切割 Coon 振幅
Cutting the Coon Amplitude
AI总结：
本文研究了 $q$ 形变的 Coon 振幅在分支割上的正定性，发现在指数级接近聚点的区域存在正定性破坏，并探讨了其解释及剔除负值的方法。
摘要：
Coon 振幅是 Veneziano 振幅的 $q$ 形变推广，呈现出收敛于一个聚点的半无限极点序列，并从该聚点延伸出分支割。近期多篇论文提供了令人信服的证据，表明该振幅的残差满足幺正性施加的正定性要求。本文研究正定性是否在分支割上也得到满足。结果发现，在以 $q$ 设定的尺度下，于分支割上指数级接近聚点的区域出现了正定性破坏。论文结尾部分讨论了该事实的可能解释，以及从分波系数中剔除负值的方法。附录展示了将 $q$-gamma 和 $q$-polygamma 函数与 Weierstrass 椭圆及准周期函数联系起来的工具性恒等式的推导。
英文摘要：
The Coon amplitude is a $q$-deformed generalization of the Veneziano amplitude exhibiting a semi-infinite sequence of poles that converge on an accumulation point, from which a branch cut emerges. A number of recent papers have provided compelling evidence that the residues of this amplitude satisfy the positivity requirements imposed by unitarity. This paper investigates whether positivity is also satisfied along the branch cut. It is found that positivity violations occur in a region of the branch cut exponentially close to the accumulation point according to a scale set by $q$. The closing section of the paper discusses possible interpretations of this fact and strategies for excising negativity from the partial wave coefficients. An appendix presents derivations of instrumental identities relating the $q$-gamma and $q$-polygamma functions to the Weierstrass elliptic and quasiperiodic functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
