A chiral covariant approach to $$\varvec{\rho \rho }$$ ρ ρ scattering

Gülmez, Dilege; Meißner, Ulf‐G.; Oller, J. A.

doi:10.1140/epjc/s10052-017-5018-z

Cited by 52 publications

(70 citation statements)

References 72 publications

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“…In the present paper we show the reasons for the findings of Ref. [15], stemming from an unjustified on-shell factorization of the potential, which renders it singular. The singularity does not appear in a proper loop function, which we evaluate here.…”

Section: Introductionmentioning

confidence: 76%

“…In this sense, the conclusion of Ref. [15] that the tensor resonance f 2 (1270) does not appear with the potential of Eq. (8) is correct.…”

Section: Beyond the Static ρ Exchange With On-shell Factorizationmentioning

confidence: 89%

“…[15], which is the reason for the disappearance of the tensor state, stems from keeping the q 2 dependence in the ρ exchange potential in Fig. 1(b).…”

Section: Beyond the Static ρ Exchange With On-shell Factorizationmentioning

confidence: 96%

“…[15] we have taken q 0 = 0. This corresponds to the on-shell factorization, where the interaction V is taken for an on-shell situation.…”

Section: Beyond the Static ρ Exchange With On-shell Factorizationmentioning

confidence: 99%

“…This approximation was questioned in a recent work [15] where improvements were made to give a fully relativistic approach. The authors found that in the ρρ interaction the I = J = 0 state, the f 0 (1370), was obtained, very close to the result of Ref.…”

Section: Introductionmentioning

confidence: 99%

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On the chiral covariant approach to ρρ scattering

2017

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We examine in detail a recent work (D. Gülmez, U.-G. Meißner and J. A. Oller, Eur. Phys. J. C 77:460 (2017)), where improvements to make ρρ scattering relativistically covariant are made. The paper has the remarkable conclusion that the J = 2 state disappears with a potential which is much more attractive than for J = 0, where a bound state is found. We trace this abnormal conclusion to the fact that an "on-shell" factorization of the potential is done in a region where this potential is singular and develops a large discontinuous and unphysical imaginary part. A method is developed, evaluating the loops with full ρ propagators, and we show that they do not develop singularities and do not have an imaginary part below threshold. With this result for the loops we define an effective potential, which when used with the Bethe-Salpeter equation provides a state with J = 2 around the energy of the f2(1270). In addition, the coupling of the state to ρρ is evaluated and we find that this coupling and the T matrix around the energy of the bound state are remarkably similar to those obtained with a drastic approximation used previously, in which the q 2 terms of the propagators of the exchanged ρ mesons are dropped, once the cut-off in the ρρ loop function is tuned to reproduce the bound state at the same energy. *

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Section: Introductionmentioning

confidence: 76%

“…In this sense, the conclusion of Ref. [15] that the tensor resonance f 2 (1270) does not appear with the potential of Eq. (8) is correct.…”

Section: Beyond the Static ρ Exchange With On-shell Factorizationmentioning

confidence: 89%

“…[15], which is the reason for the disappearance of the tensor state, stems from keeping the q 2 dependence in the ρ exchange potential in Fig. 1(b).…”

Section: Beyond the Static ρ Exchange With On-shell Factorizationmentioning

confidence: 96%

“…[15] we have taken q 0 = 0. This corresponds to the on-shell factorization, where the interaction V is taken for an on-shell situation.…”

Section: Beyond the Static ρ Exchange With On-shell Factorizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the chiral covariant approach to ρρ scattering

2017

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Generating cosmological perturbations in non-singular Horndeski cosmologies

Ageeva

Petrov

Rubakov

2023

J. High Energ. Phys.

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We construct a concrete model of Horndeski bounce with strong gravity in the past. Within this model we show that the correct spectra of cosmological perturbations may be generated at early contracting epoch, with mild fine-tuning ensuring that the scalar spectral tilt nS and tensor-to-scalar ratio r are consistent with observations. The smallness of r is governed by the smallness of the scalar sound speed. Arbitrarily small values of r are forbidden in our setup because of the strong coupling in the past. Nevertheless, we show that it is possible to generate perturbations in a controllable way, i.e. in the regime where the background evolution and perturbations are legitimately described within classical field theory and weakly coupled quantum theory.

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The exact discontinuity of a partial wave along the left-hand cut and the exact N∕D method in non-relativistic scattering

Oller

Entem

2019

Annals of Physics

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We first deduce the analytical continuation in the complex planes of the initial and final three-momenta of the Lippmann-Schwinger equation in coupled or uncoupled partial-wave amplitudes. This result allows us to deduce a master equation whose solution is the exact discontinuity of the on-shell partial-wave amplitudes along the left-hand cut. This equation is always a linear non-singular integral equation whose solution is fixed exclusively by the knowledge of the potential, applicable to either regular or singular potentials. The capability of calculating exactly this discontinuity allows one to settle the exact N/D method in two-body non-relativistic scattering for coupled and uncoupled waves. We exemplify this new advance in scattering theory by explicitly checking the agreement between the Lippmann-Schwinger equation with the corresponding solutions of the exact N/D method for some examples that involve regular and singular potentials, either attractive or repulsive.

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A chiral covariant approach to $$\varvec{\rho \rho }$$ ρ ρ scattering

Cited by 52 publications

References 72 publications

On the chiral covariant approach to ρρ scattering

On the chiral covariant approach to ρρ scattering

Generating cosmological perturbations in non-singular Horndeski cosmologies

The exact discontinuity of a partial wave along the left-hand cut and the exact N∕D method in non-relativistic scattering

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