We explore inequality constraints as a new tool for evaluating generic Feynman integrals in the Euclidean region. A convergent Feynman integral is non-negative if the integrand is non-negative. Reducing these integrals to linear combinations of master integrals, we obtain infinitely many linear inequality constraints on the values of the master integrals. The constraints can be solved as a semidefinite programming (SDP) problem in mathematical optimization, producing rigorous two-sided bounds for the integrals, which converge rapidly and allow high-precision evaluations. We show examples for integrals up to three loops including treatment of dimensional regularization.
Mao Zeng did his undergraduate and master study at Cambridge University, UK, and did PhD study at Stony Brook University, USA, under the supervision of George Sterman. He has held research positions at UCLA, ETH Zurich, and Oxford University, before joining Edinburgh University for a lecturer position. He has worked on perturbative QCD, scattering amplitudes, and gravitational waves.
Prof. Xiaohui Liu