{"arxiv_id":"hep-th/9412063","incoming":{"papers":37,"sentences":43,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":25,"sentences":25,"quotes":[{"arxiv_id":"2408.14304","title":"The asymptotic Hopf Algebra of Feynman Integrals","url":"/paper/2408.14304","section":"Expansion by subgraph","sentence":"We will now outline the procedure for expansion by subgraph as developed by Smirnov [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"2005.12389","title":"Simplified leptoquark models for precision $l_i \\rightarrow l_f \\gamma$ experiments: two-loop structure of $O(\\alpha_S Y^2)$ corrections","url":"/paper/2005.12389","section":"Methodology","sentence":"The rules for a correct asymptotic expansion around a large mass limit have been elaborated in Refs. [ref] in the form of an expansion in sub-diagrams defined as F_G(q,M,m,ϵ) ∑_σ F_G/σ(q,M,m,ϵ) ·T_q^σ,m^σ F_σ(q^σ,M,m^σ,ϵ).","intent_p":0.97,"contests_p":null},{"arxiv_id":"1710.08311","title":"Leptonic CP violation in the charged sector and effective field theory approach","url":"/paper/1710.08311","section":"Anomalous dimensions and matching between LEFT and SMEFT","sentence":"The latter is obtained by straightforward application of the strategy of regions [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"2604.14741","title":"The OPE Approach to Renormalization: Operator Mixing","url":"/paper/2604.14741","section":"OPE in the situation of operator mixing","sentence":"To reduce the number of scales, we assume that in the Euclidean sense, $|p|≫|k_i|$, where $|p|=√(p^2_0+𝐩^2)$ [ref] , so that the hard and soft dynamics factorize via the following OPE: [equation] in which $O^R_α$ is another set of (preferably simpler) mixed operators.","intent_p":0.93,"contests_p":null},{"arxiv_id":"1907.06957","title":"The light-fermion contribution to the exact Higgs-gluon form factor in QCD","url":"/paper/1907.06957","section":"Calculation of master integrals","sentence":"For this purpose, we expand the master integrals by subgraphs [ref] as it is implemented in the computer program [ref] .","intent_p":1.0,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":3,"sentences":3,"quotes":[{"arxiv_id":"2307.00387","title":"Simplifying the large mass expansion","url":"/paper/2307.00387","section":"Introduction","sentence":"The behaviour of a given Feynman integral in the large mass limit can be described [ref] (see also [ref] and Chapter 9 of [ref] ) by a simple formula with a summation over subgraphs which include all the large masses and whose connectivity components are one-particle-irreducible with respect to the lines with small masses.","intent_p":0.89,"contests_p":null},{"arxiv_id":"1801.10523","title":"Determine Arbitrary Feynman Integrals by Vacuum Integrals","url":"/paper/1801.10523","section":"Introduction","sentence":"Although asymptotic expansion of Feynman integrals itself is not new [ref] , the novelty here is that our expansion is with respect to an auxiliary parameter introduced by hand and thus can be applied to any problem.","intent_p":0.81,"contests_p":null},{"arxiv_id":"1705.05136","title":"Three-loop massive tadpoles and polylogarithms through weight six","url":"/paper/1705.05136","section":"Introduction","sentence":"More than two decades ago, the integration-by-parts relations [ref] and asymptotic expansions [ref] became common in the Feynman diagram calculus.","intent_p":0.99,"contests_p":null}]}],"unlabelled_sentences":15},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/hep-th/9412063"}}