An Efficient On-shell Framework for EFT Matching

Abstract

Standard techniques for one-loop EFT matching often have gauge and basis redundancies, while strictly 4-dimensional on-shell methods fail to capture rational terms. To resolve this, we develop an efficient, channel-based on-shell framework for one-loop matching. Our method reconstructs the local hard-region amplitude by sewing tree amplitudes across double cuts, employing a mass-shift prescription to recover d-dimensional internal states. This d-dimensional sewing retains rational terms and integrates them seamlessly with ordinary cut-constructible contributions. The local amplitude is expanded in the hard region and directly projected onto non-redundant, on-shell EFT amplitude bases. With tadpoles and kinematically independent bubbles systematically fixed by an explicit subtraction convention, our framework successfully merges the rigorous extraction of rational Wilson coefficients with the gauge-invariant elegance of modern amplitude methods.