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002799342 005__ 20231004095915.0
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002799342 0247_ $$2DOI$$9APS$$a10.1103/PhysRevD.106.L111301$$qpublication
002799342 037__ $$9arXiv$$aarXiv:2201.02576$$chep-ph
002799342 037__ $$9arXiv:reportnumber$$aCERN-TH-2021-230
002799342 037__ $$9arXiv:reportnumber$$aUUITP-66/21
002799342 035__ $$9arXiv$$aoai:arXiv.org:2201.02576
002799342 035__ $$9Inspire$$aoai:inspirehep.net:2005637$$d2023-10-03T09:19:33Z$$h2023-10-04T02:22:28Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002799342 035__ $$9Inspire$$a2005637
002799342 041__ $$aeng
002799342 100__ $$aDubovyk, Ievgen$$uSilesia U.$$vInstitute of Physics, University of Silesia, Katowice, Poland
002799342 245__ $$9APS$$aEvaluation of multiloop multiscale Feynman integrals for precision physics
002799342 246__ $$9arXiv$$aEvaluation of multi-loop multi-scale Feynman integrals for precision physics
002799342 269__ $$c2022-01-07
002799342 260__ $$c2022-12-01
002799342 300__ $$a7 p
002799342 520__ $$9APS$$aModern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders will require three-loop electroweak and mixed electroweak-QCD corrections to single-particle production and decay processes and two-loop electroweak corrections to pair-production processes. This article presents a new seminumerical approach to multiloop multiscale Feynman integrals calculations which will be able to fill the gap between rigid experimental demands and theory. The approach is based on differential equations with boundary terms specified at Euclidean kinematic points. These Euclidean boundary terms can be computed numerically with high accuracy using sector decomposition or other numerical methods. They are then mapped to the physical kinematic configuration by repeatedly solving the differential equation system in terms of series solutions. An automatic and general method is proposed for constructing a basis of master integrals such that the differential equations are finite. The approach also provides a prescription for the analytic continuation across physical thresholds. Our implementation is able to deliver 8 or more digits of precision, and has a built-in mechanism for checking the accuracy of the obtained results. Its efficacy is illustrated with state-of-the-art examples for three-loop self-energy and vertex integrals and two-loop box integrals.
002799342 520__ $$9arXiv$$aModern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders will require three-loop electroweak and mixed electroweak-QCD corrections to single-particle production and decay processes and two-loop electroweak corrections to pair production processes, all of which are beyond the reach of existing analytical and numerical techniques in their current form. This article presents a new semi-numerical approach based on differential equations with boundary terms specified at Euclidean kinematic points. These Euclidean boundary terms can be computed numerically with high accuracy using sector decomposition or other numerical methods. They are then mapped to the physical kinematic configuration with a series solution of the differential equation system. The method is able to deliver 8 or more digits precision, and it has a built-in mechanism for checking the accuracy of the obtained results. Its efficacy is illustrated with examples for three-loop self-energy and vertex integrals and two-loop box integrals.
002799342 540__ $$3preprint$$aCC BY 4.0$$uhttp://creativecommons.org/licenses/by/4.0/
002799342 540__ $$3publication$$aCC BY 4.0$$fSCOAP3$$uhttps://creativecommons.org/licenses/by/4.0/
002799342 542__ $$3publication$$dauthors$$g2022
002799342 595__ $$aCERN-TH
002799342 65017 $$2SzGeCERN$$aParticle Physics - Phenomenology
002799342 690C_ $$aCERN
002799342 690C_ $$aARTICLE
002799342 700__ $$aFreitas, Ayres$$uPittsburgh U.$$vPittsburgh Particle physics, Astrophysics and Cosmology Center (PITT PACC), Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
002799342 700__ $$aGluza, Janusz$$uSilesia U.$$vInstitute of Physics, University of Silesia, Katowice, Poland
002799342 700__ $$aGrzanka, Krzysztof$$uSilesia U.$$vInstitute of Physics, University of Silesia, Katowice, Poland
002799342 700__ $$aHidding, Martijn$$uUppsala U.$$vDepartment of Physics and Astronomy, Uppsala University, SE-75120 Uppsala, Sweden
002799342 700__ $$aUsovitsch, Johann$$uCERN$$vTheoretical Physics Department, CERN, 1211 Geneva, Switzerland
002799342 773__ $$cL111301$$mpublication$$n11$$pPhys. Rev. D$$v106$$y2022
002799342 8564_ $$82345754$$s12739$$uhttps://cds.cern.ch/record/2799342/files/SE3looptopsv2.png$$y00003 Three loop self-energy non-planar integral defined in (\ref{eq:taNp1}). $\text{Z}$ and $\text{t}$ stands for the massive SM Z gauge boson and the top quark, respectively.
002799342 8564_ $$82345755$$s541826$$uhttps://cds.cern.ch/record/2799342/files/2201.02576.pdf$$yFulltext
002799342 8564_ $$82345756$$s17048$$uhttps://cds.cern.ch/record/2799342/files/SE3loopv2.png$$y00001 Three loop self-energy non-planar and planar vertex diagrams which correspond to integrals in \eqref{eq:lhnp} and \eqref{eq:vtwPl}, respectively. W, Z and t stand for the W-boson, Z-boson and top quark, respectively.
002799342 8564_ $$82345757$$s16219$$uhttps://cds.cern.ch/record/2799342/files/Box_m1m2v2.png$$y00004 Two-loop box diagram with four scales: $s,t,m_1,m_2$.
002799342 8564_ $$82345758$$s61189$$uhttps://cds.cern.ch/record/2799342/files/euler_mink_boundary_1.png$$y00000 Illustration of the DE transport method. The boundary conditions for the integral $f_i$ are evaluated at one or several Euclidean points $\rm A_k$, where the integral is purely real and one can obtain robustly converging numerical results with the SD method (using the package {\tt pySecDec} in our case). The boundary value(s) are transported to the physical kinematic point, using solutions of the DE system eq.~\eqref{eq:general-de} derived with {\tt DiffExp}, yielding the final result indicated by the red dot in the figure. The numerical uncertainty of a boundary value translates to an error estimate of the final result, as illustrated by the error bars in a zoomed-in area in the dotted circle, which permits a non-trivial cross-check if several boundary values $\rm A_k$ are employed.
002799342 8564_ $$82345759$$s10664$$uhttps://cds.cern.ch/record/2799342/files/V3loop.png$$y00002 Three loop self-energy non-planar and planar vertex diagrams which correspond to integrals in \eqref{eq:lhnp} and \eqref{eq:vtwPl}, respectively. W, Z and t stand for the W-boson, Z-boson and top quark, respectively.
002799342 8564_ $$82424776$$s310352$$uhttps://cds.cern.ch/record/2799342/files/Publication.pdf$$yFulltext
002799342 960__ $$a13
002799342 980__ $$aARTICLE