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arXiv 1404.3797hep-ph
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$D^+\to K^-π^+π^+$与$Kπ$ I=1/2和3/2通道的末态相互作用

Final state interaction in $D^+\to K^-π^+π^+$ with $Kπ$ I=1/2 and 3/2 channels

K. S. F. F. Guimaræs, O. Lourenço, W. de Paula, T. Frederico, A. C. dos Reis

摘要:

计算了末态相互作用对$D^+$衰变的贡献,并在光阵面相对论三体模型中计算了$K^-π^+π^+$通道的末态相互作用。考虑了衰变道中K介子与两个π介子之间的再散射过程。离壳衰减振幅是四维Bethe-Salpeter方程的解,该方程以Faddeev形式分解。投影到光前的耦合的积分方程组是通过一个准潜在的方法。在共振同位旋$1/2$和非共振同位旋$3/2$通道中引入了S波$Kπ$相互作用。数值解的光前三维非均匀积分方程的衰减振幅的Faddeev分量进行微扰。循环展开收敛速度快,在实际应用中,相对于两个循环的结果,三个循环的贡献可以忽略不计。在部分子水平的输入振幅的模型参数的依赖性被利用,并在实验分析中发现的相位,拟合与适当选择的部分子振幅的同位旋分量的真实权重。数据表明,总的同位旋$5/2$占主导地位的$3/2$一个小的混合物。非对称衰变振幅的模量,它提出了一个深谷和以下增加的$Kπ$质量以上$1.5$ GeV,是相当再现。这表明量子数$0^+$归属于同位旋1/2 $K^*(1630)$共振。

英文摘要:

The final state interaction contribution to $D^+$ decays is computed for the $K^-π^+π^+$ channel within a light-front relativistic three-body model for the final state interaction. The rescattering process between the kaon and two pions in the decay channel is considered. The off-shell decay amplitude is a solution of a four-dimensional Bethe-Salpeter equation, which is decomposed in a Faddeev form. The projection onto the light-front of the coupled set of integral equations is performed via a quasi-potential approach. The S-wave $Kπ$ interaction is introduced in the resonant isospin $1/2$ and the non-resonant isospin $3/2$ channels. The numerical solution of the light-front tridimensional inhomogeneous integral equations for the Faddeev components of the decay amplitude is performed perturbatively. The loop-expansion converges fast, and the three-loop contribution can be neglected in respect to the two-loop results for the practical application. The dependence on the model parameters in respect to the input amplitude at the partonic level is exploited and the phase found in the experimental analysis, is fitted with an appropriate choice of the real weights of the isospin components of the partonic amplitude. The data suggests a small mixture of total isospin $5/2$ to the dominant $3/2$ one. The modulus of the unsymmetrized decay amplitude, which presents a deep valley and a following increase for $Kπ$ masses above $1.5$ GeV, is fairly reproduced. This suggests the assignment of the quantum numbers $0^+$ to the isospin 1/2 $K^*(1630)$ resonance.

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