Two-loop matching of renormalizable operators: general considerations and applications

• Main Authors: Henning Bahl, Ivan Sobolev
• Format: Article
• Language: English
• Published: SpringerOpen 2021-03-01
• Series: Journal of High Energy Physics
• Subjects: Beyond Standard Model; Effective Field Theories
• Online Access: https://doi.org/10.1007/JHEP03(2021)286

Abstract Low-energy effective field theories (EFT) encode information about the physics at high energies — i.e., the high-energy theory (HET). To extract this information the EFT and the HET have to be matched to each other. At the one-loop level, general results for the matching of renormalizable operators have already been obtained in the literature. In the present paper, we take a step towards a better understanding of renormalizable operator matching at the two-loop level: focusing on the diagrammatic method, we discuss in detail the various contributions to two-loop matching conditions and compare different approaches to derive them. Moreover, we discuss which observables are best suited for the derivation of matching conditions. As a concrete application, we calculate the O α t α s $$ \mathcal{O}\left({\alpha}_t{\alpha}_s\right) $$ and O α t 2 $$ \mathcal{O}\left({\alpha}_t^2\right) $$ matching conditions of the scalar four-point couplings between the Standard Model (SM) and the Two-Higgs-Doublet Model (THDM) as well as the THDM and the Minimal Supersymmetric Standard Model (MSSM). We use the derived formulas to improve the prediction of the SM-like Higgs mass in the MSSM using the THDM as EFT.