标题： 标量有效场理论在单环层次中的正性界限 显示英文标题

标题： Positivity Bounds in Scalar Effective Field Theories at One-loop Level

摘要： 有效场论中的参数如果要求一个符合量子场论基本原理的紫外完备性，可能会受到某些正定性限制。 这些限制在树图级别相对直接，但当环图效应重要时会变得更为模糊。 以标量理论为例，我们仔细考察了一个情况，在这种情况下，前向弹性振幅的主要贡献出现在一环图级别，并指出了正定性限制对理论参数空间含义中的一些细微之处。 特别是，由一环图产生的维度-8算符系数（如果在树图级别产生的话应为正值），以及它们的$\beta$-函数通常不受正定性限制，因为它们可能对应于光学定理下的交叉截面干涉项，这些项可能具有任意符号。 只有在考虑同一环图阶次的所有贡献时，包括来自维度-4和维度-6算符系数的贡献，才能得出严格的正定性限制，这些贡献在一环图级别具有重要影响。 我们的结果可能对正定性限制实验测试的稳健性有重要意义。 显示英文摘要

摘要： Parameters in an effective field theory can be subject to certain positivity bounds if one requires a UV completion that obeys the fundamental principles of quantum field theory. These bounds are relatively straightforward at the tree level, but would become more obscure when loop effects are important. Using scalar theories as examples, we carefully exam the positivity bounds in a case where the leading contribution to a forward elastic amplitude arises at the one-loop level, and point out certain subtleties in terms of the implications of positivity bounds on the theory parameter space. In particular, the one-loop generated dimension-8 operator coefficients (that would be positive if generated at the tree level), as well as their $\beta$-functions are generally not subject to positivity bounds as they might correspond to interference terms of the cross sections under the optical theorem, which could have either sign. A strict positivity bound can only be implied when all contributions at the same loop order are considered, including the ones from dim-4 and dim-6 operator coefficients, which have important effects at the one-loop level. Our results may have important implications on the robustness of experimental tests of positivity bounds.