C. Rosenzweig

Dual topological unitarization: An ordered approach to Hadron theory

Abstract A review is given of developments between 1973 and 1977 that have added the concept of order to general S -matrix principles with the aim of constructing a bootstrap theory of hadrons.

Asymptotic planarity: An S-matrix basis for the Okubo-Zweig-Iizuka rule☆

A mechanism is exhibited that monotonically depresses the cylinder component of the topological expansion with increasing t, and it is conjectured that all non-planar S-matrix components diminish as t increases, exchange degeneracy and the Okubo-Zweig-Iizuka rule becoming more accurately satisfied. Such asymptotic planarity is compared to the field-theoretical concept of asymptotic freedom. The characteristics low-t cylinder “quenching interval” is found to be the inverse of the mean value over a two-reggeon loop, of 12π2(α′)2(t1 − t2)2/(−t), where t1 and t2 are the squared masses of the loop reggeons and α′ is the trajectory slope. For leading trajectories the low-t cylinder quenching interval is predicted by this formula to be roughly 0.5 GeV2-consistent with the observed pomeron intercept and slope, with the p-ω and f-A2 mass differences and with the (φ,ω) deviation from ideal mixing. As t grows negatively over a corresponding interval, it is predicted that the pomeron will become nearly a pure SU(3) singlet. If the pion mass helps to set the scale for reggeon loops coupled to unnatural-parity trajectories, the cylinder quenching interval will be larger, explaining the large (η, η′) deviation from ideal mixing as well as the large π-η mass difference. Even when the small-t cylinder quenching is rapid (“precocious planarity”) the large-t approach to the planar limit turns out to be gentle. A by-product of this study is an explanation of the approximate reality and linearity of trajectories at large t.

A systematic lifting of exchange-degeneracy that clarifies the relationship between pomeron, reggeons and SU3-symmetry violation

Abstract The cylinder correction to the planar S matrix splits I = 0 from I = 1, lifts exchange degeneracy of I = 0 states and induces deviations from ideal mixing. All three effects are approximately described by one parameter which gives the shift of the ω intercept below the ϱ, the couplings of f, f′, ω, ф, the shift of the f above the ϱ, and its tendency to become an SU3 singlet heretofore labeled at t = 0 as the pomeron.

Exact Quantization Conditions

The method of Froman and Froman for proving exact quantization conditions is reviewed. This formalism, unlike the usual WKB approximation to which it bears a close resemblance, requires consideration of the behavior of the potential everywhere it is defined. This approach leads to proofs that certain quantization conditions are exact without having to compare the results to solutions of the Schrodinger equation obtained by other means. Using the formalism, we prove the correctness of all previously known exact quantization rules for the one‐dimensional and radial cases. Furthermore, it is shown that exact quantization rules can be proved for two other potentials. For one of these, no analytic solutions to the Schrodinger equation are known. For the latter case, the proof is checked by numerical integration of the Schrodinger equation for a special case.

Regge couplings and intercepts from the planar dual bootstrap

Abstract Planar unitarization of dual models is examined in terms of renormalized diagrams. The shift of the Reggeon intercept 1 − α(0) and the renormalized coupling g 2 N 16π are both expected of order unity in a model with SU( N ) Chan-Paton factors. In four space-time dimensions Regge behaviour makes the shift of the dual photon mass reminiscent of Schwingers mechanism.

DUAL-RESONANCE AMPLITUDE FOR SPINNING PARTICLES.

SummaryWe obtain a nonoperatorial, dual-resonance amplitude for the scattering of an arbitrary number of spinning particles on the mass shell.RiassuntoSi ottiene una ampiezza di risonanza duale, non operatoriale per lo scattering di un numero arbitrario di particelle rotanti sullo strato della massa.РезюмеМы получаем неоператорную, дуальную резонансную амплитуду для рассеония произвольного числа вращающихся частиц на массовой поверхнясти.

THE POMERON-f IDENTITY and HADRONIC TOTAL CROSS SECTIONS AT MODERATE ENERGY

Abstract The topological expansion of the S-matrix implies that the pomeron and f are the same Regge trajectory. We confront this hypothesis with data by successfully fitting σtot at moderate energies in a Regge model containing only one prominent vacuum trajectory, plus the ϱ and ω. Couplings and intercepts obey the constraints imposed by the topological expansion. The cylinder coupling is found to be 0.16. Existing data on ππ total cross sections are studied via FESR. The pomeron-f identity is consistent with the analysis. The conventional picture is not.

Electromagnetic duality, Landau ghosts, superconductivity, QCD and all that

Abstract Electric-magnetic duality allows us to describe the dynamics of a medium via either an electric or a magnetic formulation. One immediate result is that a gluon with a 1 k 4 propagator must be propagating in a magnetic superconducting medium. Another consequence is that there are no QCD Van der Waals forces. We predict the existence of short range Yukawa forces whose range is directly related to an important confinement parameter; the QCD London penetration depth. We prove the following and its dual; magnetic charges anti-screen electric potentials. Based on this result we present two conjectures. (1) The vertex of a charged particle and a “dual” photon carries an extra factor of i. (2) Magnetic monopoles exorcise the Landau ghost.

How does a pseudoscalar glueball come unglued

Abstract The η ′(960) and ι (1440) are treated as glueballs in the framework of effective chiral lagrangians which satisfy the axial anomaly equation. The narrow width of the η ′ can be qualitatively understood. An associated large breaking of flavor SU(3) is shown to be ameliorated as the model is made more realistic by lowering scalar meson masses from infinity. The π δ decay of the ι (1440) can be reasonably well estimated without the need of introducing any new parameters.

Unitarity sum rules and soft-pion amplitudes

SummaryWe examine unitarity bounds on scattering amplitudes by using « unitarity sum rules » at high energy. Threshold conditions emerge when certain mass parameters approach zero. For ππ scattering a bound similar to (but somewhat weaker than) the Adler condition is shown to be needed in order to avoid a dangerous mass (infra-red) singularity. A different argument, which uses crucially the pseudoscalar nature of the pion and a few very plausible dynamical assumptions, yields a stronger bound as well as the possibility of extension to general pion amplitudes. We finally discuss our results as well as the possibility of understanding spontaneously broken symmetries from generalS-matrix principles.RiassuntoSi esaminano i vincoli di unitarietà sulle ampiezze di scattering usando « regole di somma di unitarietà » ad alta energia. Le condizioni di soglia emergono quando certi parametri di massa si avvicinano a zero. Per lo scatteringππ si dimostra che è necessario un vincolo simile (ma alquanto più debole che) la condizione di Adler allo scopo di evitare una pericolosa singolarità (infrarossa) di massa. Un argomento diverso, che usa in modo cruciale la natura pseudoscalare del pione e poche plausibilissime ipotesi dinamiche, dà un vincolo più forte ed anche la possibilità di una estensione alle ampiezze pioniche generiche. Infine si discutono i risultati ed anche la possibilità di comprendere le simmetrie spontaneamente infrante sulla base dei principi generali della matriceS.РеэумеИсполяэуя «унитарные правила сумм» при высоких знергиях, мы исследуем унитарные границы для амплитуд рассеяния. Воэникаут пороговые условия, когда некоторые массовые параметры стремятся к нулу. Покаэывается, что дляππ рассеяния необходима граница, подобная (но отчасти слабее, чем) условиу Адлера, для того чтобы иэбезатя опаснои массовои (инфракраснои) сингулярности. Другои аргумент, которыи сушественно исполяэует псевдоскалярнуу природу ииона и несколяко оченя правдоподобных динамических предполозении, приводит к более силянои границе, а такзе к воэмозности обобшения на случаи обших пионных амплитуд. В эаклучение мы обсуздаем нащи реэулятаты, а тазе воэмозностя интерпретации спонтанно нарущенных симметрии иэ обшихS-матричных принципов.