Rising total cross sections and the flavoring of the pomeron

The relationship of the non-diffractive renormalization of the bare pomeron via$\text{K}\text{K}$ and $\text{B}\text{B}$ production - or its “flavoring” by λ quark loops and di-quark loops - and the shape of the NN total cross section is studied in some detail. The “unflavored” bare pomeron P? generated by non-strange quark loops with intercept $\text{α}\text{=0.85}$ is non-diffractively renormalized into the “flavored” (Gribov) bare pomeron P with intercept α above one (α = 1.06 here). We utilize inclusive data on $\text{K}\text{K}\text{and}\text{B}\text{B}$ production as well as inelastic diffraction to constrain parameters, and we fit the combination $\text{1}\text{2}\text{(σ}{}_{\mathrm{<mtext>pp</mtext>}}\text{+ σ}{}_{\mathrm{<mtext>p</mtext><mtext>p</mtext>}}\text{)}$ from s = 10 GeV² through ISR energies, including the new Fermilab data, to high accuracy. No pronounced long wavelength oscillations are observed. We suggest that these data favor the Chew-Rosenzweig realization of the topological expansion over that of Harari-Freund. We show that our scheme is consistent with the rising behavior of 2σ_KN ? σ_πN.     

Baryons in dual unitarization and dynamical thresholds

Baryon exchange and baryon resonance production is introduced in the dual unitarisation scheme. The dynamical threshold for the production of meson and baryon resonances is incorporated. It is shown that the intercepts of the ω and the f, which are generated by baryons, are suppressed by the above dynamical threshold effects to $\text{α}{}_{\mathrm{\omega }}\text{(0) ? 0}$ and α_f(0) < 0. The pomeron is shifted slightly upwards by baryon production. An upper limit is determined for the ratio of the crossed and uncrossed produced baryon lines. The breaking of the Freund-Rosner-Walz rule is discussed.     

Baryon-antibaryon annihilations,unitarity and the pomeron

We show that baryon-antibaryon annihilations into mesons contribute, via unitarity, mainly to the pomeron term in the total $\text{B}$B cross section. The meson-exchange term is mainly built by non-annihilation processes. These results are contrary to previous ideas according to which $\text{B}$B annihilations are responsible for the difference between $\text{σ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(}\text{B}\text{B}\text{)}$ and σ_tot(BB) and contribute to the meson exchange term. Our conclusions are based on an explicit duality diagram model which we discuss in some detail. However, a much wider class of models give similar results. Experimental tests of our ideas are proposed.     

Composite model of quarks and leptons related to composite structures of SO(10)

It is demonstrated that the composite structure of quarks and leptons can be embedded in the SO(10) model of the strong and electroweak interactions. There appear two entities: two bosonic spinors ξ and ξ′ of SO(4) and a fermionic spinor B of SO(6). All the $\text{16's}$ of fermions can be expressed as (ξjB_α) and $\text{(ξ′j}\text{B}{}^1{}_{\mathrm{\alpha }}\text{)}$, where j=1 or 2 and α=0, 1, 2, 3 indicating the color SU(4) indices. Further consideration leads us to find a basic entity, ζ transforming as 5 under SU(5), of which the charge is $\text{(+}\text{1}\text{2}\text{, 0, ?}\text{1}\text{6}\text{, ?}\text{1}\text{6}\text{) ?}\text{1}\text{6}\text{)}$ and ξ,ξ′ and B can be constructed from ζ and $\text{ζ}$. Although ξ,ξ′ and B obey the SO(10) gauge group, ζ cannot be controlled by SO(10). Some unknown interactions may govern the behavior of ζ at very high energies, where the unification based on SO(10) with ξ,ξ′ and B is destroyed.     

The Wilson-Andrei number for the SU(3) Kondo model

We give asymptotic forms for the high- and low-field magnetic susceptibility for the SU(3) linear dispersion Kondo model for T = 0. The ratio $\text{T}{}_{\mathrm{<mtext>K</mtext>}}\text{T}{}_{\mathrm{<mtext>H</mtext>}}$ is also calculated for the standard SU(2j + 1) Kondo model for general j. From these results the Wilson number W_j, defined by $\text{χ0 =}\text{Wj(gμ)}{}^2\text{j(j + 1)}\text{3kT}{}_{\mathrm{<mtext>K</mtext>}}$ where χ0 is the zero-temperature zero-field susceptibility, which has been calculated by Andrei and Lowenstein for $\text{j =}\text{1}\text{2}$, is deduced for the SU(3) model j = 1.     

Baryon exchange effects in dual unitarisation

The effects of baryon exchanges in the renormalisation of Regge trajectories are studied in the dual unitarisation scheme. The main results are that: (i) the pomeron is boosted above α = 1, giving rising total cross sections beyond baryon-antibaryon thresholds, and (ii) the ω trajectory remains approximately at α = 0.5 but acquires a sizeable admixture of the exotic $\text{q}\text{q}\text{qq}$ state, which enhances its coupling to baryons. There are in addition a number of other interesting predictions.     

A dynamical theory for the rishon model

We propose a composite model for quarks and leptons based on an exact SU(3)_C × SU(3)_H gauge theory and two fundamental $\text{J=}\text{1}\text{2}$ fermions: a charged T-rishon and a neutral V-rishon. Quarks, leptons and W-bosons are SU(3)_H-singlet composites of rishons. A dynamically broken effective SU(3)_C × SU(2)_L × SU(2)_R × U(1)_B?L gauge theory emerges at the composite level. The theory is “natural”, anomaly free, has no fundamental scalar particles, and describes at least three generations of quarks and leptons.     

Multi-Regge limit of the Shapiro-Virasoro model; A sister for the pomeron

The structure of the four-, five-and six-point functions in the Shapiro-Virasoro model in multi-Regge and double-helicity pole limits is studied in detail. A pomeron propagator is derived along with the pomeron-particle-pomeron vertex function. The structure of both is investigated and evidence provided for the existence of a pomeron sister trajectory, related to the usual trajectory, αp, by $\text{β}\text{p}\text{=}\text{1}\text{2}\text{α}\text{p}\text{? 1}$; this is demonstrated to exist and its contribution to the full amplitude derived. Throughout, a correspondence between regions of angular integration in the Shapiro-Virasoro model and twisted configurations in the conventional dual model is emphasised.     

Impact parameter analysis of KN and πN scattering in the intermediate energy region

We have evaluated the s-channel-helicity partial-wave amplitudes for $\text{K}\text{N and πN}$ scattering as functions of the impact parameter using partial-wave data in the energy range P_L≈1.0–2.0 GeV/c. We find that the $\text{K}\text{N}$ background and resonance amplitudes exhibit features consistent with the dual absorptive picture for pomeron and f + ω and A₂ + ? exchanges. Comparison of the πN low-energy amplitude with the partial-wave decomposition of a quantitative Regge model gives evidence for local duality between the s-channel resonance and t- and u-channel Regge exchanges.     

Phenomenological SU(1, 1) supergravity

We investigate the structure of phenomenological supergravity models which permit the hierarchy problem to be “solved” in the sense that $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and m_W are determined dynamically to be exp [-O(1)/α] × m_P. Such models must have a flat hidden sector potential, which is only possible if the theory has an underlying SU(1, 1) invariance. Flat SU(1, 1) theories necessarily have a zero cosmological constant and the hidden sector is an Einstein space with . The SU(1, 1) invariance is necessarily broken down to U(1) by the gravitino mass. If $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is the only source of SU(1, 1) breaking then the tree-level gaugino masses are small and $\text{A =}\text{3}\text{2}$, while values of A up to 3 and non-zero gaugino masses are possible if other sources of SU(1, 1) breaking are tolerated. Yukawa couplings may scale as some power of $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{m}{}_{\mathrm{<mtext>P</mtext>}}$ in these models where $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is generated dynamically, which may explain the hierarchy of Higgs-fermion Yukawa couplings: $\text{m}{}_{\mathrm{<mtext>f</mtext>}}\text{m}{}_{\mathrm{<mtext>W</mtext>}}\text{=}\text{O}\text{(}\text{m}{}_{\mathrm{<mtext>W</mtext>}}\text{m}{}_{\mathrm{<mtext>P</mtext>}}\text{)}{}^{\mathrm{\lambda >0}}$? These models also permit the spontaneous violation of CP in the Yukawa coupling matrix. Numerical studies yield 20 GeV < m_t < 100 GeV in these phenomenological SU(1, 1) supergravity models. Speculations are presented about their relation to a fundamental theory based on extended supergravity.     

A possible description of baryon dynamics in dual and gauge theories

We present an attempt to generalize to baryons a framework recently proposed in order to unify gauge, dual and Regge-Gribov theories of mesons. We find it necessary to depart from the $\text{1}\text{N}{}_{\mathrm{<mtext>colour</mtext>}}$ expansion of quantum chromodynamics (QCD) and to replace it by a more general definition of a “dual” approximation of QCD, based on the zero-width limit. Theoretical and phenomenological consequences of the scheme are derived. For N_colour = 3, the baryon resembles a Y shaped string; three families of new “baryonium” bound states are predicted and rough estimates of intercepts and slopes of the associated Regge trajectories are given. A new type of Zweig-like selection rule is found to hold in leading order and its violations through higher-order topologies are discussed. Duality diagrams for baryons are ambiguous unless implemented with extra lines indicating the flow of certain colour indices. Duality between scattering and annihilation channels is found in B$\text{B}$ scattering and its consequences are discussed. Some justification is given for the quark counting rule for total cross sections. Finally, implications of our scheme for the Regge-Gribov calculus in processes involving baryons are discussed.     

Unitarity,phenomenology, and the bare Pomeron

The possibility of utilizing the multifireball expansion and a bare Pomeron at $\text{α}\text{?}{}_{\mathrm{o}}\text{=0.85}$ as an approximation to a solution of the s-channel unitarity equations explicitly connecting 2-body and inelastic phenomenology is discussed. A scale for Pomeron renormalization effects is inferred.     

SU (4) × SU (4) symmetry breaking and its implications for SU (3) × SU (3) breaking

We investigate models where the SU (4) × SU (4) symmetry breaking Hamiltonian, $\text{H}$_SB, belongs to the (15, 15) and $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ representations, and show how they are equivalent to models of SU (3) × SU (3) breaking where $\text{H}$_SB belongs to a mixture of different representations. The results for the ππ scattering lengths in the (15, 15) model are outside the experimental limits, but the $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ model yields solutions with a wide range of values for the scattering lengths within the experimental bounds.     

Low-energy behaviour of realistic locally-supersymmetric grand unified theories

The recently proposed cosmologically acceptable N=1 supergravity models based on the SU(5) unification group define unambigously the minimal particle content of the theory. This fact allows us to determine quite precisely their low-energy behaviour. The SU(2)×U(1) breaking to U(1)_e.m. is a consequence of radiative corrections of the supergravity induced soft breaking terms. The proposed mechanism (which is model independent) introduces naturally a hierarchy between the M_W and M_X scales. Calculating the low-energy effective potential we shot that a corrects SU(2)×U(1) breaking is obtained without any limit (except the experimental one) on the top-quark mass. The masses of the supersymmetric partners of mater and gauge fermions can be low and consequently accessible experimentally (sleptons, s quarks, gauginos $\text{? 20–50}\text{GeV}$). A neutral Higgs is also predicted wirth a mass $\text{m}{}_{\mathrm{H}}\text{?O(5)}\text{GeV}$. In addition, we show that if m_t?45 GeV, the gravitino and gluino masses are bounded from below by $\text{10}\text{GeV}\text{? m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{15}\text{GeV}\text{? m}{}_{\mathrm{<mtext>gluino</mtext>}}$. The values of sin²θ_W (in the two-loop approximation) and the $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$ ratio predicted are in very good agreement with the experimentally measured values.     

On the oscillatory modes of quarks in baryons

The color bond structure of a quark-antiquark system is extended, in the long-range approximation, self-consistently to the baryonic three-quark bond structure for SU(3)_c and generally to the N-quark bond structure for SU(N)_c. The universal (N-independent) mass square eigenvalues for massless quarks are

$\text{M}{}^2\text{=(H}{}_{\mathrm{N}}\text{)}{}^2\text{?2m}{}_{\mathrm{\rho }}{}^2\text{∑}\text{α=1}\text{3N?3}\text{ν}{}_{\mathrm{\alpha }}\text{+}\text{constant}\text{, ν}{}_{\mathrm{\alpha }}\text{=0,1,2,…}$

.     

The η-η′ mixing angle and the relative radiative decay rates Γ(ψ→ηγ)Γ(ψ→η′γ)

The problem of η-η′ mixing is reexamined within the nonet scheme. It is shown that the mixing angle θ_p is quite sensitive to a small SU(3) violating $\text{27}$ piece. Taking SU(3) violating q$\text{q}$ annihilation terms into account, we obtain a large ratio $\text{Γ(ψ→ηγ)}\text{Γ(ψ→η′γ)}$ which is largely independent of the mixing angle and agrees with the measured value to within 20–30%.     

Influence of self-fields on the Vlasov equilibrium and stability properties of relativistic electron beam-plasma systems

The influence of self-fields on the equilibrium and stability properties of relativistic beam-plasma systems is studied within the framework of the Vlasov-Maxwell equations. The analysis is carried out in linear geometry, where the relativistic electron beam propagates through a background plasma (assumed nonrelativistic) along a uniform guide field $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, It is assumed that $\text{ν}\text{γ}{}_0\text{? 1}$ for the beam electrons (ν is Budker's parameter, and γ₀mc² is the electron energy), but no a priori assumption is made that the beam density is small (or large) in comparison with the plasma density, or that conditions of charge neutrality or current neutrality prevail in equilibrium. It is shown that the equilibrium self-electric and self-magnetic fields, $\text{E}{}_{\mathrm{r}}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{r}}$ and $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$, can have a large effect on equilibrium and stability behavior. Equilibrium properties are calculated for beam (j = b) and plasma (j = e, i) distribution functions of the form f_b⁰(H, P_θ, P_z) = F(H ? ω_rbP_θ) × δ(P_z ? P₀)(j = b), and $\text{f}{}_{\mathrm{j}}{}^0\text{(H, P}{}_{\mathrm{\theta }}\text{, P}{}_{\mathrm{z}}\text{) = f}{}_{\mathrm{j}}{}^0\text{(H ? ω}{}_{\mathrm{rj}}\text{P}{}_{\mathrm{\theta }}\text{? V}{}_{\mathrm{j}}\text{P}{}_{\mathrm{z}}\text{?}\text{m}{}_{\mathrm{i}}\text{V}{}_{\mathrm{j}}{}^2\text{2}\text{)}$ (j = e, i), where H is the energy, P_θ is the canonical angular momentum, P_z is the axial canonical momentum, and ω_rj (the angular velocity of mean rotation for j = b, e, i), V_j (the mean axial velocity for j = e, i), and P₀ are constants. The linearized Vlasov-Maxwell equations are then used to investigate stability properties in circumstances where the equilibrium densities of the various components (j = b, e, i) are approximately constant. The corresponding electrostatic dispersion relation and ordinary-mode electromagnetic dispersion relation are derived (including self-field effects) for body-wave perturbations localized to the beam interior (r <R_b). These dispersion relations are analyzed in the limit of a cold beam and cold plasma background, to illustrate the basic effect that lack of charge neutrality and/or current neutrality can have on the two-stream and filamentation instabilities. It is shown that relative rotation (induced by self-fields) between the various components (j = b, e, i) can (a) result in modified two-stream instability for propagation nearly perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, and (b) significantly extend the band of unstable k_z-values for axial two-stream instability. Moreover, in circumstances where the beam-plasma system is charge-neutralized but not current-neutralized, it is shown that the azimuthal self-magnetic field $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$ has a stabilizing influence on the filamentation instability for ordinary-mode propagation perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$.     

Elastic scattering slope and total cross section relations

The empirical equality of $\text{B}{}^2\text{σ}{}_{\mathrm{<mtext>t</mtext>}}$ is noted, for the pomeron terms in NN, πN, KN, ?N, ωN, and φN scattering, where B is the elastic slope parameter and σ_t is the total cross section. This ratio increases slowly with energy, but remains the same in all channels. This is equivalent to a relation between the diffractive interaction radii and opacities; the opacity scales with the square of the radius. We conjecture that this systematics extends to ψN scattering. We contrast $\text{B}{}^2\text{σ}{}_{\mathrm{<mtext>t</mtext>}}$ universaility with the slope predictions of an f-coupled pomeron model. Some other predictions of the f-dominance hypothesis are tested against data.