Importance of chiral constraints for the pole content of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mover accent="true"><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover><mml:mi>N</mml:mi></mml:math> scattering amplitude

Bruns, Peter C.; Cieplý, A.

doi:10.1016/j.nuclphysa.2020.121702

Cited by 11 publications

(10 citation statements)

References 54 publications

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“…However, as convincingly shown in Ref. [68], that approach violates constraints imposed by chiral symmetry. The origin of this violation can be traced back to the off-shell treatment of the chiral-effective vertices, in combination with the use of non-relativistic approximations and the chosen regularization scheme.…”

Section: Where Do We Stand?mentioning

confidence: 62%

Two-Pole Structures in QCD: Facts, Not Fantasy!

Meißner

2020

Symmetry

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The two-pole structure refers to the fact that particular single states in the spectrum as listed in the PDG tables are often two states. The story began with the Λ ( 1405 ) , when in 2001, using unitarized chiral perturbation theory, it was observed that there are two poles in the complex plane, one close to the K ¯ p and the other close to the π Σ threshold. This was later understood combining the SU(3) limit and group-theoretical arguments. Different unitarization approaches that all lead to the two-pole structure have been considered in the mean time, showing some spread in the pole positions. This fact is now part of the PDG book, although it is not yet listed in the summary tables. Here, I discuss the open ends and critically review approaches that cannot deal with this issue. In the meson sector, some excited charm mesons are good candidates for such a two-pole structure. Next, I consider in detail the D 0 * ( 2300 ) , which is another candidate for this scenario. Combining lattice QCD with chiral unitary approaches in the finite volume, the precise data of the Hadron Spectrum Collaboration for coupled-channel D π , D η , D s K ¯ scattering in the isospin I = 1 / 2 channel indeed reveal its two-pole structure. Further states in the heavy meson sector with I = 1 / 2 exhibiting this phenomenon are predicted, especially in the beauty meson sector. I also discuss the relation of these two-pole structures and the possible molecular nature of the states under consideration.

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Section: Where Do We Stand?mentioning

confidence: 62%

Two-Pole Structures in QCD: Facts, Not Fantasy!

Meißner

2020

Symmetry

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“…This raised a debate on the one-pole versus two-pole structure of (1405) state, see, e.g., Refs. [55][56][57][58][59]. Note that the mentioned studies finding only a single pole have some deficiencies as detailed e.g.…”

Section: Introductionmentioning

confidence: 99%

The $${\varvec{\Lambda (1405)}}$$ in resummed chiral effective field theory

et al. 2021

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We study the unitarized meson–baryon scattering amplitude at leading order in the strangeness $$S=-1$$ S = - 1 sector using time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of chiral effective field theory. By solving the coupled-channel integral equations with the full off-shell dependence of the effective potential and applying subtractive renormalization, we analyze the renormalized scattering amplitudes and obtain the two-pole structure of the $$\Lambda (1405)$$ Λ ( 1405 ) resonance. We also point out the necessity of including higher-order terms.

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“…Before drawing our conclusions concerning the fits with this potential, it could be appropriate to comment on two papers [22,23], criticizing it. In both papers the starting point is the same as in [4]: the lowest order Weinberg-Tomozawa (WT) term of the chiral expansion of the SU(3) meson-baryon interaction Lagrangian.…”

Section: About the Acceptance Of The Potentialmentioning

confidence: 99%

“…The second paper ( [23]) consists of two parts. In the first one the potential [4] is scrutinized remaining in the non-relativistic framework.…”

Section: About the Acceptance Of The Potentialmentioning

confidence: 99%

“…The simultaneous application of both limits to a system or process does not seem to be reasonable. One can, of course, blame the non-relativistic approach, however, if the potential is basically designed for calculations in n > 2 systems, where relativistic treatment is not really available, then the fitting of potential parameters to the two-body data has to be performed under the same conditions In the second part of [23] the authors propose an extension of the disputed potential using relativistic kinematics without the on-shell approximation combined with a separable potential type regularization based on cut-off (form factor) functions. Keeping the number of adjustable parameters as low as possible-and consequently a not too convincing-fit to experimental data was performed and, indeed, two poles on the unphysical π sheet were found.…”

Section: About the Acceptance Of The Potentialmentioning

confidence: 99%

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Lessons from Fitting the Lowest Order Energy Independent Chiral Based $$\bar{K}N$$ Potential to Experimental Data

Révai

2020

Few-Body Syst

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It is shown, that fitting parameters of a $$\bar{K}N$$ K ¯ N interaction model to different sets of experimental data can lead to physical conclusions which might provide a deeper insight into the physics of this multichannel system. The available experimental data are divided into three parts: the “classical” set consisting of the low-energy $$K^-p$$ K - p cross sections and the threshold branching ratios, the SIDDHARTA 1s level shift in kaonic hydrogen and the CLAS photoproduction data. We have fitted the parameters of the potential to different combinations of these data. We found, that the two poles corresponding to the $$I=0$$ I = 0 nuclear quasi-bound state $$(\Lambda (1405))$$ ( Λ ( 1405 ) ) and to the $$K^-p$$ K - p 1s atomic level seem to resist to their simultaneous reproduction at the right place, though a more or less satisfactory compromise can be achieved. Potentials with the $$\Lambda (1405)$$ Λ ( 1405 ) pole pinned down close to the PDG value fail to reproduce the classical two-body data with an acceptable accuracy. We also added comments on two papers criticizing the potential used in the fits.

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Importance of chiral constraints for the pole content of the K¯N scattering amplitude

Cited by 11 publications

References 54 publications

Two-Pole Structures in QCD: Facts, Not Fantasy!

Two-Pole Structures in QCD: Facts, Not Fantasy!

The $${\varvec{\Lambda (1405)}}$$ in resummed chiral effective field theory

Lessons from Fitting the Lowest Order Energy Independent Chiral Based $$\bar{K}N$$ Potential to Experimental Data

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