A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations
Robert M. Schabinger
备注：
20 pages; My apologies to Krzysztof Kajda for misspelling his name in v1; in v3: the labeling of the variables in (4.5) and eqs. (4.20) and (4.21) was adjusted to match the notation used in the rest of Section 4. I thank York Schroeder for pointing out the notational inconsistency
Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower argued that the reduction to master integrals is complicated by the presence of integrals with doubled propagator denominators in the integration by parts relations and they introduced a novel reduction procedure which eliminates all such integrals from the start. Their approach has the advantage that it automatically produces integral bases which mesh well with generalized unitarity. The heart of their procedure is an algorithm which utilizes the weighty machinery of computational commutative algebra to produce complete sets of unitarity-compatible integration by parts relations. In this paper, we propose a conceptually simpler algorithm for the generation of complete sets of unitarity-compatible integration by parts relations based on recent results in the mathematical literature. A striking feature of our algorithm is that it can be described entirely in terms of straightforward linear algebra.
Two-body and Three-body Contacts for Identical Bosons near Unitarity
在最近的超冷囚禁Rb-85原子的实验中，Makotyn等人研究了量子简并玻色气体在幺正极限下的散射长度无限大。我们发现，所观察到的动量分布是兼容的一个普遍的关系，表示高动量尾巴的2体和3体接触。我们确定了数密度n约为20 n ^{4/3}和2 n ^{5/3}的幺正玻色气体的两体和三体接触密度。我们还表明，所观察到的原子损失率与3原子非弹性碰撞的损失率是一致的，它的贡献与三体接触成正比，但与2原子非弹性碰撞的损失率是不一致的，它的贡献与2体接触成正比.指出在么正性附近和么正性处利用维里定理可以独立地测量接触。
Renormalization of effective field theories via on-shell methods: the case of axion-like particles
Dipartimento di Fisica e Astronomia, Università di Padova（帕多瓦大学物理与天文学系）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay（巴黎萨克雷大学理论物理研究所（CEA、CNRS））；Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern（伯尔尼大学理论物理研究所爱因斯坦基础物理中心）
Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector
我们表明，对偶共形对称性，主要是在平面$\mathcal N = 4$超杨-米尔斯理论研究，有有趣的后果费曼积分在非超对称理论，如QCD，包括非平面部门。一个简单的观察是，对偶共形变换保持了任何平面积分的么正性切割条件，包括那些没有对偶共形对称的积分。这样的变换生成的微分方程没有提高传播幂，通常系统的右手边与维度正则化参数$ε$成比例。对偶共形变换的一个非平凡子群，使所有的外部动量不变，生成积分的部分关系，而不提高传播功率，再现，在一个更简单的形式，以前的结果从计算代数几何的几个例子，多达两个循环和五条腿。通过将两圈三点和四点非平面图展开为平面图，我们发现了对偶共形对称的一个非平面模拟。对于平面情况，这用于生成分部积分关系和微分方程。这意味着对称性与$\mathcal N = 4$ super-Yang-Mills理论的双圈四点振幅的非平面扇区的解析性质有关。
