{"title":"无平方传播量的环积分微分方程","authors":"J. Bosma, K. J. Larsen, Yang Zhang","doi":"10.22323/1.303.0064","DOIUrl":null,"url":null,"abstract":"We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two- and three-loop diagrams. For these diagrams, the differential equations can thus be computed using \"unitarity-compatible\" integration-by-parts reductions, which simplify the reduction problem by avoiding integrals with higher-power propagators.","PeriodicalId":140132,"journal":{"name":"Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2018)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Differential equations for loop integrals without squared propagators\",\"authors\":\"J. Bosma, K. J. Larsen, Yang Zhang\",\"doi\":\"10.22323/1.303.0064\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two- and three-loop diagrams. For these diagrams, the differential equations can thus be computed using \\\"unitarity-compatible\\\" integration-by-parts reductions, which simplify the reduction problem by avoiding integrals with higher-power propagators.\",\"PeriodicalId\":140132,\"journal\":{\"name\":\"Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2018)\",\"volume\":\"12 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2018)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22323/1.303.0064\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2018)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22323/1.303.0064","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Differential equations for loop integrals without squared propagators
We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two- and three-loop diagrams. For these diagrams, the differential equations can thus be computed using "unitarity-compatible" integration-by-parts reductions, which simplify the reduction problem by avoiding integrals with higher-power propagators.