Chiral corrections to the S-wave pion-nucleon scattering lengths

Bernard, Véronique; Kaiser, Norbert; Meißner, Ulf‐G.

doi:10.1016/0370-2693(93)90956-i

Cited by 99 publications

(72 citation statements)

References 17 publications

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“…This manifests in the large size of the LECs c 3 and c 4 in Table 1 due to the ∆(1232) contribution to them, evaluated in Refs. [62,63]. The large impact of the ∆(1232) is the well-known reason for the large size of subleading TPE, but once its leading effects are taken into account at O(p 3 ) the chiral expansion stabilizes [31,48], as we have also concluded in the discussion following Eq.…”

Section: S 0 Wavesupporting

confidence: 55%

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Nucleon-nucleon scattering from dispersion relations: Next-to-next-to-leading order study

Oller

2016

Phys. Rev. C

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We study nucleon-nucleon (N N ) scattering by applying the N/D method in chiral perturbation theory up to next-to-next-to-leading (NNLO) order in the calculation of the imaginary part of the N N partial-wave amplitudes along the left-hand-cut, which is the dynamical input for this approach. A quite good reproduction of the Nijmegen partial-wave analysis phase shifts and mixing angles is obtained, which implies a steady improvement in the accurateness achieved by increasing the chiral order in the calculation of the dynamical input. A power counting for the subtraction constants is established, which is appropriate for those subtractions attached to both the left-and right-hand cuts. We discuss that it is not necessary to modify the N N chiral potential at NNLO to agree with data, but instead one should perform the iteration of two-nucleon intermediate states to finally achieve analytic and unitarity N N partial-wave amplitudes in a well-defined way. We also confirm at NNLO the long-range correlations between the N N S-wave effective ranges and scattering lengths, when employing only once-subtracted dispersion relations, that holds up to around 10% when compared with experimental values.

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Section: S 0 Wavesupporting

confidence: 55%

“…The present NNLO calculation from Eqs. (62) and (65) reproduces the Nijmegen PWA mixing angle ǫ 1 much better than the NLO result from the same set of equations, which is shown by the (magenta) dot-dashed lines. This improvement in the description of ǫ 1 when passing from NLO to NNLO is also seen in Ref.…”

Section: Coupledmentioning

confidence: 82%

Nucleon-nucleon scattering from dispersion relations: Next-to-next-to-leading order study

Oller

2016

Phys. Rev. C

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“…But compared with the result of the previous approach [35], the change is sizable, even in isospin-symmetric matter. This is again due to the explicit density dependence of the moment of inertia (37), and the changes in the solutions of the classical equations (43). Note that with increasing density the moment of inertia Λ * decreases since χ 02 s < 0.…”

Section: Resultsmentioning

confidence: 99%

“…[35]. In addition to the strong isospin-breaking in the mesonic sector it explicitly takes into account the different influences of the isospin-asymmetric environment on the charged (π ± ) and neutral (π 0 ) pion fields via a builtin energy dependence in the s-wave pion-nucleon (π ± N) scattering lengths [37,38,39,40,41] and the p-wave optical potential [42]. This additional energy dependence also alters the predictions for iso-symmetric matter considerably.…”

Section: Introductionmentioning

confidence: 99%

Neutron-proton mass difference in isospin-asymmetric nuclear matter

et al. 2007

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Abstract. Isospin-breaking effects in the baryonic sector are studied in the framework of a medium-modified Skyrme model. The neutron-proton mass difference in infinite, asymmetric nuclear matter is discussed. In order to describe the influence of the nuclear environment on the skyrmions, we include energy-dependent charged and neutral pion optical potentials in the s-and p-wave channels. The present approach predicts that the neutron-proton mass difference is mainly dictated by its strong part and that it strongly decreases in neutron matter.

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“…Higher-order corrections to a + and a − involve low-energy constants (LECs) [3]. Unfortunately, the lack of information about the LECs and large cancellations between individual contributions strongly restrict the predictive power of the chiral expansion for a + .…”

Section: Introductionmentioning

confidence: 99%

Extraction of S-wave pN scattering lengths from data on pionic atoms

Baru¹

2012

Proceedings of Sixth International Conference on Quarks and Nuclear Physics — PoS(QNP2012)

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For many years a combined analysis of pionic hydrogen and deuterium atoms has been known as a good tool to extract information on the isovector and especially on the isoscalar s-wave πN scattering length. However, given the smallness of the isoscalar scattering length, the analysis becomes useful only if the pion-deuteron scattering length is controlled theoretically to a high accuracy comparable to the experimental precision. To achieve the required few-percent accuracy one needs theoretical control over all isospin-conserving three-body πNN → πNN operators up to one order before the contribution of the dominant unknown (N † N) 2 ππ contact term. This term appears at next-to-next-to-leading order in Weinberg counting. In addition, one needs to include isospin-violating effects in both two-body (πN) and three-body (πNN) operators. In this talk we discuss the results of the recent analysis where these isospin-conserving and -violating effects have been carefully taken into account. Based on this analysis, we present the up-to-date values of the s-wave πN scattering lengths.

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Chiral corrections to the S-wave pion-nucleon scattering lengths

Cited by 99 publications

References 17 publications

Nucleon-nucleon scattering from dispersion relations: Next-to-next-to-leading order study

Nucleon-nucleon scattering from dispersion relations: Next-to-next-to-leading order study

Neutron-proton mass difference in isospin-asymmetric nuclear matter

Extraction of S-wave pN scattering lengths from data on pionic atoms

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