Speaker
Description
Precise predictions for cross-sections at present and future particle colliders require reliable methods for evaluating multi-loop Feynman integrals, which are often beyond the reach of direct analytic techniques. In this talk, I will present new numerical approaches that exploit general structural properties of quantum field theory—such as positivity and analyticity—to compute Feynman integrals efficiently from limited input data. A key new insight is that, in the Euclidean region, scalar Feynman integrals obey complete monotonicity, a powerful and largely unexplored constraint that, when combined with their differential equations, allows their numerical values to be tightly constrained within a systematic bootstrap framework. Moreover, in a broad range of space-time dimensions and propagator powers, Feynman integrals fall into the class of Stieltjes functions, which guarantees the convergence of Padé approximations in the complex plane. This provides a natural framework for constructing accurate rational approximations that remain valid under analytic continuation to physical scattering regions. These ideas point toward a broadly applicable paradigm for numerical multi-loop calculations relevant to collider phenomenology, while highlighting deep connections between Feynman integrals and fundamental principles of quantum field theory.