Samuel Abreu, Ruth Britto, C. Duhr, E. Gardi, J. Matthew
Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection theory. We propose a new application of intersection theory to construct a coaction on generalized hypergeometric functions. When applied to dimensionally regularized Feynman integrals, this coaction reproduces the coaction on multiple polylogarithms order by order in the parameter of dimensional regularization.
{"title":"Generalized hypergeometric functions and intersection theory for Feynman integrals","authors":"Samuel Abreu, Ruth Britto, C. Duhr, E. Gardi, J. Matthew","doi":"10.22323/1.375.0067","DOIUrl":"https://doi.org/10.22323/1.375.0067","url":null,"abstract":"Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection theory. We propose a new application of intersection theory to construct a coaction on generalized hypergeometric functions. When applied to dimensionally regularized Feynman integrals, this coaction reproduces the coaction on multiple polylogarithms order by order in the parameter of dimensional regularization.","PeriodicalId":440413,"journal":{"name":"Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)","volume":"617 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126904132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
FiniteFlow is a public framework for defining and executing numerical algorithms over finite fields and reconstructing multivariate rational functions. The framework allows to build complex algorithms by combining basic building blocks into graphical representations of the calculation, known as dataflow graphs. It offers an easy-to-use Mathematica interface for implementing efficient custom algorithms without any low-level coding. We report on some new features of FiniteFlow which have been published after its initial release, give some simple example of usage for common tasks and review recent cutting-edge applications to two-loop five-point scattering and the four-loop cusp anomalous dimension.
{"title":"Analytic multi-loop results using finite fields and dataflow graphs with FiniteFlow","authors":"T. Peraro","doi":"10.22323/1.375.0077","DOIUrl":"https://doi.org/10.22323/1.375.0077","url":null,"abstract":"FiniteFlow is a public framework for defining and executing numerical algorithms over finite fields and reconstructing multivariate rational functions. The framework allows to build complex algorithms by combining basic building blocks into graphical representations of the calculation, known as dataflow graphs. It offers an easy-to-use Mathematica interface for implementing efficient custom algorithms without any low-level coding. We report on some new features of FiniteFlow which have been published after its initial release, give some simple example of usage for common tasks and review recent cutting-edge applications to two-loop five-point scattering and the four-loop cusp anomalous dimension.","PeriodicalId":440413,"journal":{"name":"Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125278001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The proper renormalization of mixing angles in quantum field theories is a long-standing problem. It is relevant for the renormalization of the quark mixing matrix in the Standard Model and for various mixing scenarios in theories beyond. In this contribution we specifically consider theories with extended scalar sectors. We describe renormalization schemes for mixing angles based on combinations of observables or symmetry requirements such as rigid or background-field gauge invariance and compare their properties to previous approaches such as $bar{MS}$ schemes. We formulate specific renormalization conditions for the mixing angles in the Two-Higgs-Doublet Model and the Higgs-Singlet Extension of the Standard Model and calculate electroweak corrections to Higgs-boson decays via W- or Z-boson pairs within these models for a selection of (new and old) renormalization schemes.
{"title":"Renormalization schemes for mixing angles in extended Higgs sectors","authors":"A. Denner, S. Dittmaier, J. Lang","doi":"10.22323/1.375.0076","DOIUrl":"https://doi.org/10.22323/1.375.0076","url":null,"abstract":"The proper renormalization of mixing angles in quantum field theories is a long-standing problem. It is relevant for the renormalization of the quark mixing matrix in the Standard Model and for various mixing scenarios in theories beyond. In this contribution we specifically consider theories with extended scalar sectors. We describe renormalization schemes for mixing angles based on combinations of observables or symmetry requirements such as rigid or background-field gauge invariance and compare their properties to previous approaches such as $bar{MS}$ schemes. We formulate specific renormalization conditions for the mixing angles in the Two-Higgs-Doublet Model and the Higgs-Singlet Extension of the Standard Model and calculate electroweak corrections to Higgs-boson decays via W- or Z-boson pairs within these models for a selection of (new and old) renormalization schemes.","PeriodicalId":440413,"journal":{"name":"Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)","volume":"183 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121004198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I discuss the latest developments of FDR in the context of quantum field theory calculations relevant for high-energy particle physics phenomenology. In particular, I focus on NNLO computations and on the use of FDR in connection with effective field theories.
{"title":"QFT with FDR","authors":"R. Pittau","doi":"10.22323/1.375.0075","DOIUrl":"https://doi.org/10.22323/1.375.0075","url":null,"abstract":"I discuss the latest developments of FDR in the context of quantum field theory calculations relevant for high-energy particle physics phenomenology. In particular, I focus on NNLO computations and on the use of FDR in connection with effective field theories.","PeriodicalId":440413,"journal":{"name":"Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122816694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of the loop graph. In addition, the uncut propagators gain a modified $i delta$-prescription, named dual-propagators. In this new framework one can go beyond graphs and calculate the integrand of loop amplitudes as a weighted sum of tree graphs, which form a tree-like object. These objects can be computed efficiently via recurrence relations.
{"title":"A new formulation of the loop-tree duality at higher loops","authors":"R. Runkel, Z. SzHor, J. Vesga, S. Weinzierl","doi":"10.22323/1.375.0073","DOIUrl":"https://doi.org/10.22323/1.375.0073","url":null,"abstract":"We present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of the loop graph. In addition, the uncut propagators gain a modified $i delta$-prescription, named dual-propagators. In this new framework one can go beyond graphs and calculate the integrand of loop amplitudes as a weighted sum of tree graphs, which form a tree-like object. These objects can be computed efficiently via recurrence relations.","PeriodicalId":440413,"journal":{"name":"Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115645701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We discuss the relation between the infrared singularities of on-shell partonic form factors and parton distribution functions (PDFs) near the elastic limit, through their factorisation in terms of Wilson-line correlators. Ultimately we identify the difference between the anomalous dimensions controlling single poles of these two quantities to all loops in terms of the closed parallelogram Wilson loop. To arrive at this result we first use the common hard-collinear behaviour of the two to derive a relation between their respective soft singularities, and then show that the latter is manifested in terms of differing Wilson-line geometries. We perform explicit diagrammatic calculations in configuration space through two loops to verify the relation. More generally, the emerging picture allows us to classify collinear singularities in eikonal quantities depending on whether they are associated with finite (closed) Wilson-line segments or infinite (open) ones.
{"title":"Wilson-line geometries and the relation between IR singularities of form factors and the large-x limit of DGLAP splitting functions","authors":"Calum Milloy, G. Falcioni, E. Gardi","doi":"10.22323/1.375.0055","DOIUrl":"https://doi.org/10.22323/1.375.0055","url":null,"abstract":"We discuss the relation between the infrared singularities of on-shell partonic form factors and parton distribution functions (PDFs) near the elastic limit, through their factorisation in terms of Wilson-line correlators. Ultimately we identify the difference between the anomalous dimensions controlling single poles of these two quantities to all loops in terms of the closed parallelogram Wilson loop. To arrive at this result we first use the common hard-collinear behaviour of the two to derive a relation between their respective soft singularities, and then show that the latter is manifested in terms of differing Wilson-line geometries. We perform explicit diagrammatic calculations in configuration space through two loops to verify the relation. More generally, the emerging picture allows us to classify collinear singularities in eikonal quantities depending on whether they are associated with finite (closed) Wilson-line segments or infinite (open) ones.","PeriodicalId":440413,"journal":{"name":"Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)","volume":"51 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113972423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Behring, J. Blumlein, A. D. Freitas, A. Goedicke, S. Klein, Andreas van Manteuffel, Carsten Schneider, K. Schonwald
We present results on the calculation of the polarized 2- and 3-loop anomalous dimensions in a massive computation of the associated operator matrix element. We also discuss the treatment of $gamma_5$ and derive results in the M-scheme.10
{"title":"The Polarized Three-Loop Anomalous Dimensionsfrom a Massive Calculation","authors":"A. Behring, J. Blumlein, A. D. Freitas, A. Goedicke, S. Klein, Andreas van Manteuffel, Carsten Schneider, K. Schonwald","doi":"10.22323/1.375.0047","DOIUrl":"https://doi.org/10.22323/1.375.0047","url":null,"abstract":"We present results on the calculation of the polarized 2- and 3-loop anomalous dimensions in a massive computation of the associated operator matrix element. We also discuss the treatment of $gamma_5$ and derive results in the M-scheme.10","PeriodicalId":440413,"journal":{"name":"Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132677957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
At $e^+ , e^-$ colliders the QED--initial state radiation forms a large part of the radiative corrections. Their precise and fast evaluation is an essential asset for the experiments at LEP, the ILC and the FCC-ee, operating at high luminosity. A long standing problem in the analytic calculation of the $O(alpha^2)$ initial state corrections concerns a discrepancy which has been observed between the result of Berends et al. (1988) cite{Berends:1987ab} in the limit $m_e^2 ll s$ and the result by Bl{"u}mlein et al. (2011) cite{Blumlein:2011mi} using massive operator matrix elements deriving this limit directly. In order to resolve this important issue we recalculated this process by integrating directly over the phase space without any approximation. For parts of the corrections we find exact solutions of the cross section in terms of iterated integrals over square root valued letters representing incomplete elliptic integrals and iterations over them. The expansion in the limit $m_e^2 ll s$ reveals errors in the constant $O(alpha^2)$ term of the former calculation and yields agreement with the calculation based on massive operator matrix elements, which has impact on the experimental analysis programs. This finding also explicitly proofs the factorization of massive initial state particles in the high energy limit including the terms of $O(alpha^2)$ for this process.
在$e^+ , e^-$对撞机上，QED初始态辐射构成了辐射修正的很大一部分。它们的精确和快速评估是LEP, ILC和FCC-ee实验在高亮度下工作的重要资产。在$O(alpha^2)$初始状态修正的解析计算中，一个长期存在的问题涉及到Berends et al. (1988) cite{Berends:1987ab}在极限$m_e^2 ll s$中的结果与bl mlein et al. (2011) {}cite{Blumlein:2011mi}使用大量算子矩阵元素直接推导该极限的结果之间的差异。为了解决这个重要的问题，我们重新计算了这个过程，直接在相空间上积分，没有任何近似。对于部分修正，我们找到了横截面的精确解，用代表不完全椭圆积分的平方根值字母的迭代积分和迭代积分来表示。极限$m_e^2 ll s$展开式揭示了以往计算中常数$O(alpha^2)$项的误差，与基于大量算子矩阵元素的计算结果一致，对实验分析程序产生了影响。这一发现也明确地证明了在高能极限下大质量初始态粒子的分解，包括该过程的$O(alpha^2)$项。
{"title":"Revisiting the $O(alpha^2)$ Initial State QED Corrections to e+ e- Annihilation into a Neutral Boson","authors":"J. Blumlein, A. D. Freitas, C. Raab, K. Schonwald","doi":"10.22323/1.375.0046","DOIUrl":"https://doi.org/10.22323/1.375.0046","url":null,"abstract":"At $e^+ , e^-$ colliders the QED--initial state radiation forms a large part of the radiative corrections. Their precise and fast evaluation is an essential asset for the experiments at LEP, the ILC and the FCC-ee, operating at high luminosity. A long standing problem in the analytic calculation of the $O(alpha^2)$ initial state corrections concerns a discrepancy which has been observed between the result of Berends et al. (1988) cite{Berends:1987ab} in the limit $m_e^2 ll s$ and the result by Bl{\"u}mlein et al. (2011) cite{Blumlein:2011mi} using massive operator matrix elements deriving this limit directly. In order to resolve this important issue we recalculated this process by integrating directly over the phase space without any approximation. For parts of the corrections we find exact solutions of the cross section in terms of iterated integrals over square root valued letters representing incomplete elliptic integrals and iterations over them. The expansion in the limit $m_e^2 ll s$ reveals errors in the constant $O(alpha^2)$ term of the former calculation and yields agreement with the calculation based on massive operator matrix elements, which has impact on the experimental analysis programs. This finding also explicitly proofs the factorization of massive initial state particles in the high energy limit including the terms of $O(alpha^2)$ for this process.","PeriodicalId":440413,"journal":{"name":"Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134527012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present the computation of Higgs boson production in association with a jet at the LHC including QCD corrections up to NNLO. The calculation includes the subsequent decay of the Higgs boson into four leptons, allowing for the full reconstruction of the final-state kinematics. In anticipation of improved LHC measurements based on the full Run II dataset, we present a study for single- and double-differential cross sections within the fiducial volume as defined in prior ATLAS analyses. Higher-order corrections are found to have a sizeable impact on both normalisation and shape of differential cross sections.
{"title":"NNLO QCD Corrections for Higgs-plus-jet Production in the Four-lepton Decay Mode","authors":"Xuan Chen, T. Gehrmann, N. Glover, A. Huss","doi":"10.22323/1.375.0003","DOIUrl":"https://doi.org/10.22323/1.375.0003","url":null,"abstract":"We present the computation of Higgs boson production in association with a jet at the LHC including QCD corrections up to NNLO. The calculation includes the subsequent decay of the Higgs boson into four leptons, allowing for the full reconstruction of the final-state kinematics. In anticipation of improved LHC measurements based on the full Run II dataset, we present a study for single- and double-differential cross sections within the fiducial volume as defined in prior ATLAS analyses. Higher-order corrections are found to have a sizeable impact on both normalisation and shape of differential cross sections.","PeriodicalId":440413,"journal":{"name":"Proceedings of 14th International Symposium on Radiative Corrections — PoS(RADCOR2019)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124797950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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