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

Higgs-mass predictions in the MSSM and beyond

“…In 2020, Ref. [248] computed the O(y 4 t g 2 s ) contributions to λ i for arbitrary complex values of all of the relevant parameters, as well as the O(y 6 t ) contributions in the limit of degenerate stop masses.…”

“…The contribution to λ from twoloop diagrams involving the heavier Higgs doublet and top quarks was subsequently computed in Ref. [248]. After the RG evolution of the quartic coupling down to the EW scale, typically at Q = M t , the mass of the lighter Higgs boson can be computed including the known SM results for the radiative corrections.…”

“…The matching conditions for the quartic Higgs couplings of the 2HDM also include the two-loop O(y 4 t g 2 s ) and O(y 6 t ) contributions from Ref. [248]. • FlexibleSUSY contains several modules for the EFT calculation of the MSSM Higgs masses.…”

Resummation of terms enhanced by trilinear squark-Higgs couplings in the MSSM

“…For further details in the case of a 2-loop matching of Green functions, see ref. [16]. Here, we want to illuminate some aspects of IR-regularization by small mass terms and DREG/ DRED in the context of the broken and the unbroken phase.…”

“…Interestingly, the measured value M h = (125.10 ± 0.14 GeV) [1,2] lies in the mass range that can be accommodated by SUSY models, however it typically requires a rather heavy SUSY particle spectrum. Hence many recent precision calculations of the Higgs boson mass utilized EFT methods [3][4][5][6][7][8][9][10][11][12][13][14][15][16] including hybrid methods which combine EFT and fixed-order calculations [17][18][19][20][21][22][23][24][25][26][27][28][29][30], see refs. [31,32] for recent reviews.…”