalar-baryon systems. We study the coupled systems with strangeness $-1$ and focus on studying the isospin-1 resonance(s), especially in the energy region around 1400 MeV. By constraining the model parameters to fit the cross section data available on several processes involving relevant channels, we find resonances in the isoscalar as well as the isovector sector in the energy region around 1400 MeV.
We study heavy baryons with exotic flavor quantum numbers formed by a heavy meson and a nucleon (DbarN and BN) with positive parity. One pion exchange interaction, providing a tensor force, dominates as a long range force to bind the DbarN and BN ystems. In the heavy quark mass limit, pseudoscalar meson and vector meson are degenerate and the binding mechanism by the tensor force analogous to that in the nuclear systems becomes important. As a result, we obtain the DbarN and BN resonant states in the J^P=1/2^+, 3/2^+ and 5/2^+ channels with I=0.
We explore the role of a scalar meson exchange interaction between quarks in a semirelativistic constituent quark model where the quarks are also subject to a linear confinement. We search for a variational solution and study how the spectrum evolves when the strength of the scalar meson exchange increases. Our results have good implications on the description of the low-lying baryon masses, especially on the long-standing problem of the relative position of the first positive-parity (Roper resonance) and the first orbitally excited states.
A non-relativistic quark coalescence model is formulated for polarized vector mesons and baryons of spin-1/2 octet and spin-3/2 decuplet. With the spin density matrix, one can compute in a uniform way the polarizations of vector mesons and baryons from those of quarks and antiquarks with explicit momentum dependence. The results are compared to that obtained from kinetic and statistical models for hadrons.
