六个粒子，无限乐观：面向六点振幅的正性界
Six Particles, Infinite Optimism: Towards Positivity Bounds for Six-Point Amplitudes
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中文总结 AI 辅助
本文通过计算N-标量理论树级振幅，隔离不受符号不定耦合影响的扇区，发现六、五、四点Wilson系数构成正半定矩阵，为高点多体振幅正性界提供指导。
中文摘要 AI 辅助
将成熟的$S$-矩阵正性和自举界从$2 \ o 2$散射过程系统推广到更高点振幅，至今仍未实现。为解决这一问题，我们考虑单标量有效场论（EFT）的一大类树级紫外（UV）完备化。具体而言，我们在$D=4$维中考虑最一般的可重整化$N$-标量理论。通过显式计算四点、五点及六点散射的树级振幅，并在低能下展开，我们能够搜索展开系数之间的正性关系。我们发现，一般而言，由于来自特定一类对符号不定三次耦合呈线性的费曼图的污染，正性界不可用。然而，通过隔离全交叉对称低能振幅中不受这些符号不定三次耦合影响的一个扇区，我们发现选定的六点、五点及四点Wilson系数可组织成正半定矩阵。尽管违反这些正性陈述仅意味着给定EFT与我们的UV完备化类别不一致，但该结果有助于指导更一般的针对高点多体相互作用的正性界可能呈现及不可能呈现的形式。
英文摘要
The systematic generalisation of the well-established $S$-matrix positivity and bootstrap bounds from $2 \to 2$ scattering processes to higher-point amplitudes has, to date, remained elusive. To address this, we consider a large class of tree-level UV-completions of a single-scalar EFT. Specifically, we consider the most general renormalisable $N$-scalar theory in $D=4$. By explicitly computing tree-level amplitudes for four-, five- and six-point scattering and expanding at low energies, we can search for positivity relations among the expansion coefficients. We find that quite generally positivity bounds are unavailable due to contamination from a specific class of Feynman diagrams that are linear in sign-indefinite cubic couplings. However, by isolating a sector of the full crossing-symmetric low-energy amplitude that is unaffected by these sign-indefinite cubic couplings, we find that selected six-, five- and four-point Wilson coefficients organise into positive semi-definite matrices. While a violation of these positivity statements only implies that a given EFT is inconsistent with our class of UV completions, the result helps to guide towards what more general positivity bounds for higher-point interactions could, and could not, look like.
发表机构
- Abdus Salam Centre for Theoretical Physics, Imperial College（阿卜杜斯·萨拉姆理论物理中心，帝国理工学院）
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