On the Generalized πN Potential A New Representation from Fixed-t Dispersion Relations

Abstract

Starting from a recent paper [13] we derive a new representation of the left‐hand cut contribution for the πN system. This representation makes it possible to calculate the generalized πN potential accurately from phase shifts and high energy models, because it contains only the imaginary parts of the partial wave amplitudes in the physical region. The analytic properties, the region of convergence and the physical content of this representation is discussed. We propose to use this left‐hand cut contribution in bootstrap calculations, because it is more reliable than the approximate expressions which have been used in previous papers. – The left‐hand cut contributions are calculated and compared with the nucleon and Δ (1236) approximation for the ƒ 0+(−), ƒ 1−(−), ƒ −(1+) and ƒ −(2−) partial wave amplitudes.

Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

“…Defining −iΣ N as the sum of one-particle irreducible diagrams contributing to the nucleon two-point function, the dressed propagator of the nucleon is given as 5) where m N is the nucleon pole mass and Z N is the wave function renormalization constant. NP stands for the non-pole part (also for the delta propagator below).…”

“…[1,2]), not only due to the wealth of experimental data, but also because of its importance for our understanding of chiral dynamics of quantum chromodynamics (QCD). From the theory side, in order to describe such a fundamental process, dispersion relations for πN scattering have been investigated several decades ago [3][4][5] and many phenomenological models and different approaches have been proposed (see, e.g., refs. [6][7][8][9][10][11][12][13]).…”

πN Partial Wave Relations from Fixed-t Dispersion Relations

“…b) As mentioned in ii) we think that the partial wave relations give more accurate results for the real parts a t low energies than the phase shift analysis. c) Approximating in the partial wave relation a resonant Im By such a comparison one can deduce an expression for the total left hand cut contribution in the partial wave dispersion relation, which is a sum over the imaginary parts of all partial waves [25]. This expression can be calculated from phase shifts and high energy models and yields the most accurate result for the left hand cut contribution.…”

Roy-Steiner equations for pion-nucleon scattering

“…2.2. For the sake of completeness and convenience, in Appendix A the different contributions to (3.4) will be discussed along the lines of [21,[46][47][48] (correcting several typographical errors, adjusting the conventions, and partially extending the presentation therein at the same time).…”