<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-Matrix Poles Close to Threshold

Frazer, William R.; Hendry, A.W.

doi:10.1103/physrev.134.b1307

Cited by 83 publications

(40 citation statements)

References 27 publications

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“…These connections for the three intervals, E < E 1 , E 1 < E < E 2 , and E > E 2 are schematically shown in Fig. 2 [28]. When N > 2, the surface is so complicated that it is not worthwhile even trying to visualize it.…”

Section: Riemann Surfacementioning

confidence: 99%

Multi-channel analog of the effective-range expansion

Rakityansky¹,

Elander²

2011

J. Phys. A: Math. Theor.

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Similarly to the standard effective range expansion that is done near the threshold energy, we obtain a generalized power-series expansion of the multi-channel Jostmatrix that can be done near an arbitrary point on the Riemann surface of the energy within the domain of its analyticity. In order to do this, we analytically factorize its momentum dependencies at all the branching points on the Riemann surface. The remaining single-valued matrix functions of the energy are then expanded in the power-series near an arbitrary point in the domain of the complex energy plane where it is analytic. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This means that near an arbitrary point in the domain of physically interesting complex energies it is possible to obtain a semi-analytic expression for the Jost-matrix (and therefore for the Smatrix) and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles.

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Section: Riemann Surfacementioning

confidence: 99%

Multi-channel analog of the effective-range expansion

Rakityansky¹,

Elander²

2011

J. Phys. A: Math. Theor.

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“…[45] to describe the X(3872). It is known that the amplitude T 11 (s) can have a pole on either the II or IV sheet, but not on the III sheet [35]. This pole is entirely due to the opening of the heavier channel, and therefore it is a measure of the strength of the Σ + cD 0 interaction.…”

mentioning

confidence: 99%

Interpretation of the LHCbPc(4312)+Signal

et al. 2019

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“…5 It is interesting to compare the present model with that introduced by Chew, in which only 7riV scattering states are included. 4 The self-consistency conditions often used in the TTN model involve a specific assumption concerning the energy dependence of the amplitudes; these conditions are quite different from those used here. The conditions used in Ref.…”

Section: The Tt-at-jv* Modelmentioning

confidence: 95%

“…I to the static, reciprocal bootstrap model of the N and N* particles, in the approximation in which the N and N* are degenerate. 4 Our treatment differs from the treatment of Ref. 4, in that we include TN* scattering states, as well as wN states.…”

Section: The Tt-at-jv* Modelmentioning

confidence: 98%

Self-Consistent Particle Sets in a Baryon Bootstrap Model

Koerner

Capps

1965

Phys. Rev.

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An SU(n)-symmetric bootstrap model is considered in which the baryons are meson-baryon bound states. A postulate used previously in similar models of mesons is applied: that a solution to the dynamical equations should exist in which particles of the same type are degenerate. It is shown that this postulate is difficult to satisfy unless the baryons correspond to a single irreducible representation of the SU(n) group. The w-N-N* system is discussed in detail. The condition that the baryons correspond to a single irreducible representation does not favor a particular value of n for the underlying SU(n) symmetry, but does rule out the fundamental representation for the baryons, and favors the group SU(mn) over SU(m)®SU(n). Several relations between SU(£) and SU(6) symmetry schemes are pointed out.

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S-Matrix Poles Close to Threshold

Cited by 83 publications

References 27 publications

Multi-channel analog of the effective-range expansion

Multi-channel analog of the effective-range expansion

Interpretation of the LHCbPc(4312)+Signal

Self-Consistent Particle Sets in a Baryon Bootstrap Model

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