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S wave K\pi scattering and effects of \kappa in J/\psi\to {\bar K}^{*0}(892)K^+\pi^-
High Energy Physics - Phenomenology · Submitted 6 Sep 2005
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim With the amplitudes derived from the lowest order chiral Lagrangian as the kernel of a set of coupled channel Bathe-Salpeter equations, the $I=1/2$ $S$ wave $K\pi$ scattering phase shifts below 1.2 GeV can be fitted by one parameter, a subtraction constant, and a scalar resonance corresponding to the controversial $\kappa$ ($K^*_0(800)$) can be generated dynamically.
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The abstract, sentence by sentence
$K\pi$ $S$ wave scattering is studied using a chiral unitary approach (ChUT) taking into account coupled channels. With the amplitudes derived from the lowest order chiral Lagrangian as the kernel of a set of coupled channel Bathe-Salpeter equations, the $I=1/2$ $S$ wave $K\pi$ scattering phase shifts below 1.2 GeV can be fitted by one parameter, a subtraction constant, and a scalar resonance corresponding to the controversial $\kappa$ ($K^*_0(800)$) can be generated dynamically. A good description of the $I=3/2$ $S$ wave $K\pi$ scattering phase shifts below 1.2 GeV can also be obtained. An artificial singularity in the conventional cut-off method of the 2-meson loop integral of the ChUT is found. The formalism is applied to deal with the $S$ wave $K\pi$ final state interaction (FSI) in the decay $J/\psi\to {\bar K}^{*0}(892)K^+\pi^-$, and a qualitatively good fit to the data is achieved. The role of $\kappa$ in the decay is discussed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | $K\pi$ $S$ wave scattering is studied using a chiral unitary approach (ChUT) taking into account coupled channels. | contribution 0.64 | 0.86 | 0.05 | asserted 1.00 |
| s1 | With the amplitudes derived from the lowest order chiral Lagrangian as the kernel of a set of coupled channel Bathe-Salpeter equations, the $I=1/2$ $S$ wave $K\pi$ scattering phase shifts below 1.2 GeV can be fitted by one parameter, a subtraction constant, and a scalar resonance corresponding to the controversial $\kappa$ ($K^*_0(800)$) can be generated dynamically. | result 0.64 | 0.88 | 0.35 | asserted 0.97 |
| s2 | A good description of the $I=3/2$ $S$ wave $K\pi$ scattering phase shifts below 1.2 GeV can also be obtained. | result 1.00 | 0.88 | 0.08 | asserted 0.97 |
| s3 | An artificial singularity in the conventional cut-off method of the 2-meson loop integral of the ChUT is found. | result 0.92 | 0.92 | 0.07 | asserted 1.00 |
| s4 | The formalism is applied to deal with the $S$ wave $K\pi$ final state interaction (FSI) in the decay $J/\psi\to {\bar K}^{*0}(892)K^+\pi^-$, and a qualitatively good fit to the data is achieved. | result 0.83 | 0.94 | 0.28 | asserted 0.97 |
| s5 | The role of $\kappa$ in the decay is discussed. | interpretation 0.71 | 0.71 | 0.09 | unclear 0.86 |
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The paper
Original abstract
$K\pi$ $S$ wave scattering is studied using a chiral unitary approach (ChUT) taking into account coupled channels. With the amplitudes derived from the lowest order chiral Lagrangian as the kernel of a set of coupled channel Bathe-Salpeter equations, the $I=1/2$ $S$ wave $K\pi$ scattering phase shifts below 1.2 GeV can be fitted by one parameter, a subtraction constant, and a scalar resonance corresponding to the controversial $\kappa$ ($K^*_0(800)$) can be generated dynamically. A good description of the $I=3/2$ $S$ wave $K\pi$ scattering phase shifts below 1.2 GeV can also be obtained. An artificial singularity in the conventional cut-off method of the 2-meson loop integral of the ChUT is found. The formalism is applied to deal with the $S$ wave $K\pi$ final state interaction (FSI) in the decay $J/\psi\to {\bar K}^{*0}(892)K^+\pi^-$, and a qualitatively good fit to the data is achieved. The role of $\kappa$ in the decay is discussed.
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How the literature uses it
11 arXiv papers cite this in 13 sentences
Papers citing it · 5 sentences without a confident label
Uses its method or tool 6 papers
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For the $I=0$ sector, there are five coupled channels: $π^+ π^-(1)$, $π^0 π^0(2)$, $K^+ K^-(3)$, $K^0 K̅^0(4)$, $ηη(5)$, and the elements of the $5 ×5$ symmetric $V$ matrix can be written as [ref] , [equation] For the $I=1/2$ sector, there are three channels: $K^- π^+(1)$, $K̅^0 π^0(2)$, $K̅^0 η(3)$, and then, the elements of the matrix $V$ are given by [ref] , [equation] Besides, for the $I=1$ sector, three channels are coupled, $K^+ K^-(3)$, $K^0 K̅^0$, $π^0 η(3)$, and the elements of the $V$ can be obtained as follows [ref] , [equation] where $f$ is the pion decay constant which is taken as 0.093 GeV [ref] , and $m_p$ is the mass of the corresponding pseudoscalar meson.
Role of $a_0(980)$ in the decays $D^{0} \rightarrow K^{+} K^{-} \eta$ and $\pi^{+} \pi^{-} \eta$ · Formalism · 0.90
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Here, we calculate the integral using the three-momentum cut-off method, and the analytic expression of the loop function $G_i$ could be expressed as [ref] , [equation] where $σ$, $Δ$, $λ_1$, and $λ_2$ are given as follows, [equation] Here $q_max$ is a three-momentum cut-off parameter.
Theoretical study of $N(1535)$ and $\Sigma^*(1/2^-)$ in the Cabibbo-favored process $\Lambda_c^+ \to p \bar{K}^0\eta$ · $S$-wave meson-baryon interactions and $N(1535)$ · 0.93
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In the present work, in order to better understand the behaviours between different bound systems, we explore the three-momentum cutoff method to the loop functions [ref] , where the analytical expression for the loop function $G_ll(s)$ of the $l$-th channel is given by [ref] , [equation] with the definitions [equation] and the cutoff parameter $q_max$ as free parameter, see the discussions later.
Study of the molecular Properties of the $P_c$ and $P_{cs}$ States · Theoretical Framework · 0.95
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