Application of the uniformized Mittag-Leffler expansion to 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi><mml:mo>(</mml:mo><mml:mn>1405</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>

Yamada, Wren A.; Morimatsu, Osamu

doi:10.1103/physrevc.103.045201

Cited by 9 publications

(6 citation statements)

References 35 publications

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“…Using a model-independent of Uniformized Mittag-Leffler expansion, Ref. [63] fitted the experimental data well and supported the single-pole picture of the Λ(1405). Recently, also with the full off-shell dependence for the effective potentials, the two-pole structure was confirmed once again in Ref.…”

Section: Introductionmentioning

confidence: 56%

Is two-pole’s $$\varLambda (1405)$$ one state or two?

2021

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To understand the nature of two poles for the $$\varLambda (1405)$$ Λ ( 1405 ) state, we revisit the interactions of $${\bar{K}}N$$ K ¯ N and $$\pi \Sigma $$ π Σ with their coupled channels, where two-pole structure is found in the second Riemann sheet. We also dynamically generate two poles in the single channel interaction of $${\bar{K}}N$$ K ¯ N and $$\pi \Sigma $$ π Σ , respectively. Moreover, we make a further study of two poles’ properties by evaluating the couplings, the compositeness, the wave functions, and the radii for the interactions of four coupled channels, two coupled channels and the single channel. Our results show that the nature of two poles is unique. The higher-mass pole is a pure $${\bar{K}} N$$ K ¯ N molecule, and the lower-mass one is a composite state of mainly $$\pi \Sigma $$ π Σ with tiny component $${\bar{K}} N$$ K ¯ N . From our results, one can conclude that the $$\varLambda (1405)$$ Λ ( 1405 ) state may be overlapped with two different states of the same quantum numbers.

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Section: Introductionmentioning

confidence: 56%

Is two-pole’s $$\varLambda (1405)$$ one state or two?

2021

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“…II, III, we will demonstrate the general behavior of contributions of near-threshold poles on various sheets of the Riemann surface, including contributions commonly regarded as "threshold cusps", based on the formalism of the Uniformized Mittag-Leffler expansion presented in Ref. [11,12]. Then in the following section, (Sec.…”

Section: Introductionmentioning

confidence: 87%

“…In Ref. [11,12] it was shown that A can be expanded as a sum of pole terms in a form similar to that of Ref. [20][21][22][23] in the variable, z, (uniformized Mittag-Leffler expansion) as,…”

Section: Uniformized Mittag-leffler Expansionmentioning

confidence: 99%

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Near-threshold Spectrum from Uniformized Mittag-Leffler Expansion -Pole Structure of $Z(3900)$-

Yamada,

Morimatsu,

Sato

et al. 2021

Preprint

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“…For the two-channel S matrix, a uniformization variable was introduced in Ref. [5,10] and the uniformized Mittag-Leffler expansion has been examined in the past few years [3,11,12]. It was applied to a model theory and shown to work in Ref.…”

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confidence: 99%

Analytic Map of Three-Channel S Matrix -Generalized Uniformization and Mittag-Leffler Expansion-

Yamada¹,

Morimatsu²,

Sato³

2022

Preprint

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We explore the analytic structure of the three-channel S matrix by generalizing uniformization and making a single-valued map for the three-channel S matrix. First, by means of the inverse Jacobi's elliptic function we construct a transformation from eight Riemann sheets of the center-of-mass energy squared complex plane onto a torus, on which the three-channel S matrix is represented single-valued. Secondly, we show that the Mittag-Leffler expansion, a pole expansion, of the three-channel scattering amplitude includes not only topologically trivial but also nontrivial contributions and is given by the Weierstrass zeta function. Finally, we examine the obtained formula in the context of a simple three-channel model. Taking a simple non-relativistic effective field theory with contact interaction for the S = −2, I = 0, J P = 0 + , ΛΛ − NΞ − ΣΣ coupled-channel scattering, we demonstrate that the scattering amplitude as a function of the uniformization variable is, in fact, given by the Mittag-Leffler expansion with the Weierstrass zeta function and that it is dominated by contributions from neighboring poles.

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Application of the uniformized Mittag-Leffler expansion to Λ(1405)

Cited by 9 publications

References 35 publications

Is two-pole’s $$\varLambda (1405)$$ one state or two?

Is two-pole’s $$\varLambda (1405)$$ one state or two?

Near-threshold Spectrum from Uniformized Mittag-Leffler Expansion -Pole Structure of $Z(3900)$-

Analytic Map of Three-Channel S Matrix -Generalized Uniformization and Mittag-Leffler Expansion-

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