Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d

28 Dec 2018 Phan Khiem Hong Univ. of Science, Vietnam National University, Ho Chi Minh City Riemann Tord DESY and Univ. of Silesia

The long-standing problem of representing the general massive one-loop Feynman integral as a meromorphic function of the space-time dimension $d$ has been solved for the basis of scalar one- to four-point functions with indices one. In 2003 the solution of difference equations in the space-time dimension allowed to determine the necessary classes of special functions: self-energies need ordinary logarithms and Gauss hypergeometric functions $_2F_1$, vertices need additionally Kamp\'{e} de F\'{e}riet-Appell functions $F_1$, and box integrals also Lauricella-Saran functions $F_S$... (read more)

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