隐藏区域发现器：闵可夫斯基空间中费曼积分的渐近展开
Hidden Region Finder: asymptotic expansions of Feynman integrals in Minkowski space
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中文总结 AI 辅助
本文提出隐藏区域发现器算法，通过连接参数空间针状奇点与朗道条件，识别并确定闵可夫斯基空间中费曼积分渐近展开所需的隐藏区域，并在多种运动学极限下验证其有效性。
中文摘要 AI 辅助
区域方法是一种系统地推导费曼积分渐近展开的方法。对于欧几里得积分，存在一种成熟的算法，可将完整区域集合确定为由图多项式定义的牛顿多胞体的面。在许多物理相关的闵可夫斯基极限中，需要额外的区域（称为隐藏区域）才能获得正确的渐近展开。通过在参数空间中的针状奇点与相关朗道条件之间建立精确联系，我们识别出产生这些区域的一般机制，并设计了一种算法——隐藏区域发现器——来确定它们。我们表明，隐藏区域源于边参数的渐近标度（这会增强图多项式的某些单项式）与这些单项式之间的抵消（这会将其集体贡献降低到与多项式中其他项相同的阶数）之间的微妙相互作用。我们研究了无质量四点、五点和六点积分在各种宽角质壳、平面、共线、双共线和雷吉极限下的情况。在这些不同的展开中，隐藏区域以相同的一小组种子拓扑结构重复出现。在所有研究案例中，它们都可以追溯到具有多个硬散射子图的宽角配置。给定种子的不同运动学极限继承了一个共同的奇点轨迹，而每个极限则确定其自身的标度向量和抵消深度。这项探索性研究展示了所提出算法的潜力，既能揭示渐近展开中缺失的贡献，又能通过其潜在的奇点几何来组织这些贡献。
英文摘要
The Method of Regions is a systematic way to derive asymptotic expansions of Feynman integrals. For Euclidean integrals there is a well-established algorithm to determine the complete set of regions as facets of a Newton polytope defined by the graph polynomials. In many physically relevant Minkowski limits, additional regions known as hidden regions are needed to obtain the correct asymptotic expansion. By making a precise connection with pinch singularities in parameter space and the associated Landau conditions, we identify the general mechanism giving rise to these regions and devise an algorithm, the Hidden Region Finder, to determine them. We show that hidden regions arise through a delicate interplay between asymptotic scaling of the edge parameters, which enhances certain monomials of the graph polynomial, and cancellations amongst these monomials, which reduce their collective contribution to the same order as other terms in the polynomial. We explore massless four-, five- and six-point integrals in a variety of wide-angle mass-shell, planar, collinear, double-collinear and Regge limits. Across these different expansions, hidden regions recur in the same small set of seed topologies. In all cases studied, they can be traced to wide-angle configurations with multiple hard-scattering subdiagrams. Distinct kinematic limits of a given seed inherit a common singular locus, while each limit fixes its own scaling vector and cancellation depth. This exploratory study showcases the potential of the proposed algorithm both to uncover missing contributions to asymptotic expansions and to organise them through their underlying singular geometry.
发表机构
- Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh（爱丁堡大学物理与天文学学院希格斯理论物理中心）
- CERN, Theoretical Physics Department（欧洲核子研究中心理论物理部）
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