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

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 $\mathcal{O}\left({\alpha }_t{\alpha }_s\right)$ and $\mathcal{O}\left({\alpha }_t^2\right)$ 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.

42 pages, 4 figures, 4 ancillary files; matches version published in JHEP

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• Fighting off field dependence in MSSM Higgs-mass corrections of order ${\alpha }_t{\alpha }_s$ and ${\alpha }_t^2$
• Higgs Mass Predictions in the CP-Violating High-Scale NMSSM
• New Tools for Dissecting the General 2HDM