Supersymmetric inversion of effective-range expansions

Midya, Bikashkali; Evrard, Jérémie; Abramowicz, Sylvain; Suárez, O.; Sparenberg, Jean-Marc

doi:10.1103/physrevc.91.054004

Cited by 5 publications

(4 citation statements)

References 23 publications

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“…Our choice of the orders [(n + 1)/n] builds on the Refs. [9,11], but different orders do not affect our results.…”

Section: Extraction Of Resonancesmentioning

confidence: 49%

“…Higher-order terms in Eq. ( 53) also exist, see [10,11,25,26], but they are not discussed in this paper.…”

Section: A Standard Effective-range Functionmentioning

confidence: 97%

“…The expansion of the ERF -also referred to as the effectiverange expansion -can be either a power series of the energy or a Padé approximant, i.e., a rational function. In general, Padé approximants are valid on a larger domain than Taylor series [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

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Effective-range function methods for charged particle collisions

Gaspard

Sparenberg

2018

Phys. Rev. C

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Different versions of the effective-range function method for charged particle collisions are studied and compared. In addition, a novel derivation of the standard effective-range function is presented from the analysis of Coulomb wave functions in the complex plane of the energy. The recently proposed effective-range function denoted as ∆ [Phys. Rev. C 96, 034601 (2017)] and an earlier variant [Hamilton et al., Nucl. Phys. B 60, 443 (1973)] are related to the standard function. The potential interest of ∆ for the study of low-energy cross sections and weakly bound states is discussed in the framework of the proton-proton 1 S0 collision. The resonant state of the protonproton collision is successfully computed from the extrapolation of ∆ instead of the standard function. It is shown that interpolating ∆ can lead to useful extrapolation to negative energies, provided scattering data are known below one nuclear Rydberg energy (12.5 keV for the protonproton system). This property is due to the connection between ∆ and the effective-range function by Hamilton et al. that is discussed in detail. Nevertheless, such extrapolations to negative energies should be used with caution because ∆ is not analytic at zero energy. The expected analytic properties of the main functions are verified in the complex energy plane by graphical color-based representations.

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“…Our choice of the orders [(n + 1)/n] builds on the Refs. [9,11], but different orders do not affect our results.…”

Section: Extraction Of Resonancesmentioning

confidence: 49%

“…Higher-order terms in Eq. ( 53) also exist, see [10,11,25,26], but they are not discussed in this paper.…”

Section: A Standard Effective-range Functionmentioning

confidence: 97%

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Effective-range function methods for charged particle collisions

Gaspard

Sparenberg

2018

Phys. Rev. C

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“…(110). The problem can be solved by replacing the Taylor expansion with the Padé approximation [571].…”

Section: Effective Range Expansionmentioning

confidence: 99%

Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules

Li¹,

Wang²,

Wang³

et al. 2022

Preprint

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Chiral symmetry and its spontaneous breaking play an important role both in the light hadron and heavy hadron systems. In this work, we shall review the investigations on the chiral corrections to the properties of the heavy mesons and baryons within the framework of the chiral perturbation theory (χPT). We will also review the scatterings of the light pseudoscalar mesons and heavy hadrons. Moreover, the modern nuclear force was built upon the chiral effective field theory (χEFT). In the past decades many new hadron states were observed experimentally. A large group of these states are near-threshold resonances, such as the charged charmoniumlike Z c and Z cs states, bottomoniumlike Z b states, hidden-charm pentaquark P c and P cs states and the doubly charmed T cc state etc. They are very good candidates of the loosely bound molecular states composed of a pair of charmed hadrons. The same chiral dynamics not only governs the nuclei and forms the deuteron, but also dictates the above shallow bound states or resonances. We will perform an extensive review on the progress on the heavy hadronic molecular states within the framework of χEFT.

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