Current Algebras and Symmetries in Bootstrap Theory

In the first paper of this series we showed how, in the bootstrap theory, the currents associated with the hadrons could be determined from a set of self-consistency conditions. In the present paper we show that these "self-consistent" currents satisfy a current algebra. The proof is accomplished without recourse to any approximate model It includes the interesting case of nonconserved currents. The convergence of sum rules derived from current algebras is investigated in detail, and shown to be most rapid when no "nonbootstrap" terms are present. Using these convergence properties, we discuss how and when current algebras can give rise to hadron symmetries

Self-Consistent Determination of Coupling Shifts in Broken SU(3)

The possibility that certain patterns of SU(3) symmetry breaking are dynamically enhanced in baryon-meson couplings is studied by bootstrap methods. For the strong couplings, a single dominant enhancement is found. It produces very large symmetry-breaking terms, transforming like an octet, as often conjectured. Experimental consequences are listed, such as a reduction of K-baryon couplings relative to π-baryon couplings which is in accord with the experimental weakness of K relative to π production in many circumstances, such as photoproduction and multi-BeV cosmic-ray collisions. For parity-violating nonleptonic couplings, a dominant octet enhancement is again found, as mentioned in a previous paper, which leads to an excellent fit with experiment. For parity-conserving nonleptonic couplings, on the other hand, several different enhancements compete, and the only conclusion we can draw is that terms with the "abnormal" transformation properties brought in by strong symmetry-breaking corrections are present. Our work provides a dynamical derivation of various phenomenological facts associated with SU(6), such as the dominance of the 35 representation in parity-violating nonleptonic decays

Equation of State in a Strongly Interacting Relativistic System

We study the evolution of the equation of state of a strongly interacting quark system as a function of the diquark interaction strength. We show that for the system to avoid collapsing into a pressureless Boson gas at sufficiently strong diquark coupling strength, the diquark-diquark repulsion has to be self-consistently taken into account. In particular, we find that the tendency at zero temperature of the strongly interacting diquark gas to condense into the system ground state is compensated by the repulsion between diquarks if the diquark-diquark coupling constant is higher than a critical value $\lambda_C=7.65$. Considering such diquark-diquark repulsion, a positive pressure with no significant variation along the whole strongly interacting region is obtained. A consequence of the diquark-diquark repulsion is that the system maintains its BCS character in the whole strongly interacting region.Comment: 9 pages, 7 figs, To appear in Phys. Rev.

Experimental Restrictions on Ne'eman's Fifth Interaction

Recently, Ne'eman has proposed a "fifth interaction" between the strangeness current and a neutral vector meson χ, for the purpose of breaking SU(3) symmetry. We show that a χ mass less than 2mπ would be inconsistent with a variety of experiments, including K-mesonic atoms, the long-range pp potential, K1 regeneration from a K2 beam, the Lamb shift, modern refinements of the Cavendish "ice-bucket" experiment, and the absence of π0→γ+χ and χ→e++e-. The remaining possibility, that mχ exceeds 2mπ, is discussed briefly

Determination of Asymptotic Parameters in the Statistical Bootstrap Model

The statistical bootstrap model predicts that the density of hadron states ρ(m) approaches cmaebm asymptotically. We consider the consequences of extending the bootstrap condition in the model from asymptotic down to finite masses. This allows us to determine the parameters a, b, and c for various assignments of the hadron volume and low-mass input spectrum, and for the extreme cases of excluding all exotic particles or including all of them. In all cases, a=-3 for ρtot (summed over all internal quantum numbers). The parameter b varies somewhat from case to case but is always of order mπ^-1; thus we predict the maximum temperature T0=b^-1≈mπ in rough agreement with Hagedorn's empirical determination. The inclusion of exotic states has little effect on ρtot but does redistribute the partial level densities according to a simple rule. The predicted level densities (excluding exotic states) are compared with present data

Weak and electromagnetic interactions of the hadrons in bootstrap theory

This is the first of a series of papers on the properties of the weak and electromagnetic currents of the hadrons in the bootstrap theory of strong interactions. In a bootstrap theory, there are many self-consistency conditions relating these weak and electromagnetic parameters to each other. We develop a formalism designed to take the fullest advantage of such bootstrap-like relations. In fact, we conjecture that the weak and electromagnetic properties of the hadrons are determined to a large extent, and perhaps completely, by self-consistency requirements. Some simple calculations of the weak and electromagnetic parameters pertaining to the octet of baryons and decuplet of resonances are given. The comparison of the results of these calculations with the experimental numbers indicates that the above conjecture holds, at least in this case

Wide-angle pair production and quantum electrodynamics at small distances

Wide-angle photoproduction of high-energy electron-positron pairs in hydrogen is proposed and analyzed as a test of quantum electrodynamics at distances ≤10^-13 cm. The effect of proton structure can be removed in terms of the two form factors measured in the elastic electron-proton scattering process. Cross sections are presented for two classes of pair production experiments: (1) those detecting one of the final particles, and (2) coincidence experiments. In addition to kinematic, anomalous moment, and nucleon form-factor corrections to the Bethe-Heitler formula, dynamical corrections to the proton current and radiative corrections are calculated. The final theoretical formula is believed to be accurate to 2%. A simple cutoff model suggests that a 5% accuracy in an experiment of type (1) tests the electron propagator at distances ∼0.7×10^-13 cm, while a 10% accuracy in a coincidence arrangement of type (2) probes the electron propagator at ∼0.3×10^-13 cm

Eikonal Regge Model for Elastic Scattering Processes

The Frautschi-Margolis version of the Regge eikonal model is extended to include secondary Regge trajectories. Physical properties of the model are discussed. In particular, the "shrinkage" of dσ/dt observed at present energies (rapid shrinkage for pp and K+p, little or no shrinkage for π±p and K-p, antishrinkage for pp is related to the energy dependence of σtot pp and K+p nearly flat, π±p and K-p falling slowly, pp falling rapidly)

Method for the Self-Consistent Determination of Regge Pole Parameters

A method is suggested for approximately bootstrapping Regge trajectories, thereby avoiding the cutoff problems of the usual bootstrap calculation. The method is based on dispersion relations for Regge trajectories and on unitarity applied at l=α. Successively more realistic approximations are described which bring in more information on the potential, and more trajectories. The approximate Regge parameters are guaranteed to have the desired threshold and asymptotic properties

Experimental consequences of the hypothesis of Regge poles

In the nonrelativistic case of the Schrödinger equation, composite particles correspond to Regge poles in scattering amplitudes (poles in the complex plane of angular momentum). It has been suggested that the same may be true in relativistic theory. In that case, the scattering amplitude in which such a particle is exchanged behaves at high energies like sα(t)[sinπα(t)]-1, where s is the energy variable and t the momentum transfer variable. When t=tR, the mass squared of the particle, then α equals an integer n related to the spin of the particle. In contrast, we may consider the case of a field theory in which the exchanged particle is treated as elementary and we examine each order of perturbation theory. When n>1, we can usually not renormalize successfully; when n≤1 and the theory is renormalizable, then the high-energy behavior is typically sn(t-tR)-1φ(t). Thus an experimental distinction is possible between the two situations. That is particularly interesting in view of the conjecture of Blankenbecler and Goldberger that the nucleon may be composite and that of Chew and Frautschi that all strongly interacting particles may be composite dynamical combinations of one another. We suggest a set of rules for finding the high-energy behavior of scattering cross sections according to the Regge pole hypothesis and apply them to π-π, π-N, and N-N scattering. We show how these cross sections differ from those expected when there are "elementary" nucleons and mesons treated in renormalized perturbation theory. For the case of N-N scattering, we analyze some preliminary experimental data and find indications that an "elementary" neutral vector meson is probably not present. Various reactions are proposed to test the "elementary" or "composite" nature of other baryons and mesons. Higher energies may be needed than are available at present