Low-lying Mesons Research Articles

Unitarity and hadron self-energy: the breaking ofSU 6 in the meson spectrum

In this paper the problem of unitarity effects in hadron self-energies is studied. The resulting framework is then applied, within the recently proposed quark geometrodynamical theory, to the (approximate) calculation of mass shifts andSU6 symmetry-breaking patterns of the low-lying mesons. We derive a correct description of the mass splittings in the (35,L=1)SU6×O3 multiplet, good experimental agreement for the Zweig-forbidden decay (ϕ→3π) and predictB(f′(150))→→π+π-≃0.025.

A basic guide for the glueball spotter

After a brief review of the theoretical and phenomenological motivation for the existence of gluonic resonances, we examine the expected properties of such states, and consider possible tests for their presence in the hadronic spectrum below 1.5 GeV in mass. The scalar mesons can be classified as an approximately ideally mixed nonet with an additional isoscalar, the S ∗, with all the expected properties of a scalar glueball. It is suggested that the η′ contains a large proportion of glue as well as strange quarks and that, if the E(1420) is not a pseudoscalar, two further pseudoscalars await discovery in the low-lying meson spectrum. The pomeron, a narrow resonance in the ππ D-wave, must be found with a mass around or slightly below that of the S ∗. If the pomeron has a daughter vector glueball which, as has been argued, is fairly close to the φ mass, then it should also have a mother 3 −− glueball with a similar mass. The D(1285) may well be a 2 −+ glueball.

NonleptonicKdecay rate in terms of spectral-function integrals: A short-distance approach

In unified gauge theories of the weak and electromagnetic interactions it is shown that the matrix element for the decay ${K}_{S}^{0}\ensuremath{\rightarrow}2\ensuremath{\pi}$ can reliably be expressed in terms of integrals over spectral functions if (i) modified spectral-function sum rules of the Das, Mathur, and Okubo type are valid, or if (ii) the strong interactions are asymptotically free and the Glashow-Iliopoulos-Maiani mechanism holds. In these cases the contributions of the low-lying pseudoscalar and vector mesons to the spectral-function integrals suffice to account for the decay rate.

Heavy quarks and strong binding: A field theory of hadron structure

We investigate in canonical field theory the possibility that quarks may exist in isolation as very heavy particles, ${M}_{\mathrm{quark}}>>1$ GeV, yet form strongly bound hadronic states, ${M}_{\mathrm{hadron}}\ensuremath{\sim}1$ GeV. In a model with spin-\textonehalf{} quarks coupled to scalar gluons we find that a mechanism exists for the formation of bound states which are much lighter than the free constituents. Following Nambu, we introduce a color interaction mediated by gauge vector mesons to quarantee that all states with nonvanishing triality have masses much larger than 1 GeV. The possibility of such a solution to a strongly coupled field theory is exhibited by a calculation employing the variational principle in tree approximation. This procedure reduces the field-theoretical problem to a set of coupled differential equations for classical fields which are just the free parameters of the variational state. A striking property of the solution is that the quark wave function is confined to a thin shell at the surface of the hadronic bound state. Though the quantum corrections to this procedure remain to be investigated systematically, we explore some of the phenomenological implications of the trial wave functions so obtained. In particular, we exhibit the low-lying meson and baryon multiplets of SU(6); their magnetic moments, charge radii, and radiative decays, and the axial charge of the baryons. States of nonvanishing momenta are constructed and the softness of the hadron shell to deformations in scattering processes is discussed qualitatively along with the implications for deep-inelastic electron scattering and dual resonance models.

Relativistic scalar quark model with strong binding

The dynamics of strong binding of heavy scalar particles (quarks) are discussed with the help of the Bethe-Salpeter equation with a smooth ladder-type kernel. For this purpose, the Bethe-Salpeter amplitudes are expanded intoO4 spherical functions and the remaining « hyper-radial » equation is solved by a variational method. These calculations are considered as a model of mesons as bound states of heavy quarks. The low-lying mesons form linear trajectories with a slope of 1 (GeV)−2. The modification of the vector-meson dominance form factor by the bound-state wave functions is calculated and found to be in good agreement with experiment.

TheK¯KΠN¯N-amplitude in a Veneziano type model with spin

The generalized Veneziano Model has been applied by Chanet al. to the processes (K¯KΠN¯N) with very impressive results, but in this treatment baryon spin was neglected. In this work we give a covariant spin and isospin decomposition of the above class of processes. Postulating factorization at the lowest meson and baryon poles and using the very stringent duality diagram prescription we are led to a Veneziano type ansatz for the various invariant amplitudes.

Relationship of Flux Quantization to Charge Quantization and the Electromagnetic Coupling Constant

The concept of a closed quantized flux loop (elementary loop) which avoids the implication of magnetic monopoles is investigated, leading to a theory of a charged lepton (muon or electron). In order to reconstruct a continuous magnetic dipole field of a source lepton, it is assumed that the flux loop adopts a statistical distribution of alternative forms characterized by a complex probability amplitude superposition, in a manner somewhat analogous to the superposition of path histories in Feynman's space-time approach to quantum mechanics. Flux quantization results from the equivalence of a line discontinuity of the phase factor of a $\ensuremath{\psi}$ function of a field lepton (due to its phase multivaluedness by $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}$) to the presence of a line of quantized flux. On the same basis as quantized flux arises from such a singularity of that phase factor, so also an electric field arises when this singularity line is moving. In particular, the source's Coulomb field results from a spinning of the quantized flux loop (about the center of the source) with an angular velocity equal to the Zitterbewegung frequency $\frac{2m{c}^{2}}{\ensuremath{\hbar}}$, if the statistical distribution of flux loopforms properly represents the magnetic dipole field of a muon or of an electron. The reconstruction of the magnetic and electric fields of a charged lepton and the comparison of them with the quantized flux $\frac{\mathrm{hc}}{e}$ gives a numerical estimate of the electromagnetic interaction constant $\frac{{e}^{2}}{\ensuremath{\hbar}c}$, i.e., an understanding of the relationship between $e$ and $\ensuremath{\hbar}$. The energy $m{c}^{2}$ and angular momentum $\frac{\ensuremath{\hbar}}{2}$ may be interpreted as electromagnetic. The theory should work for both muon and electron and is expected to give some insight into the ratio of the masses of these two leptons. A representation of quarks in terms of linked quantized flux loops is suggested to describe a low-lying meson as a linkage of an elementary loop with an antiloop, and a low-lying baryon as three interlinked elementary loops. We are here developing a model approach to problems of structure and conservation laws in particle physics. A more abstract version of a quantized flux theory of particles should be preceded by such an heuristic model.

Sharp states in the spectrum of low-lying mesons

The existence of a family of narrow, low-lying mesons of ordinary I, Y is suggested. These would coexist with the wider states usually assigned to q q: L = 1 in a quark model, and in particular would give rise to the A 2 splitting. The assignment of these states to a qq q q multiplet leads to their narrowness. Such states have been predicted by applying duality to baryon-antibaryon scattering. Their partners of “exotic” I and Y would lie higher in mass (at least one below 1.9 GeV, probably), and need not be so narrow.

Realization of chiral symmetry in the meson states through SU (4) ⊗ O(3)

We propose a saturation scheme for the equations [X a(h), X b(h)] = i ϵ abc T c , [X a(h), [X b(h), m 2]] = 1 3 δ ab[X c(h), [X c(h), m 2]] , within the lower meson states, which belong to the 15 L = 0.1 representations of SU (4) ⊗ O(3). With the introduction of two mixing parameters we are able to derive the chiral couplings of these particles in reasonable agreement with experiment. In particular the helicity properties of A 1 and B decays come out correctly.