Ph. Salin

Some remarks about gauge invariance in the isobaric model for photoproduction

>Gauge invariant formalism was given for both spin J = 3/2/sup +/ and 3/ 2- isobar terms corresponding to pi - resonances. The possible gauge invariant hamiltonian that described the interaction between a nucleon, a pi meson, and a P/sub 3/2/ isobar were considered. One interesting feature of the isobaric model was the presence of a small part of electric quadrupole. The effect due to the first P/sub 3/2// pionnucleon resonance was described by the hamiltonian and corresponded to a magnetic transition. The small part of the electric amplitude was induced by some relativistic effects due to the covariant form of the hamiltonian. (C.E.S.)

Positive and neutral pion photoproduction analysis

SummaryA covariant scattering amplitude is written down including Born terms without multipole projections, pion-nucleon isobars and twopion contribution. The resonating phase shifts of the isobars are taken to satisfy a Breit and Wigner expression, and the bipion model is applied. A satisfactory fit is obtained from threshold to 800 MeV. It turns out that first and second resonance are mainlyM1+ and E2- respectively and that one does not need the bipion contribution to explain experimental data.RiassuntoSi scrive una ampiezza di scattering covariante che comprende termini di Born senza proiezioni multipolari, isobari pioni-nucleone e contributi di due pioni. Si suppone che gli spostamenti di fase risonanti degli isobari soddisfino una espressione di Breit e Wigner, e si applica il modello bipionico. Si ottiene un accordo soddisfacente dalla soglia a 800 MeV. Risulta che la prima e la seconda risonanza sono principalmenteM1+ ed E2- rispettivamente e che non è necessario il contributo bipionico per spiegare i dati sperimentali.

Determination of dirac’s neutron form factor from electroproduction of pions

SummaryAn isobaric model for photoproduction is now extended to the virtual photon in the case of electroproduction of pions from protons. Numerical results are obtained and discussed in comparison with available data. It is shown that one might not hope to extract the pion form factor, but that the electric form factorF1n should be negative or equivalently thatFchn is negative.RiassuntoSi estende qui, nel caso di elettroproduzione di pioni da protoni, al fotone virtuale un modello isobarico della fotoproduzione. Si ottengono dei risultati numerici e si discutono confrontandoli coi dati sperimentali disponibili. Si dimostra che non si può sperare di ricavare il fattore di forma del pione, ma che il fattore di forma elettricoF1n deve essere negativo o, equivalentemente, cheFchn è negativo.

Construction of π± photoproduction amplitudes at high energy from dispersion relations and local duality

We investigate the charged-pion photoproduction amplitudes at all energies. We first show that low-energy s-channel helicity amplitudes exhibit, in most cases, a Bessel-function structure of zeroes. At high energy we therefore parametrize the imaginary parts of helicity amplitudes according to the Harari model, and compute the real parts using fixed-t dispersion relations as proposed recently. Such an evaluation of scattering amplitudes presents some very nice properties. In particular, it allows one to understand from duality arguments how the Born contribution may survive with full strength in the forward direction but not at large t-values. Furthermore FESR are identically satisfied by the model.

Gauge invariance presciptions for photoproduction amplitudes

Abstract We show that the gauge condition for a massless particle should be considered as an usual kinematical constraint, in fact a low-energy theorem, which has no dynamical implications for photoproduction reactions, and in particular that it gives no prescription on the nature of dynamical singularities for the scattering amplitude (fixed poles, moving poles, conspiring poles, cuts, Kronecker-delta singularities, etc...) which are all allowed. We also prove that no peculiar philosophy with regard to duality is imposed by gauge invariance. A special attention is devoted to π-exchange and we show that π−pϱtr0n s have structure in the forward direction, expected in very particular case where ϱ0-polarization is measured in the Jackson frame. We then deduce some implications for vector dominance, and more generally we give a very simple prescription to compute scattering amplitudes describing vector-meson production (or electroproduction) which goes smoothly to the photoproduction amplitude when the vector-meson mass goes to zero.

Model-independent analysis of density-matrix element measurements in multiparticle reactions

Abstract We present a general study of polarization measurement in multiparticle production processes, including a definition of experimentally observable quantities, the splitting into natural- and unnatural parity exchanges and a study of their relative phase, and information concerning the quantum numbers of a packet of particles. When only one single particle is detected in the final state (inclusive reactions for instance) we prove that the usual formalism for two-body reactions is applicable. Very interesting new information on multi-particle production can be reached when it can be asserted that another particle has been emitted above or below a given plane, parallel or perpendicular to the scattering plane.

REAL PARTS OF SCATTERING AMPLITUDES AND REGGE PHENOMENOLOGY.

Abstract High energy scattering amplitudes are computed using the Harari model for the imaginary parts and fixed t dispersion relations for the real parts. This procedure induces a corrective term to the real part of the Regge amplitudes whose effects are investigated in π -nucleon and K-nucleon charge exchange reactions.

Pion-Kaon Scattering

RésuméUne interaction directe méson π-méson K a été proposé comme étant l’un des processus possibles responsable des interactions méson K-nucléon. Nous essayons dans ce papier de voir ce que la représentation de Mandelstam, dans la forme simplifiée et realiste donnée parCini etFubini, permet de determiner d’une telle interaction. Nous donnons une technique générale de calcul pour les différentes ondes partielles et calculons la contribution d’une intéraction directe méson π-méson π à l’amplitude de diffusion méson π-méson K. Enfin, faisant l’hypothèse d’une ondeS importante, nous donnons pour cette dernière une expression dans l’approximation de la portée effective et évaluons l’importance des corrections dues au croisement possible des mésons π. L’étude des ondesP n’est pas abordée dans ce papier et est en cours d’investigation.RiassuntoSi è proposta una interazione diretta mesone π-mesone K come uno dei possibili processi responsabili delle interazioni mesone K-nucleone. Si cerca in questo scritto di vedere ciò che in merito a tale interazione permette di determinare la rappresentazione di Mandelstam, nella forma semplificata e realistica data daCini eFubini. Si dà una tecnica generale di calcolo per le diverse onde parziali e si calcola il contributo di una interazione diretta mesone π-mesone π all’ampiezza di scattering mesone π mesone K. Infine, facendo l’ipotesi di un’ondaS importante, si dà per quest’ ultima una espressione nell’approssimazione della portata effettiva e si valuta l’importanza delle correzioni dovute al possibile incrocio dei mesoni π. Lo studio delle ondeP non viene affrontato in questo scritto ed è in corso di studio.

CONSISTENCY CONDITIONS BETWEEN SU(3) AND EXCHANGE DEGENERACY FOR MESON-- BARYON SCATTERING.

Abstract We present and discuss non-exotic solutions for meson-baryon scattering amplitudes compatible with exact SU(3) symmetry and exchange degeneracy. We show that there exist dual solutions, i.e. solutions which reproduce themselves under crossing from one channel to the others. The physical consequences predicted by these solutions are also investigated.

Exchange degeneracy, absorption and loops in KN and KN scattering

Abstract We show that exchange degeneracy is fully compatible with all present high-energy experimental data and even, in most cases, at surprsingly we energy. We discuss the implications of the necessary absorptive corrections. At the end we obtain loops for partial waves corresponding to a set of exchange degenerate Y o ∗ all lying on a straight-line trajectory.