The contribution of the $ρ^0 - ω$ interference to the violation of the isospin invariance in the $πN$ system

Matsinos, E.

doi:10.48550/arxiv.1804.09344

Cited by 2 publications

(7 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The κ ρ values are also small, well below the corresponding results (6.1 to 6.6) obtained at the ρ(770)-meson pole via dispersion relations (for details, see Ref. [57] and the works cited therein). The results for the πN∆ coupling constant are in excellent agreement with the value of 29.20 (50), extracted directly from the decay width of the ∆(1232) resonance (see footnote 10 of Ref.…”

Section: Model Parametersmentioning

confidence: 58%

“…15 were estimated in Ref. [57] and found to be small, below the 1 % level in the low-energy region. Assuming the validity of the t dependence of the effects of the ρ 0 − ω mixing of Ref.…”

Section: The Violation Of the Isospin Invariance In The Hadronic Part...mentioning

confidence: 89%

“…Assuming the validity of the t dependence of the effects of the ρ 0 − ω mixing of Ref. [57] (imported therein from earlier works), it does not appear likely that the ρ 0 −ω mixing could play an important role in the low-energy πN interaction.…”

Section: The Violation Of the Isospin Invariance In The Hadronic Part...mentioning

confidence: 89%

“…[4] would be equal to 0.08560(16)(70) m −1 c , the one of Ref. [5] to 0.08561(9) (57), where the first uncertainty is statistical (taking account of the statistical uncertainty of the experimental result) and the second systematic (reflecting all 'external' uncertainties, i.e., the ones contained in the systematic uncertainty of the experimental result, as well as those relating to the EM corrections of Ref. [37]), see Appendix A of Ref.…”

Section: On the Inclusion In The Db − Of The A CC Values Extracted Fr...mentioning

confidence: 96%

See 3 more Smart Citations

Update of the phase-shift analysis of the low-energy $πN$ data

Matsinos¹,

Rasche²

2017

Preprint

Self Cite

View full text Add to dashboard Cite

This paper presents an updated phase-shift analysis (PSA) of the low-energy (pion laboratory kinetic energy T ≤ 100 MeV) pion-nucleon (πN ) data; this solution will be referred to as 'ZRH19'. In this research programme, the modelling of the s-and p-wave K-matrix elements is achieved by following either of two methods: a) suitable low-energy parameterisations or b) the analytical expressions obtained from a hadronic model ('ETH model') based on meson-exchange t-channel Feynman graphs, as well as on s-and u-channel graphs with N and ∆(1232) intermediate states. Analytically included in the former case are the important direct (s-channel) contributions from nearby baryon resonances in the partial waves P 33 and P 11 . As it does not impose any theoretical constraints onto the data, the analysis with the Kmatrix parameterisations is suitable for the reliable identification of the outliers in the database (DB) and for the preparation of consistent input for further analysis. After the removal of the outliers, the two elastic-scattering (ES) DBs are jointly submitted to an analysis with the ETH model; the theoretical constraints of crossing symmetry and isospin invariance are imposed at this stage. The optimal values of the model parameters and the corresponding Hessian matrices are obtained from these fits, and yield Monte-Carlo predictions for the low-energy constants of the πN system, for the πN phase shifts, and for the usual low-energy πN observables. The combined π + p and π − p charge-exchange (CX) DBs are also analysed following the same procedure. During the last two decades, our PSAs make use of the Arndt-Roper formula, enabling the controlled (i.e., regulated by the reported or assigned normalisation uncertainty of each data set) rescaling of the data sets.The essential difference to our past PSAs relates to the inclusion in the DB of the two π − p s-wave ES lengths, extracted from measurements of the strong-interaction shift of the ground state in pionic hydrogen. Although the addition of these highly accurate measurements to the DB does not give rise to dramatic differences in comparison to our recent PSAs, this modification has one important consequence: the long-standing discrepancy between the value obtained (via an extrapolation to T = 0 of the π − p s-wave scattering amplitude of the ETH model) from the analysis of the ES DBs and the results extracted from pionic hydrogen is resolved. In spite of this positive development, the other discrepancies, established in our earlier PSAs of the low-energy πN data, persist; they comprise: differences in the results of the fits to the two combined DBs -i.e., to the π ± p ES DBs, and to the combined π + p and π − p CX DBs; a general difficulty (revealed after the study of the resulting χ 2 values of the various fits to the data) in the description of the π − p CX DB when imposing on the data the theoretical constraints of crossing symmetry and isospin invariance; the presence of bias in the scale factors in case of the fit to the combined π + p and π − p CX DBs; ...

show abstract

Section: Model Parametersmentioning

confidence: 58%

Section: The Violation Of the Isospin Invariance In The Hadronic Part...mentioning

confidence: 89%

Section: The Violation Of the Isospin Invariance In The Hadronic Part...mentioning

confidence: 89%

Section: On the Inclusion In The Db − Of The A CC Values Extracted Fr...mentioning

confidence: 96%

See 2 more Smart Citations

Update of the phase-shift analysis of the low-energy $πN$ data

Matsinos¹,

Rasche²

2017

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…One of the possibilities in which models, based on hadronic exchanges, could accommodate a departure from the isospin invariance would have to involve ρ 0 −ω mixing Feynman diagrams; however, the impact of this mechanism is suppressed at low energy, see Ref. [58] and the works cited therein. Experience shows that any optimisation, involving the π − p CX DB, departs from the expected statistical norms, resulting in a sizeable increase in χ 2 min and in a pronounced energy dependence of the scale factors z j .…”

Section: Can Global Fits To All Low-energy πN Data Be Performed?mentioning

confidence: 99%

What has been learnt from the analysis of the low-energy pion-nucleon data during the past three decades?

Matsinos¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Over twenty-five years ago, two analyses of the pion-nucleon (πN ) data at low energy (i.e., for pion laboratory kinetic energy T ≤ 100 MeV) reported on the departure of the extracted scattering amplitudes, corresponding to the two elastic-scattering reactions π ± p → π ± p and to the π − p charge-exchange reaction π − p → π 0 n, from the triangle identity, which these amplitudes fulfil if the isospin invariance holds in the hadronic part of the πN interaction. This discrepancy indicates that at least one of the following assumptions is not valid: first, that the absolute normalisation of the bulk of the low-energy πN datasets is correct; second, that any residual contributions to the corrections, which aim at the removal of the effects of electromagnetic (EM) origin from the measurements, are not significant; and third, that the isospin invariance holds in the hadronic part of the πN interaction. In view of the incompatibility of the results of the various schemes of removal of the so-called trivial EM effects at the πN threshold (T = 0 MeV), the likelihood of residual effects of EM origin in the extracted πN scattering amplitudes (from the data in the scattering region, i.e., above the πN threshold) must be reassessed. This work emphasises the importance of the development of a unified scheme for the determination of reliable EM corrections, applicable at the πN threshold and in the scattering region, in providing a resolution to the established discrepancy at low energy.

show abstract

The contribution of the $ρ^0 - ω$ interference to the violation of the isospin invariance in the $πN$ system

Cited by 2 publications

References 40 publications

Update of the phase-shift analysis of the low-energy $πN$ data

Update of the phase-shift analysis of the low-energy $πN$ data

What has been learnt from the analysis of the low-energy pion-nucleon data during the past three decades?

Contact Info

Product

Resources

About