πN Partial Wave Relations from Fixed-t Dispersion Relations

Baacke, J.; Steiner, Frank

doi:10.1002/prop.19700180104

Cited by 38 publications

(13 citation statements)

References 29 publications

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“…Even more, HDRs are the unique choice if one demands that the curves pass through all kinematic channels, avoid double-spectral regions, do not introduce ostensible kinematic cuts into the partial-wave amplitudes, and still yield manageable kernel functions[107]. In view of the efforts[107,[189][190][191]] that led to s-channel PWDRs for πN scattering and thus provided the first step towards the construction of a Roy-equation analog for processes with πN crossing properties, the resulting full system of partial-wave hyperbolic dispersion relations is referred to as Roy-Steiner equations.…”

mentioning

confidence: 99%

Roy–Steiner-equation analysis of pion–nucleon scattering

Hoferichter

Elvira²,

Kubis³

et al. 2016

Physics Reports

248

260

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Abstract. Low-energy pion-nucleon scattering is relevant for many areas in nuclear and hadronic physics, ranging from the scalar couplings of the nucleon to the long-range part of two-pion-exchange potentials and three-nucleon forces in Chiral Effective Field Theory. In this talk, we show how the fruitful combination of dispersion-theoretical methods, in particular in the form of Roy-Steiner equations, with modern high-precision data on hadronic atoms allows one to determine the pion-nucleon scattering amplitudes at low energies with unprecedented accuracy. Special attention will be paid to the extraction of the pion-nucleon σ-term, and we discuss in detail the current tension with recent lattice results, as well as the determination of the low-energy constants of chiral perturbation theory. c

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mentioning

confidence: 99%

Roy–Steiner-equation analysis of pion–nucleon scattering

Hoferichter

Elvira²,

Kubis³

et al. 2016

Physics Reports

248

260

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“…Similar dispersive analyses have also been carried out for πN [124,149,150,[155][156][157], γ ( * ) γ ( * ) → ππ [158][159][160][161][162], e + e − → π + π − [163], γπ → ππ [164,165] and γK → πK [166]. The approach for obtaining rigorous and precise poles from dispersively constrained data fits, is also well-suited for the recent lattice calculations that we hope may shed further light on these issues.…”

Section: Cfd I=1 P-wavementioning

confidence: 84%

Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances $$\sigma /f_0(500) $$ and $$\kappa /K_0^*(700) $$

Peláez

Rodas

Elvira

2021

Eur. Phys. J. Spec. Top.

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For several decades, the σ/f0(500) and κ/K * 0 (700) resonances have been subject to long-standing debate. Both their existence and properties were controversial until very recently. In this tutorial review we compare model-independent dispersive and analytic techniques versus unitarized Chiral Perturbation Theory, when applied to the lightest scalar mesons σ/f0(500) and κ/K * 0 (700). Generically, the former have settled the long-standing controversy about the existence of these states, providing a precise determination of their parameters, whereas unitarization of chiral effective theories allows us to understand their nature, spectroscopic classification and dependence on QCD parameters. Here we review in a pedagogical way their uses, advantages and caveats.

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“…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).…”

Section: Partial-wave Hyperbolic Dispersion Relationsmentioning

confidence: 99%

Roy-Steiner equations for pion-nucleon scattering

Ditsche¹,

Hoferichter²,

Kubis³

et al. 2013

Proceedings of the 7th International Workshop on Chiral Dynamics — PoS(CD12)

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Starting from hyperbolic dispersion relations for the invariant amplitudes of pion-nucleon scattering together with crossing symmetry and unitarity, one can derive a closed system of integral equations for the partial waves of both the s-channel (πN → πN) and the t-channel (ππ →NN) reaction, called Roy-Steiner equations. After giving a brief overview of the Roy-Steiner system for πN scattering, we demonstrate that the solution of the t-channel subsystem, which represents the first step in solving the full system, can be achieved by means of Muskhelishvili-Omnès techniques. In particular, we present results for the P-waves featuring in the dispersive analysis of the electromagnetic form factors of the nucleon.

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πN Partial Wave Relations from Fixed-t Dispersion Relations

Cited by 38 publications

References 29 publications

Roy–Steiner-equation analysis of pion–nucleon scattering

Roy–Steiner-equation analysis of pion–nucleon scattering

Precision dispersive approaches versus unitarized chiral perturbation theory for the lightest scalar resonances $$\sigma /f_0(500) $$ and $$\kappa /K_0^*(700) $$

Roy-Steiner equations for pion-nucleon scattering

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