Inelastic Effects and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mo>−</mml:mo><mml:mi>N</mml:mi></mml:math>Resonances

Aaron, R.; Amado, R. D.

doi:10.1103/physrevlett.27.1316

Cited by 31 publications

(10 citation statements)

References 17 publications

(8 reference statements)

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“…This is evident if one confronts the Weinberg-Tomozawa theorem of the chiral SU(2) symmetry with (75). The expression (75) demonstrates further that this renormalization of f appears poorly convergent in the kaon mass. Note in particular the anomalously large term π m K /m N .…”

Section: Weinberg-tomozawa Interaction and Convergence Of χPtmentioning

confidence: 96%

“…The correction terms in (75) induced by the kaon-hyperon loop, which is subtracted at the nucleon mass, exemplify the fact that the parameter f is renormalized by the strangeness sector and therefore must not be identified with the chiral limit value of f as derived for the SU(2) chiral Lagrangian. This is evident if one confronts the Weinberg-Tomozawa theorem of the chiral SU(2) symmetry with (75).…”

Section: Weinberg-tomozawa Interaction and Convergence Of χPtmentioning

confidence: 99%

“…The fact that baryon resonances exhibit large hadronic decay widths may be taken as an indication that the coupled-channel dynamics is the driving mechanism for the creation of baryon resonances. Related arguments have been put forward in [75,76]. Indeed, for instance the N(1520) resonance, was successfully described in terms of coupled channel dynamics, including the vector-meson nucleon channels as an important ingredient [77], but without assuming a preformed resonance structure in the interaction kernel.…”

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confidence: 99%

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Relativistic chiral SU(3) symmetry, large-Nc sum rules and meson–baryon scattering

Lutz¹,

2002

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The relativistic chiral SU (3) Lagrangian is used to describe kaon-nucleon scattering imposing constraints from the pion-nucleon sector and the axial-vector coupling constants of the baryon octet states. We solve the covariant coupled-channel BetheSalpeter equation with the interaction kernel truncated at chiral order Q 3 where we include only those terms which are leading in the large N c limit of QCD. The baryon decuplet states are an important explicit ingredient in our scheme, because together with the baryon octet states they form the large N c baryon ground states of QCD. Part of our technical developments is a minimal chiral subtraction scheme within dimensional regularization, which leads to a manifest realization of the covariant chiral counting rules. All SU(3) symmetry-breaking effects are well controlled by the combined chiral and large N c expansion, but still found to play a crucial role in understanding the empirical data. We achieve an excellent description of the data set typically up to laboratory momenta of p lab ≃ 500 MeV.

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Section: Weinberg-tomozawa Interaction and Convergence Of χPtmentioning

confidence: 96%

Section: Weinberg-tomozawa Interaction and Convergence Of χPtmentioning

confidence: 99%

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confidence: 99%

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Relativistic chiral SU(3) symmetry, large-Nc sum rules and meson–baryon scattering

Lutz¹,

2002

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“…With the assumption that all interactions are due to the formation and decay of isobars, they developed a set of covariant three-dimensional equations for describing both the πN elastic scattering and πN → ππN reaction. They however had only obtained [23,24,25,26] a very qualitative description of the πN data and only investigated very briefly the electromagnetic meson production reactions. Their results suggested the limitation of the isobar model and the need of additional mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Dynamical coupled-channel model of meson production reactions in the nucleon resonance region

2007

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A dynamical coupled-channel model is presented for investigating the nucleon resonances (N * ) in the meson production reactions induced by pions and photons. Our objective is to extract the N * parameters and to investigate the meson production reaction mechanisms for mapping out the quark-gluon substructure of N * from the data. The model is based on an energy-independent Hamiltonian which is derived from a set of Lagrangians by using a unitary transformation method. The constructed model Hamiltonian consists of (a) Γ V for describing the vertex interactions N * ↔ M B, ππN with M B = γN, πN, ηN, π∆, ρN, σN , and ρ ↔ ππ and σ ↔ ππ, (b) v 22 for the non-resonant M B → M ′ B ′ and ππ → ππ interactions, (3) v M B,ππN for the non-resonant M B → ππN transitions, and (4) v ππN,ππN for the non-resonant ππN → ππN interactions. By applying the projection operator techniques, we derive a set of coupled-channel equations which satisfy the unitarity conditions within the channel space spanned by the considered two-particle M B states and the three-particle ππN state. The resulting amplitudes are written as a sum of non-resonant and resonant amplitudes such that the meson cloud effects on the N * decay can be explicitly calculated for interpreting the extracted N * parameters in terms of hadron structure calculations. We present and explain in detail a numerical method based on a spline-function expansion for solving the resulting coupled-channel equations which contain logarithmically divergent one-particle-exchange driving terms Z (E) M B,M ′ B ′ resulted from the ππN unitarity cut. This method is convenient, and perhaps more practical and accurate than the commonly employed methods of contour rotation/deformation, for calculating the two-pion production observables. For completeness in explaining our numerical procedures, we also present explicitly the formula for efficient calculations of a very large number of partial-wave matrix elements which are the input to the coupled-channel equations. Results for two pion photo-production are presented to illustrate the dynamical consequence of the one-particle-exchange driving term Z (E) M B,M ′ B ′ of the coupled-channel equations. We show that this mechanism, which contains the effects due to ππN unitarity cut, can generate rapidly varying structure in the reaction amplitudes associated with the unstable particle channels π∆, ρN , and σN , in agreement with the analysis of Aaron and Amado [Phys. Rev. D13, 2581(1976]. It also has large effects in determining the two-pion production cross sections. Our results indicate that cautions must be taken to interpret the N * parameters extracted from using models which do not include ππN cut effects. Strategies for performing a complete dynamical coupled-channel analysis of all of available data of meson photo-production and electro-production are discussed.

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“…The Aaron-Amado-Young model with the inclusion of the 7T7T interaction in the j = t = 1 (p-resonance) channel and 7rN interactions in the Pu and P33 channels has been applied by Aaron and Amado [Aar3] to describe the -D13, -D33, and Pi3 partial waves which show a typical counterclockwise looping characteristic of pseudoresonances produced by inelastic thresholds. They were able to give a good description of these three partial waves after adding phenomenological repulsive interactions in the D33 and P 13 channels.…”

Section: A-3 Three Body Modelsmentioning

confidence: 99%

Back Matter

1990

ΠNN Systems

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The following two appendices are aimed at providing the reader of some basic features and ingredients of two-body subsystems, which may be used as input to the description of the 7rNN system. Of course, we could have limited these appendices to include only those aspects which have eventually been used in the 7rNN equations: the separable models, and perhaps the chiral model which may be used in Born approximations to describe some 7rNN processes. However, we have gone a little further to also include the results of other approaches. This is just to give the reader some feeling of what has been going on in those subjects. Some of them are in fact quite fashionable these days, and many articles are still coming out for which one needs extended review articles! The interested reader should go ahead and look up the current publications to understand the frontier of those subjects. 251 A.l. Separable Potential ModelsSeparable potentials are the interactions most widely used in the numerical solution of the three-body problem. As we have shown throughout the theoretical chapters 1-4, they simplify enormously the integral equations by reducing them from two continuous variables to only one continuous variable.In the case of the 7rN subsystem a large number of separable potential models exist for the six dominant partial waves with I = 0 and 1, S\\ , Sn , P\\ , JP31 , P\$ , and P33 . The reason for this proliferation of models being, that the 7rN subsystem is treated sometimes nonrelativistically, or only the pion is considered a relativistic particle (RPK), while some other times both particles are treated relativistically. Even in this last case, the choice of relativistic two-body equation is essentially a matter of taste, since models exist based on the Lippmann-Schwinger equation with relativistic kinematics, the Blankenbeckler-Sugar equation, the Kadyshevski equation, or the Bethe-Salpeter equation. Also a very popular prescription in the case of the Pu and P33 partial waves, has been to parametrize them by means of energy-dependent separable potentials.The general form of the pion-nucleon T-matrix in a state of orbital angular momentum £ produced by a potential of the separable form The ranges of the Su and S31 waves are 2.63 and 3.04 /ra -1 . In the case of the 531 wave they found that in order to fit the Almehed-Lovelace phase [Alml], the form factor must have a hole at the origin, so that in this case they multiplied Eq. (A.ll)by l-0.5048e"P 2 .The and in the case of the Pu partial wave a rank-two separable potential. These models, however, have never been applied to any physical problem. A.2. Chew-Low ModelsChew-Low theory is the simplest possible meson field theory which is real istic enough to predict some of the main features of the 7rN subsystem (like the P33 resonance) and yet also simple enough that it can be solved by numerical methods or even for some special cases in analytical form. This theory is based on two assumptions: a) The only mechanism contributing to 7rN scattering is the emission and a...

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Inelastic Effects andπ−NResonances

Cited by 31 publications

References 17 publications

Relativistic chiral SU(3) symmetry, large-Nc sum rules and meson–baryon scattering

Relativistic chiral SU(3) symmetry, large-Nc sum rules and meson–baryon scattering

Dynamical coupled-channel model of meson production reactions in the nucleon resonance region

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