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

General S-Matrix Methods for Calculation of Perturbations on the Strong Interactions

Recently, the authors proposed an on-the-mass-shell, S-matrix method for computing the effects of small perturbations on the masses and coupling constants of strongly interacting particles. In the present paper, the method is generalized to the multichannel case. The use of group-theoretical techniques in reducing the complexity of the method is described in detail

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

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

Some general features of the bootstrap theory of octet enhancement

Some general features of the boostrap theory of octet enhancement, which can be understood without detailed calculations, are discussed. These features include: (i) the connection of this theory to the vector-mixing theory of symmetry breaking advocated by Sakurai, and to the tadpole theory of Coleman and Glashow; (ii) an understanding of why it is representations of low multiplicity that are dynamically emphasized in symmetry breaking; (iii) a demonstration that the theory remains valid when a number of assumptions made in previous applications are dropped

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

Reggeization of Pion Exchange in Production Processes

Couplings of the pion Regge trajectory are discussed. We find that the kinematic factors prescribed by Wang must be supplemented by further kinematic terms. A simple physical interpretation is given for these additional terms. Our considerations lead to a model of pion trajectory couplings, which is in reasonable agreement with those experiments on vector- and tensor-meson production in which pion exchange is expected to dominate the forward peak

Unlocking Color and Flavor in Superconducting Strange Quark Matter

We explore the phase diagram of strongly interacting matter with massless u and d quarks as a function of the strange quark mass m_s and the chemical potential mu for baryon number. Neglecting electromagnetism, we describe the different baryonic and quark matter phases at zero temperature. For quark matter, we support our model-independent arguments with a quantitative analysis of a model which uses a four-fermion interaction abstracted from single-gluon exchange. For any finite m_s, at sufficiently large mu we find quark matter in a color-flavor locked state which leaves a global vector-like SU(2)_{color+L+R} symmetry unbroken. As a consequence, chiral symmetry is always broken in sufficiently dense quark matter. As the density is reduced, for sufficiently large m_s we observe a first order transition from the color-flavor locked phase to a color superconducting phase analogous to that in two flavor QCD. At this unlocking transition chiral symmetry is restored. For realistic values of m_s our analysis indicates that chiral symmetry breaking may be present for all densities down to those characteristic of baryonic matter. This supports the idea that quark matter and baryonic matter may be continuously connected in nature. We map the gaps at the quark Fermi surfaces in the high density color-flavor locked phase onto gaps at the baryon Fermi surfaces at low densities.Comment: Latex with eps figures, 28 pages, minor corrections, references update

Different Hagedorn temperatures for mesons and baryons from experimental mass spectra, compound hadrons, and combinatorial saturation

We analyze the light-flavor particle mass spectra and show that in the region up to ~1.8GeV the Hagedorn temperature for baryons is about 30% smaller than for mesons, reflecting the fact that the number of baryon states grows more rapidly with the mass. We also show that the spectra are well reproduced in a model where hadrons are compound objects of quanta, whose available number increases with mass. The rapid growth of number of hadronic states is a combinatorial effect. We also point out that an upper limit on the excitation energy of these quanta results in a maximum number of hadron states that can be formed. According to this combinatorial saturation, no more light-flavor hadron resonances exist above a certain mass.Comment: powers in Eqs. (7,8) corrected and a reference adde