Empirical<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:mfrac></mml:math>Potential and Castillejo-Dalitz-Dyson Poles in the Pion-Nucleon<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn>11</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>State

Bart, George R.; Warnock, Robert

doi:10.1103/physrevlett.22.1081

Cited by 8 publications

(2 citation statements)

References 19 publications

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“…In the P 11 partial wave a numerically large contribution of the nucleon pole graph to the potential makes it impossible for the solution (8) to exist without a CDD pole. Similar findings were discussed previously in models [54,55] also based on a single-channel approximation. After inclusion of one CDD pole, we can reproduce the P 33 partial wave with only the zeroth order coefficient in the expansion (21).…”

Section: πN Elastic Scatteringsupporting

confidence: 90%

Photon– and pion–nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian

Gasparyan

Lutz²

2010

Nuclear Physics A

119

160

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We present and apply a novel scheme for studying photon-and pion-nucleon scattering beyond the threshold region. Partial-wave amplitudes for the γ N and π N states are obtained by an analytic extrapolation of subthreshold reaction amplitudes computed in chiral perturbation theory, where the constraints set by electromagneticgauge invariance, causality and unitarity are used to stabilize the extrapolation. Based on the chiral Lagrangian we recover the empirical s-and p-wave amplitudes up to energies √ s 1300 MeV in terms of the parameters relevant at order Q 3 .

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Section: πN Elastic Scatteringsupporting

confidence: 90%

Photon– and pion–nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian

Gasparyan

Lutz²

2010

Nuclear Physics A

119

160

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“…The decomposition of the contributions of the single-particle exchange diagrams into long and short-range components has allowed us to tackle the problem of the divergence of the kernel of the integral equation for N or D. This procedure seems more reasonable and less arbitrary than the cut-off procedure. The advantage of using the Chew-Mandelstam method in dealing with inelasticity is that it requires a smaller number of CDD poles than the Frye-Warnock method when applied to the $11-P~I amplitude (or no CDD poles at all) [9]. The idea of a resonant form for the inelasticity function R(W) near the inelastic threshold is crucial for obtaining the Roper resonance and a satisfactory P-wave fit ifCDD poles are to be avoided.…”

Section: Discussionmentioning

confidence: 99%

TheS 11-P 11 phase shifts of pion-nucleon scattering

Barron

Daboul

1975

Z Physik A

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Abstract. The $11 and PH partial amplitude is calculated using the N/D method. The present calculation differs from the previous ones in the handling of the divergent behavior of the forces due to first-order diagrams, by parameterizing the short-range forces, and in the way of including inelasticity. We obtain the nucleon as a bound state with correct mass and residue and the correct Six and P~ scattering lengths. The calculated S-wave and P-wave phase shifts and absorption coefficients are in substantial agreement with those from the CERN Theoretical and Almehed-Lovelace phase shift analyses.

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Regge Models and Dispersion Relations for Partial Waves

Kaschluhnxs

Müller–Preussker

1976

Fortschr. Phys.

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The asymptotic behaviour of partial wave amplitudes is calculated supposing various Regge models for the total scattering amplitude A(s, t, u). The high energy partial wave behaviour obtained is combined with the validity of partial wave dispersion relations. It is shown that consistency of these assumptions can only be achieved by demanding 1) a definite asymptotic behaviour of the discontinuity of the left hand cut of partial wave amplitudes, 2 ) the validity of partial wave sum rules of similar kind as the well-known finite energy sum rules for All steps of the derivation shall first be demonstated for elastic scattering of identical scalar particles. Then within the helicity formalism the results are generalized for particles with arbitrary spin and different masses. Finally the question is studied whether the sum rules can be employed to determine unknown CDD-pole parameters in an N / D approach for the I = J = 1/2 state in x N scattering. It is shown that the sum rules of highest order are able to do that. the total amplitude.

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EmpiricalNDPotential and Castillejo-Dalitz-Dyson Poles in the Pion-NucleonP11State

Cited by 8 publications

References 19 publications

Photon– and pion–nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian

Photon– and pion–nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian

TheS 11-P 11 phase shifts of pion-nucleon scattering

Regge Models and Dispersion Relations for Partial Waves

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