Dynamically generated resonances

In this talk I report on recent work related to the dynamical generation of baryonic resonances, some made up from pseudoscalar meson-baryon, others from vector meson-baryon and a third type from two meson-one baryon systems. We can establish a correspondence with known baryonic resonances, reinforcing conclusions previously drawn and bringing new light on the nature of some baryonic resonances of higher mass.     

S = −1 resonances in two meson-one baryon systems

We study the two meson-one baryon systems by solving Faddeev equations, using chiral dynamics. The calculations, carried out for the $\pi \overline{K} N$ system and its coupled channels for the case of strangeness = ?1, in the S-wave, lead to a dynamical generation of many strangeness = ?1 resonances in the 1500–1800?MeV region. While building the formalism, we found important cancellations between different sources of three-body forces.     

A comparison of πππ, Kππ, πKKKK system produced in the reactions meson +p→3 mesons + p

A comparison is made of the low-mass three-meson systems (πππ), (Kππ), $\text{(π}\text{K}\text{K}\text{)}$ and $\text{(}\text{K}\text{K}\text{K}\text{)}$ diffractively produced in the reaction meson + proton → three mesons + proton. Several striking similarities and a few important differences are observed: (i) the reactions are consistent with the assumption that the three mesons decay entirely into a 0^? meson and a 0⁺, 1^? or 2⁺ resonance; (ii) the three-meson mass spectra have a peak ≈ 250 MeV above the effective threshold M_eff of the dominant decay mode and then fall off approximately as (mass)^?3;(iii) the average spin 〈J〉 = 0.55 + 1.1 Q_eff, where Q_eff = M - M_eff; (iv) the average orbital angular momentum 〈l〉 increases according to 〈l〉 = 0.75 Q_eff; (v) the three-meson states are produced dominantly in unnatural spin-parity states and no evidence for their being resonant is found; (vi) the only natural spin-parity states found are the well-established 2⁺ resonances A₂ and K¹ (1420); they have similar properties to the non-resonant unnatural parity states except for a dip at t = 0 in the dσ/dt distributions; (vii) both the unnatural and natural spin-parity states are produced mostly by an exchange of natural parity; (viii) there is evidence for two types of production mechanism with different polarization properties, one approximately conserving helicity in the t-channel and the other in the s-channel.     

Photoexcitation of baryon resonances

The study of baryon resonances via meson photoproduction reactions on the free proton, nucleons bound in light nuclei, and in the nuclear medium is discussed. Special emphasis is laid on the production of neutral mesons which due to the suppression of non-resonant backgrounds are particularly well suited for the study of excited states of the nucleon. Experiments carried out during the last ten years with the TAPS-detector at the Mainz MAMI accelerator have contributed very significantly to the detailed investigation of the four lowest lying baryon resonances the P₃₃ (1232), the P₁₁ (1440), the D₁₃(1520) and the S₁₁(1535). Future experiments with TAPS at the ELSA accelerator have a large potential for the investigation of higher lying resonances via many different decay channels.     

Probabilistic quark-model approach to proton fragmentation

A probabilistic approach is formulated to study the behaviour of the incident hadron quark flavours in the fragmentation process of high energy protons in lowp _T reactions. Analysis of available data onpp collisions, mainly on hyperon and antibaryon multiplicities, leads to estimates of the probabilities for the different ways in which the incident valence quarks recombine into final hadrons. We find that all three incident quarks emerge in one and the same outgoing nucleon (or nucleon resonance) with probabilityA ₃=0.35–0.4, that two of them emerge in one baryon and the third in another hadron (mostly a meson or meson resonance) with probabilityA ₂=0.6–0.5, and that they emerge in three distinct hadrons (mostly mesons or meson resonances) with probabilityA ₁=0.05–0.1. We find good support for a very simple probabilistic picture of the fragmentation process.     

Charmed Mesons in Nuclei with Heavy-Quark Spin Symmetry

We study the properties of charmed pseudoscalar and vector mesons in dense matter within a unitary meson–baryon coupled-channel model which incorporates heavy-quark spin symmetry. This is accomplished by extending the SU(3) Weinberg–Tomozawa Lagrangian to incorporate spin-flavor symmetry and implement a suitable flavor symmetry breaking. Several resonances with negative parity are generated dynamically by the s-wave interaction between pseudoscalar and vector meson multiplets with 1/2⁺ and 3/2⁺ baryons. Those states are then compared to experimental data as well as theoretical models. Next, Pauli-blocking effects and meson self-energies are introduced in a self-consistent manner to obtain the open-charm meson spectral functions in a dense nuclear environment. We finally discuss the formation of D-mesic nuclei.     

Effects of pseudoscalar-baryon channels in the dynamically generated vector-baryon resonances

We study the interaction of vector mesons with the octet of stable baryons in the framework of the local hidden gauge formalism using a coupled-channels unitary approach, including also the pseudoscalar-baryon channels which couple to the same quantum numbers. We examine the scattering amplitudes and their poles, which can be associated to the known J ^P = 1/2⁻, 3/2⁻ baryon resonances, and determine the role of the pseudoscalar-baryon channels, changing the width and eventually the mass of the resonances generated with only the basis of vector-baryon states.     

Hyperfine interactions as clues to the structure of elementary particles

The history of hyperfine interactions in hadron physics is reviewed. The recent treatment of hyperfine splittings in meson spectroscopy by Frank and O'Donnell is generalized and applied to baryons as well as mesons by the use of techniques developed for treating hyperfine interactions in atomic physics. New relations between meson and baryon mass splittings are obtained following from the assumption that mesons and baryons are made of the same quarks and have the same color hyperfine interactions at the quark level, with corrections due to color factors and differences between baryon and meson wave functions. Work supported by the U.S. Department of Energy, Division of High Energy Physics, Contract W-31-109-ENG-38 and by the Minerva Foundation, Munich, Germany. 1985–86 Argonne Fellow on leave from the Wiezmann Institute of Science, Rehovot, Israel.     

Test of duality in baryon-antibaryon amplitudes from Reggeon-particle scattering

By studying the backward production data for meson resonances we investigate the dual properties of baryon-Reggeised antibaryon elastic scattering. We find strong support for the duality prediction that meson resonances in the baryon antibaryon channel should be dual to an exotic trajectory.     

Dilepton and vector meson production in heavy-ion reactions

We present a nonperturbative dynamical study of dilepton and vector meson production in heavy-ion collisions from 1 to 2 GeV/A bombarding energies incorporating all known sources relevant in this energy range. The dynamical evolution of the nucleus-nucleus collision is described by a transport equation of the Boltzmann-Uehling-Uhlenbeck type evolving phase-space distribution functions for nucleons, baryon resonances, pions,η’s,ρ’s andσ’s with their isospin degrees of freedom. We investigate in particular the sensitivity of the calculated yields to predicted changes of theρ andω mesons in dense matter.     

Sea quark effects in non-topological chiral soliton models and the Nambu-Jona-Lasinio approach

The Nambu-Jona-Lasinio model (NJL) in the chiral invariant SU (2)-sector with scalar couplings is solved numerically in the Hartree approximation (zero boson loop) for baryon number B=1. To this end first the polarized vacuum solution (B=0) is constructed using appropriately parametrized non-dynamic meson fields on the chiral circle. The cut-off Λ is fixed to reproduce the pion decay constant. With this choice a full treatment of the polarized vacuum is shown in second-order gradient expansion to be equivalent to considering kinetic energies of the mesons. Solutions of the NJL model with baryon number B=1 are obtained by adding N_c=3 valence quarks to the full polarized vacuum and subjecting them to the same meson fields. If one adds the valence quarks to the kinetic energy of the mesons the usual chiral soliton model with valence quarks (CSM) is obtained. For both, NJL and CSM, the equilibrium radii of the B=1 solution are evaluated and shown to be rather close to each other. The present approach shows no vacuum instabilities. The resulting radii are different from those of the renormalized one-quark-loop model.     

Quark dynamics and strong meson decays

The strong decays of meson resonances are treated in a dynamical quark model. The model is formulated in the framework of general field theory and therefore all calculations are fully relativistic covariant. Spectrum and wave functions are derived from a Bethe-Salpeter equation describing the binding of heavy quarks by a smooth, very strong interaction. The mesonic vertices are calculated with help of these BS amplitudes in triangle graph approximation, thereby guaranteeing a symmetric treatment of all mesons involved in the process. A particular spin dependence of the interaction has the consequence that the super-strong quark binding forces lead to mesonic forces of moderate strength only (saturation of quark forces!).The applications refer to the decays of vector mesons, tensor mesons, scalar mesons into pseudoscalars and vectors and are extended to resonances in the R region. In particular, we include the decays into two pions of the radial excited ?′(1600). The helicity structure of the decays of the axial vector meson is discussed.     

Baryon masses in relativistic potential models

We study the spectrum of a semi relativistic three-body hamiltonian. The hyperspherical method proves to be very efficient. We show that the ground states of baryons can be calculated with good accuracy. However, when using the meson potential, together with the colour assumption \(Vqq = \tfrac{1}{2}Vq\bar q\) , baryon Regge slopes come out noticeably too small. We analyze this problem and show that a quarkdiquark structure for baryons cures this defect. Altogether the construction of a global unified potential model for mesons and baryons seems quite hopeful.     

Charmed hadrons in nuclear medium

We study the properties of charmed hadrons in dense matter within a coupled-channel approach which accounts for Pauli blocking effects and meson self-energies in a self-consistent manner. We analyze the behaviour in this dense environment of dynamically-generated baryonic resonances as well as the open-charm meson spectral functions. We discuss the implications of the in-medium properties of open-charm mesons on the DsO(2317) and the predicted X(3700) scalar resonances.     

Resonances Generated by the Vector Meson-Baryon Dynamics

We have recently studied vector meson-octet baryon (VB) interactions with the aim to find dynamical generation of resonances in such systems. For this, we consider the s-, t-, u-channel diagrams along with a contact interaction originating from the hidden local symmetry Lagrangian. We find the contribution from all these sources, except the s-channel, to be important. The amplitudes obtained by solving the coupled channel Bethe–Salpeter equations for the systems with total strangeness zero show generation of one isospin 3/2, spin 1/2 resonance and three isospin 1/2 resonances: two with spin 3/2 and one with spin 1/2. We identify these resonances with Δ (1900) S ₃₁, N*(2080) D ₁₃, N* (1700) D ₁₃, and N*(2090) S ₁₁, respectively. Further, we briefly discuss the results of our investigation of the VB systems when coupled to the pseudoscalar meson-baryon (PB) channels. We find that the low-lying resonances couple strongly to the VB channels, a result which can be useful in studying the reactions involving pseudoscalar and vector meson exchanges. In case of the higher mass resonances (in the 1,800–2,200 MeV region), we find that some of the states claimed as dynamically generated states in the VB system can disappear due to their coupling to the PB channels. We also find that new states can appear from PB–VB coupled channel dynamics; for example, we find that a Σ resonance near 1,400 MeV gets developed due to such an effect.     

Comment on “Understanding the scalar meson q\bar{q} nonet”

It is shown that the incomplete scalar meson nonets found by T?rnqvist [1] and T?rnqvist & Roos [2], employing a new version of the Helsinki unitarised quark model, should in fact be complete, including an as yet unconfirmed light below 1 GeV (old ) and the established (1500). A detailed comparison is presented with the predictions of the Nijmegen unitarised meson model, in which two complete scalar nonets show up below 1.5 GeV [3]. The reason for the flavour-nonet breaking found in [1,2] we argue to originate in the use of coupling constants for the three-meson vertex which are not independent of flavour. Also some statements made in [1] are critically reviewed. Received: 17 February 1999 / Published online: 15 July 1999     

On meson resonances and chiral symmetry

We study meson resonances with quantum numbers J^P=1⁺ in terms of the chiral SU(3) Lagrangian. At leading order a parameter-free prediction is obtained for the scattering of Goldstone bosons off vector mesons with J^P=1⁻ once we insist on approximate crossing symmetry of the unitarized scattering amplitude. A resonance spectrum arises that is remarkably close to the empirical pattern. In particular, we find that the strangeness-zero resonances h₁(1380), f₁(1285) and b₁(1235) are formed due to strong and channels. This leads to large coupling constants of those resonances to the latter states.     

Regge trajectories in the quark model

We prove that the large angular momentum behaviour of the leading Regge trajectory of a meson (q \(\bar q\) ) or a baryon (qqq) can be obtained by minimizing the classical energy of the system for given angular momentum. A two-body quark-antiquark linear potential plus relativistic kinematics produces asymptotically linear Regge trajectories for mesons. For baryons we take either a sum of two-body potentials with half strength or a string of minimum length connecting the quarks, and find in both cases that the favoured configuration is a quark-diquark system and that the baryon and meson trajectories have the same slope. Short-distance singularities of the potential are shown to be unimportant.     

Vector meson radiation in relativistic heavy-ion collisions

The (σ, ω) model in the mean-field approximation where the meson fields are treated classically, describes much of observed nuclear structure and has been employed to describe the nuclear equation of state up to the quark-gluon phase transition. The acceleration of the meson sources, for example, in relativistic heavy-ion collisions, should result in bremsstrahlung-like radiation of the meson fields. The many mesons emitted serve to justify the use of classical meson fields. The slowing of the nuclei during the collision is modeled here as a smooth transition from initial to final velocity. Under ultra-relativistic conditions, vector radiation dominates. The angular distribution of energy flux shows a characteristic shape. It appears that if the vector meson field couples to the conserved baryon current, independent of the baryonic degrees of freedom, this mechanism will contribute to the radiation seen in relativistic heavy-ion collisions. The possible influence of the quark-gluon plasma is also considered.