Matching renormalisable couplings: simple schemes and a plot

Abstract

We discuss different choices that can be made when matching a general high-energy theorywith the restriction that it should not contain heavy gauge bosons -onto a general renormalisable effective field theory at one loop, with particular attention to the quartic scalar couplings and Yukawa couplings. This includes a generalisation of the counterterm scheme that was found to be useful in the case of high-scale/split supersymmetry, but we show the important differences when there are new heavy scalar fields in singlet or triplet representations of SU (2). We also analytically compare our methods and choices with the approach of matching pole masses, proving the equivalence with one of our choices. We outline how to make the extraction of quartic couplings using pole masses more efficient, an approach that we hope will generalise beyond one loop. We give examples of the impact of different scheme choices in a toy model; we also discuss the MSSM and give the threshold corrections to the Higgs quartic coupling in Dirac gaugino models.

Full two-loop QCD corrections to the Higgs mass in the MSSM with heavy superpartners

“…large enough to allow for m h ≈ 125 GeV. Other recent developments of the EFT approach include: the study of MSSM scenarios in which both Higgs doublets are light, so that the effective theory valid below the SUSY scale is a two-Higgs-doublet model (THDM) [67,68,76]; the application of functional techniques to the full one-loop matching of the MSSM onto the SM [91]; the calculation of one-loop matching conditions between the couplings of two generic renormalizable theories [92,93], which can then be adapted to SUSY (or non-SUSY) models other than the MSSM. In this paper we focus again on the simplest EFT setup in which the theory valid below the SUSY scale is the SM, and we take a further step towards the full NNLL resummation of the large logarithmic corrections.…”

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

“…In the limit m → 0, infrared divergences appear in the calculation. These cancel out in the difference between the results in the HET and the EFT (for an extensive discussion at the one-loop level see [31]).…”

“…Also generally applicable formulas for the derivation of one-loop matching conditions have been derived. While in recent years, most efforts concentrated on the one-loop matching of higher-dimensional operators has been considered in [17][18][19][20][21][22][23][24][25][26][27][28][29][30], also the one-loop matching of renormalizable operators [31,32] can provide information about the HET. In contrast, no general two-loop results are available yet.…”

“…The matching conditions for the EFT parameters can be derived in different ways. One possibility is to use the effective action: the integral over the "heavy" degrees of freedom in the path integral can be performed explicitly; alternatively, the effective action can be calculated up to the quartic order, and after that, equations of motions can be used to integrate out the "heavy" fields (see [31] for a detailed discussion of these approaches at the one-loop level). Instead of employing the effective action, we focus in this paper on the diagrammatic method restricting us to the matching of renormalizable operators.…”

Improved MSSM Higgs mass calculation using the 3-loop FlexibleEFTHiggs approach including xt-resummation

“…There are different approaches to calculate the Higgs boson mass in supersymmetric models, which can be roughly classified into fixed-order , 1 EFT [40][41][42][43][44][45][46][47][48][49][50][51], and hybrid [52][53][54][55][56][57][58][59][60][61] approaches, which combine the virtues of the former two. Fixed-order approaches truncate the perturbation series at a certain order in loops and couplings, neglecting in particular large logarithmic corrections arising at higher orders.…”