Coupled channel study on the S-wave interaction

Johannesson, N.; Petersen, Jens

doi:10.1016/0550-3213(74)90320-4

Cited by 27 publications

(23 citation statements)

References 15 publications

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“…Next, one splits the integration range as before and drops terms which are O(p 8 ). Equating the representations (11) and (16) then determines the unknown function in the former expression leaving just one undetermined constant. Introducing the following notation for the various high-energy integrals which are involved,…”

Section: Dispersive Representation Of F + (S T)mentioning

confidence: 99%

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$\pi K$ sum rules and the SU(3) chiral expansion

2001

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A recently proposed set of sum rules, based on the pion-Kaon scattering amplitudes and their crossing-symmetric conjugates are analysed in detail. A key role is played by the $l=0$ $\pi\pi\to K\overline K$ amplitude which requires an extrapolation to be performed. It is shown how this is tightly constrained from analyticity, chiral counting and the available experimental data, and its stability is tested. A re-evaluation of the $O(p^4)$ chiral couplings $L_1$, $L_2$, $L_3$ is obtained, as well as a new evaluation of the large $N_c$ suppressed coupling $L_4$.Comment: 28 pages, 7 figures [v1: small corrections and improvements

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Section: Dispersive Representation Of F + (S T)mentioning

confidence: 99%

“…[15] in which only results not depending on this amplitude were presented. Extrapolation of the ππ → KK amplitude, in particular for the S-wave, is a problem which was considered a long time ago [16,17]. We discuss this question in some detail in sec.…”

Section: Introductionmentioning

confidence: 99%

$\pi K$ sum rules and the SU(3) chiral expansion

2001

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“…By a partial wave analysis, one obtains the experimental results on particleparticle scattering in terms scattering phase shifts in channels of definite quantum numbers. In the case of strong interaction, experimental results on hadron-hadron scattering phase shifts are available in the literature [1,2,3,4,5]. On the theoretical side, Quantum Chromodynamics (QCD) is believed to be the underlying theory of strong interactions.…”

Section: Introductionmentioning

confidence: 99%

Two particle states and theS-matrix elements in multi-channel scattering

Feng

Liu

2005

J. High Energy Phys.

227

234

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Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions in all three directions. A relation between the exact energy eigenvalue in the box and the two-channel S-matrix elements in the continuum is obtained. This result can be viewed as a generalization of the well-known Lüscher's formula which establishes a similar relation in elastic scattering.

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“…For Steiner-Roy equations based on other dispersion relations, see ref. [22,23,24]. In contrast to the dispersion relations for the full amplitudes, the range of validity of these equations is restricted by the Lehmann ellipse(s).…”

Section: Partial Wave Equationsmentioning

confidence: 99%

Comparison of $\pi K$ scattering in SU(3) chiral perturbation theory and dispersion relations

Ananthanarayan

Büttiker

2001

Eur. Phys. J. C

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We establish the framework for the comparison of πK scattering amplitudes from SU (3) chiral perturbation theory with suitable dispersive representations which result from the combination of certain fixed-t dispersion relations with dispersion relations on hyperbolic curves. This allows for predictions for some combinations of low energy constants appearing in higher order calculations of chiral perturbation theory. Using a simple parametrization for the lowest partial waves, first estimates for some combinations are presented.

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Coupled channel study on the S-wave interaction

Cited by 27 publications

References 15 publications

$\pi K$ sum rules and the SU(3) chiral expansion

$\pi K$ sum rules and the SU(3) chiral expansion

Two particle states and theS-matrix elements in multi-channel scattering

Comparison of $\pi K$ scattering in SU(3) chiral perturbation theory and dispersion relations

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