We examine the space of allowed S-matrices on the Adler zeros' plane using the recently resurrected (numerical) S-matrix bootstrap program for pion scattering. Two physical quantities, an averaged total scattering cross-section, and an averaged entanglement power for the boundary S-matrices, are studied. Emerging linearity in the leading Regge trajectory is correlated with a reduction in both these quantities. We identify two potentially viable regions where the S-matrices give decent agreement with low energy S- and P-wave scattering lengths and have leading Regge trajectory compatible with experiments. We also study the line of minimum averaged total cross section in the Adler zeros' plane. The Lovelace-Shapiro model, which was a precursor to modern string theory, is given by a straight line in the Adler zeros' plane and, quite remarkably, we find that this line intersects the space of allowed S-matrices near both these regions.

中文翻译：

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S-Matrix 引导程序的选择规则

我们使用最近复活的（数值）S 矩阵引导程序来检查阿德勒零点平面上允许的 S 矩阵的空间，用于 pion 散射。研究了两个物理量、平均总散射截面和边界 S 矩阵的平均纠缠功率。领先的 Regge 轨迹中出现的线性与这两个数量的减少相关。我们确定了两个可能可行的区域，其中 S 矩阵与低能量 S 和 P 波散射长度相当一致，并且具有与实验兼容的领先 Regge 轨迹。我们还研究了阿德勒零点平面中最小平均总横截面的线。Lovelace-Shapiro 模型是现代弦理论的先驱，它由阿德勒零点平面中的一条直线给出，并且，