Feynman integrals from positivity constraints [Virtual talk]

by Mao Zeng (Uni Edinburgh)

Thursday 11 May 2023, 13:15 → 15:15 Europe/Berlin

We explore inequality constraints as a new tool for numerically evaluating Feynman integrals. A convergent Feynman integral is non-negative if the integrand is non-negative. Re-writing these integrals as linear combinations of building blocks known as master integrals, we obtain infinitely many inequality constraints on the values of the master integrals. The constraints can be solved as a mathematical optimization problem known as semidefinite programming, producing rigorous two-sided bounds for the integrals, which converge rapidly and allow high-precision evaluations. We present examples for evaluating massive integrals with up to three loops in dimensional regularization.