Abstract
Higher-order corrections to the MSSM Higgs-boson masses are desirable for accurate predictions currently testable at the LHC. By comparing the prediction with the measured value of the discovered Higgs signal, viable parameter regions can be inferred. For an improved theory accuracy, we compute all two-loop corrections involving the strong coupling for the Higgs-boson mass spectrum of the MSSM with complex parameters. Apart from the dependence on the strong coupling, these contributions depend on the weak coupling and Yukawa couplings, leading to terms of mathcal {O}{left( alpha alpha _sright) } and mathcal {O}{left( sqrt{alpha _{q_1}}sqrt{alpha _{q_2}}alpha _sright) }, (q_{1,2}=t,b,c,s,u,d). The full dependence on the external momentum and all relevant mass scales is taken into account. The calculation is performed in the Feynman-diagrammatic approach which is flexible in the choice of the employed renormalization scheme. For the phenomenological results presented here, a renormalization scheme consistent with higher-order corrections included in the code FeynHiggs is adopted. For the evaluation of the results, a total of 513 two-loop two-point integrals with up to five different mass scales are computed fully numerically using the program SecDec. A comparison with existing results in the limit of real parameters and/or vanishing external momentum is carried out, and the impact on the lightest Higgs-boson mass is discussed, including the dependence on complex phases. The new results will be included in the public code FeynHiggs.
Highlights
The full dependence on the external momentum and all relevant mass scales is taken into account
Thereby the Higgs sector is C Pconserving at the tree level, but potentially large loop contributions involving complex parameters from other supersymmetric (SUSY) sectors can lead to an admixture of the C Peven states h, H, and the C P-odd A resulting in the mass eigenstates h1, h2, h3 [6,7,8,9,10]
A large amount of work has been invested into calculating higher-order corrections to the mass spectrum within the MSSM with real parameters [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67] as well as the MSSM with complex parameters [6,7,8,9,10,65,66,67,68,69,70,71,72,73,74,75,76]
Summary
The requirement of minimizing VH at the vacuum expectation values v1 and v2 is equivalent to the requirement of vanishing tadpoles of the physical fields, which in turn implies the condition ξ = 0 at tree level. The Higgs sector of the MSSM is C P-conserving at lowest order. This implies in Eq (2.2) that Mφχ is equal to zero, and φ1,2 do not mix with χ1,2 at tree-level. The remaining (2 × 2)-matrices Mφ, Mχ , Mφ± can be transformed into the mass eigenstate basis with the help of orthogonal matrices D(x), using the abbreviations sx ≡ sin x, cx ≡ cos x, VH = −Th h − TH H − TA A − TG G
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