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

The differential equation in the external invariant p(2) 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 p(2) = 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 p(2) plane. A numerical method to obtain results for values of p(2) at and close to thresholds and pseudo-thresholds is discussed in details. (C) 2004 Elsevier B.V. All rights reserved.