How (not) to renormalize integral equations with singular potentials in effective field theory

Epelbaum, E.; Gasparyan, A. M.; Gegelia, J.; Meißner, Ulf‐G.

doi:10.1140/epja/i2018-12632-1

Cited by 68 publications

(79 citation statements)

References 97 publications

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“…The appearance of a finite cutoff that needs to be kept of the order of the breakdown scale [24,25,26,27,28] is an unavoidable feature of the employed non-relativistic approach with the scattering amplitude being generated non-perturbatively by solving the Schrödinger or Lippmann-Schwinger equations for a potential truncated at a finite chiral order, see Ref. [29] for a discussion of some common misconceptions in connection with non-perturbative renormalization of chiral EFT for the two-nucleon system. To the best of my knowledge, the only available approach which allows one to eliminate the UV cutoff in calculations based on the non-perturbative treatment of the one-pion exchange potential in the way compatible with the principles of EFT is the one proposed in Ref.…”

Section: Pos(cd2018)006mentioning

confidence: 99%

High-precision nuclear forces : Where do we stand?

Epelbaum¹

2020

Proceedings of the 9th International Workshop on Chiral Dynamics — PoS(CD2018)

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Section: Pos(cd2018)006mentioning

confidence: 99%

High-precision nuclear forces : Where do we stand?

Epelbaum¹

2020

Proceedings of the 9th International Workshop on Chiral Dynamics — PoS(CD2018)

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“…The standard way to cure this problem in practical calculations is to employ a finite UV cutoff of the order of a natural hard scale in the problem, so that the unwanted higher-order contributions turn out to be suppressed [43]; see also a recent discussion in Ref. [44]. For an alternative approach with relativized integral equations of the Kadyshevsky type in the context of a nucleon-nucleon (NN) and heavy-meson EFTs see Refs.…”

Section: B Renormalizability Of the Heavy-hadron Eft With Pionsmentioning

confidence: 99%

Spin partners WbJ from the line shapes of the Zb(10610) and
Baru
¹
,
Epelbaum
²
,
Filin
³

et al. 2019
Phys. Rev. D
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In a recent paper [Phys. Rev. D 98, 074023 (2018)], the most up-to-date experimental data for all measured production and decay channels of the bottomoniumlike states Z b ð10610Þ and Z b ð10650Þ were analyzed in a field-theoretical coupled-channel approach which respects analyticity and unitarity and incorporates both the pion exchange and a short-ranged potential nonperturbatively. All parameters of the interaction were fixed directly from data, and pole positions for both Z b states were determined. In this work we employ the same approach to predict in a parameter-free way the pole positions and the line shapes in the elastic and inelastic channels of the (still to be discovered) spin partners of the Z b states. They are conventionally referred to as W bJ 's with the quantum numbers J PC ¼ J þþ (J ¼ 0, 1, 2). It is demonstrated that the results of our most advanced pionful fit, which gives the best χ 2 =d:o:f: for the data in the Z b channels, are consistent with all W bJ states being above-threshold resonances which manifest themselves as well-pronounced hump structures in the line shapes. On the contrary, in the pionless approach, all W bJ 's are virtual states which can be seen as enhanced threshold cusps in the inelastic line shapes. Since the two above scenarios provide different imprints on the observables, the role of the one-pion exchange in the B ðÃÞBðÃÞ systems can be inferred from the once available experimental data directly.

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“…The resulting cutoff dependence of the amplitude supports the conclusions of Refs. [56,68] about the incompatibility of such "non-perturbative renormalization" with the principles of EFT.…”

Section: Discussionmentioning

confidence: 99%

Towards baryon-baryon scattering in manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory

et al. 2019

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We study baryon-baryon scattering by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory. We derive the corresponding diagrammatic rules paying special attention to complications caused by momentumdependent interactions and propagators of particles with non-zero spin. We define the effective potential as a sum of two-baryon irreducible contributions of time-ordered diagrams and derive a system of integral equations for the scattering amplitude, which provides a coupled-channel generalization of the Kadyshevsky equation. The obtained leading-order baryon-baryon potentials are perturbatively renormalizable, and the corresponding integral equations have unique solutions in all partial waves. We discuss the issue of additional finite subtractions required to improve the ultraviolet convergence of (finite) loop integrals on the example of nucleon-nucleon scattering in the 3 P 0 partial wave. Assuming that corrections beyond leading order can be treated perturbatively, we obtain a fully renormalizable formalism which can be employed to study baryon-baryon scattering.

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How (not) to renormalize integral equations with singular potentials in effective field theory

Cited by 68 publications

References 97 publications

High-precision nuclear forces : Where do we stand?

High-precision nuclear forces : Where do we stand?

Spin partners WbJ from the line shapes of the Zb(10610) and
Baru
¹
,
Epelbaum
²
,
Filin
³

et al. 2019
Phys. Rev. D
Self Cite

Towards baryon-baryon scattering in manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory

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How (not) to renormalize integral equations with singular potentials in effective field theory

Cited by 68 publications

References 97 publications

High-precision nuclear forces : Where do we stand?

High-precision nuclear forces : Where do we stand?

Spin partners WbJ from the line shapes of the Zb(10610) and Baru1, Epelbaum2, Filin3 et al. 2019Phys. Rev. DSelf Cite

Towards baryon-baryon scattering in manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory

Contact Info

Product

Resources

About

Spin partners WbJ from the line shapes of the Zb(10610) and
Baru
¹
,
Epelbaum
²
,
Filin
³

et al. 2019
Phys. Rev. D
Self Cite