Analytic computing methods for precision calculations in quantum field theory. (English) Zbl 1392.81192
Summary: An overview is presented on the current status of main mathematical computation methods for the multiloop corrections to single-scale observables in quantum field theory and the associated mathematical number and function spaces and algebras. At present, massless single-scale quantities can be calculated analytically in QCD to 4-loop order and single mass and double mass quantities to 3-loop order, while zero-scale quantities have been calculated to 5-loop order. The precision requirements of the planned measurements, particularly at the FCC-ee, form important challenges to theory, and will need important extensions of the presently known methods.
MSC:
| 81T18 | Feynman diagrams |
| 81V05 | Strong interaction, including quantum chromodynamics |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 46L60 | Applications of selfadjoint operator algebras to physics |
Keywords:
Feynman diagrams; master integrals; analytic calculation; differential equations; summation techniques; Mellin-Barnes integral; iterative integrals; nested sums; elliptic solutionsReferences:
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