标题： Cutkosky规则和1循环$κ$-变形幅度 显示英文标题

标题： Cutkosky rules and 1-loop $κ$-deformed amplitudes

摘要： 在本文中，我们证明Cutkosky切割规则在展开式中仍然逐项有效，该展开式是关于传播子的$\kappa$的幂级数的$\kappa$变形的一环修正。 我们首先提出一个一般性论证，将展开式中的每一项与包含额外传播子（质量为$M>\kappa$）的非变形振幅联系起来。 然后我们更实际地证明了同样的事情，通过使用代数和解析恒等式，将$\kappa$变形振幅展开式的系数的奇异性结构简化为非变形环振幅的奇异性结构。 我们将明确展示到$1/\kappa$的二阶，但该技术可以推广到$1/\kappa$的更高阶。 抽象方法和更直接的方法都很容易推广到不同的变形理论。 我们将计算特定模型中传播子的$\kappa$形变一环修正的全部虚部，直到在$1/\kappa$展开中的二阶，突出该方法在形变模型现象学中的有用性。 这明确证实了关于所考虑模型中不稳定粒子衰变宽度行为的先前定性论点。 显示英文摘要

摘要： In this paper we show that the Cutkosky cutting rules are still valid term by term in the expansion in powers of $\kappa$ of the $\kappa$-deformed 1-loop correction to the propagator. We first present a general argument which relates each term in the expansion to a non-deformed amplitude containing additional propagators with mass $M>\kappa$. We then show the same thing more pragmatically, by reducing the singularity structure of the coefficients in the expansion of the $\kappa$-deformed amplitude, to the singularity structure of non-deformed loop amplitudes, by using algebraic and analytic identities. We will explicitly show this up to second order in $1/\kappa$, but the technique can be generalized to higher orders in $1/\kappa$. Both the abstract and the more direct approach easily generalize to different deformed theories. We will then compute the full imaginary part of the $\kappa$-deformed 1-loop correction to the propagator in a specific model, up to second order in the expansion in $1/\kappa$, highlighting the usefulness of the approach for the phenomenology of deformed models. This explicitly confirms previous qualitative arguments concerning the behaviour of the decay width of unstable particles in the considered model.