Abstract
We present the calculation of the light neutral CP-even Higgs mass in the MSSM for a heavy SUSY spectrum by resumming enhanced terms through fourth logarithmic order (N^{3}LL), keeping terms of leading order in the top Yukawa coupling alpha _t, and NNLO in the strong coupling alpha _s. To this goal, the three-loop matching coefficient for the quartic Higgs coupling of the SM to the MSSM is derived to order alpha _t^2alpha _s^2 by comparing the perturbative EFT to the fixed-order expression for the Higgs mass. The new matching coefficient is made available through an updated version of the program Himalaya. Numerical effects of the higher-order resummation are studied using specific examples, and sources of theoretical uncertainty on this result are discussed.
Highlights
P Yukawa coupling αt, and NNLO in the strong coupling αs
Higgs coupling of the SM to the MSSM is derived to order αt2 αs2 by comparing the perturbative effective field theory (EFT) to the fixed-order expression for the Higgs mass
Terms of order v 2 /M S2, where M S is the typical SUSY particle mass, are usually neglected in an EFT calculation, which is justified at M S 1 TeV [15]
Summary
As briefly described in the introduction, there are different approximation schemes commonly used to calculate the light. CP-even Higgs boson mass in the MSSM: The fixed-order, the EFT, and the hybrid calculation. The fixed-order calculation includes the SUSY effects through an expansion in terms of couplings up to a fixed order. In this expansion, logarithmic corrections appear, which may be large if there is a large split between the SUSY and the electroweak scale,. We describe both the fixed-order and the EFT calculation in more detail, in order to prepare for the extraction of the three-loop correction to the quartic. Due to the SUSY constraints, Y does not contain a separate parameter for the quartic Higgs coupling
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