MB NumericalMethods

We discuss the main issues which lead to numerical instabilities of multiloop MB integrals in the Minkowskian region. We then present practical procedures for overcoming the obstacles such as the transformation of variables to finite intervals, the shifting and deformation of integration contours, and the construction of MB representations that take kinematic thresholds into account. Steepest descent and Lefschetz thimbles are applied to find optimal integration contours. The numerical evaluation of phase space MB integrals is also briefly discussed.