Regular Article - Theoretical Physics
GKZ-system of the 2-loop self energy with 4 propagators
Department of Physics, Hebei University, 071002, Baoding, China
2 Hebei Key Laboratory of High-precision Computation and Application of Quantum Field Theory, 071002, Baoding, China
3 Research Center for Computational Physics of Hebei Province, 071002, Baoding, China
4 Department of Physics, Guangxi University, 530004, Nanning, China
5 Department of Physics, Chongqing University, 401331, Chongqing, China
Accepted: 24 March 2023
Published online: 21 April 2023
Applying the system of linear partial differential equations derived from the Mellin–Barnes representation and the Miller transformation, we present the GKZ-system of the Feynman integral of the 2-loop self energy diagram with 4 propagators. The codimension of the derived GKZ-system equals the number of independent dimensionless ratios among the external momentum squared and virtual mass squared. In total 536 hypergeometric functions are obtained in the neighborhoods of the origin and infinity, in which 30 linearly independent hypergeometric functions whose convergent regions have nonempty intersection constitute a fundamental solution system in a proper subset of the whole parameter space.
© The Author(s) 2023
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