EFT matching from analyticity and unitarity

We present a new on-shell method for the matching of ultraviolet models featuring massive states onto their massless effective field theory. We employ a dispersion relation in the space of complex momentum dilations to capture, in a single variable, the relevant analytic structure of scattering amplitudes at any multiplicity. Multi-variate complex analysis and crossing considerations are therefore avoided. Remarkably, no knowledge about the infrared effective field theory is required in dimensional regularisation. All matching information is extracted from the residues and discontinuities of the ultraviolet scattering amplitudes, which unitarity expresses in terms of lower-point and lower-loop results, respectively. This decomposition into simpler building blocks could deliver new insights in the structure of the effective field theories obtained from classes of ultraviolet scenarios and facilitate computations at higher loop orders.