Does the multiple-scattering series in the pion-deuteron scattering actually converge?

Kudryavtsev, A. E.; Романов, А. И.; Gani, Vakhid A.

doi:10.1134/s1063778813070090

Cited by 5 publications

(8 citation statements)

References 12 publications

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“…Therefore, the solution of Eq. (1) forā < 0 is unambiguous, so that R Inh (p, p ′ ) has a constant asymptotics, see [6], where we studied this case. But in the caseā > 0, the asymptotic behavior of the particular solution of Eq.…”

Section: Fixed-center Approximation: Basic Resultsmentioning

confidence: 97%

“…In Refs. [6,7] we studied in detail the first example, where we discussed the properties of the equation in the fixed-center approximation (FCA) for the system of one light and two heavy particles. In this model, the interaction of a light particle (L) of mass m L with a heavy particle (H) of mass m H is determined by a constant amplitude which is equal to the scattering length a.…”

Section: Fixed-center Approximation: Basic Resultsmentioning

confidence: 99%

“…Integration in the right-hand side from 0 to +∞ is replaced by integration over the finite segment [0, Λ]. As was recently found in [6,7], the numerical solutions obtained in this way within the segment [0, Λ] substantially depend on the choice of Λ. Namely, in [6,7] we found an asymptotic cyclic dependence of the solution R Λ (p, p ′ ) on the parameter Λ for p ≫ p ′ and p Λ. The ambiguity of the solution of the equation for the resolvent of the three-body problem was first noticed by L.D.…”

Section: Fixed-center Approximation: Basic Resultsmentioning

confidence: 99%

“…Fixing b in terms of the three-body scattering length a 3 , we simultaneously fix the parameter Λ, see Eq. (6). Therefore, one should treat the parameter Λ as a quantity which is related to physical observablesnamely, to the scattering length a 3 .…”

Section: Fixed-center Approximation: Basic Resultsmentioning

confidence: 99%

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Collapse to the Center and Ambiguity in the Asymptotic Behavior of the Off-Shell Scattering Amplitude in Singular Three-Body Problems

Kudryavtsev

Романов

2018

Phys. Atom. Nuclei

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We discuss some examples of equations of the three-body problem with the oscillating asymptotics at large momentum: (i) the fixed-center approximation, (ii) the unitarized equation in the fixed-center approximation, (iii) Skornyakov-Ter-Martirosyan equation, and (iv) equations with operators used in the effective field theory, i.e., which can be expanded in power-series with positive powers of momentum. We show that in the aforementioned three-body problems the situation analogous to the falling down to the center in the two-body problem takes placethere appears an infinite number of bound states. The energy of these states is not bounded from below. In that sense the situation is close to the falling down to the center in the two-body problem. *

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Section: Fixed-center Approximation: Basic Resultsmentioning

confidence: 97%

Section: Fixed-center Approximation: Basic Resultsmentioning

confidence: 99%

Section: Fixed-center Approximation: Basic Resultsmentioning

confidence: 99%

Section: Fixed-center Approximation: Basic Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Collapse to the Center and Ambiguity in the Asymptotic Behavior of the Off-Shell Scattering Amplitude in Singular Three-Body Problems

Kudryavtsev

Романов

2018

Phys. Atom. Nuclei

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“…The function R ∞ (p, p ′ ), defined by (12), is a solution of the integral equation (11). This equation could be solved (e.g., numerically) by replacing the infinite upper integration limit by a finite cut-off Λ. References [36,37] showed that the function R Λ (p, p ′ ) obtained in that way strongly depends on the value of Λ, see also [39,40]. There seems thus to be no way to get a solution of Eq.…”

Section: The Problem Of λ-Dependence In the Momentum Spacementioning

confidence: 99%

Three-body scattering problem in the fixed center approximation: The case of attraction

2016

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Abstract.We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous -they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, introducing a finite cut-off. We show that all three approaches are equivalent. We also discuss how our approach to the problem matches with the introduction of three-body contact interaction as done by other authors.

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Roy–Steiner-equation analysis of pion–nucleon scattering

Hoferichter

Elvira²,

Kubis³

et al. 2016

Physics Reports

247

260

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Abstract. Low-energy pion-nucleon scattering is relevant for many areas in nuclear and hadronic physics, ranging from the scalar couplings of the nucleon to the long-range part of two-pion-exchange potentials and three-nucleon forces in Chiral Effective Field Theory. In this talk, we show how the fruitful combination of dispersion-theoretical methods, in particular in the form of Roy-Steiner equations, with modern high-precision data on hadronic atoms allows one to determine the pion-nucleon scattering amplitudes at low energies with unprecedented accuracy. Special attention will be paid to the extraction of the pion-nucleon σ-term, and we discuss in detail the current tension with recent lattice results, as well as the determination of the low-energy constants of chiral perturbation theory. c

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Does the multiple-scattering series in the pion-deuteron scattering actually converge?

Cited by 5 publications

References 12 publications

Collapse to the Center and Ambiguity in the Asymptotic Behavior of the Off-Shell Scattering Amplitude in Singular Three-Body Problems

Collapse to the Center and Ambiguity in the Asymptotic Behavior of the Off-Shell Scattering Amplitude in Singular Three-Body Problems

Three-body scattering problem in the fixed center approximation: The case of attraction

Roy–Steiner-equation analysis of pion–nucleon scattering

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