Numerical evaluation of the general massive 2-loop 4-denominator self-mass master integral from differential equations Original Research Article

The differential equation in the external invariant p2 satisfied by the master integral of the general massive 2-loop 4-denominator self-mass diagram is exploited and the expansion of the master integral at p2=0 is obtained analytically. The system composed by this differential equation with those of the master integrals related to the general massive 2-loop sunrise diagram is numerically solved by the Runge–Kutta method in the complex p2 plane. A numerical method to obtain results for values of p2 at and close to thresholds and pseudo-thresholds is discussed in details.