Top Yukawa-Coupling Enhanced Two-Loop Corrections to the Masses of the Higgs Bosons in the MSSM with CP Violation

Recent results for the leading $\mathcal{O}{\left(\alpha_t^2\right)}$ two-loop corrections to the Higgs-boson masses of the MSSM with complex parameters are presented. The strategy of the Feynman-diagrammatic, analytical calculation is illustrated. Numerical analyses show agreement with a previous result in the limit of real parameters. Furthermore, the newly available dependence on complex MSSM parameters is investigated. Mass shifts by $\approx 1$GeV for different phases underline the importance of this contribution for a precise prediction of the Higgs-boson mass spectrum in the MSSM.Comment: 4 pages, 2 figures. Contribution to the proceedings of Toyama International Workshop on Higgs as a Probe of New Physics (HPNP2015), 11.--15. February 2015, Toyama, Japa

Two-loop top-Yukawa-coupling corrections to the Higgs boson masses in the complex MSSM

Results for the leading two-loop corrections of $\mathcal{O}{\left(\alpha_t^2\right)}$ from the Yukawa sector to the Higgs-boson masses of the MSSM with complex parameters are presented. The corresponding self-energies and their renormalization have been obtained in a Feynman-diagrammatic approach. A numerical analysis of the new contributions is performed for the mass of the lightest Higgs boson, supplemented by the full one-loop result and the $\mathcal{O}{\left(\alpha_t \alpha_s\right)}$ terms including complex phases. In the limit of the real MSSM a previous result is confirmed.Comment: 13 pages, 7 figure

Two-loop top and bottom Yukawa corrections to the Higgs-boson masses in the complex MSSM

Results for the two-loop corrections to the Higgs-boson masses of the MSSM with complex parameters of $\mathcal{O}{\left(\alpha_t^2+\alpha_t\alpha_b+\alpha_b^2\right)}$ from the Yukawa sector in the gauge-less limit are presented. The corresponding self-energies and their renormalization have been obtained in the Feynman-diagrammatic approach. The impact of the new contributions on the Higgs spectrum is investigated. Furthermore, a comparison with an existing result in the limit of the MSSM with real parameters is carried out. The new results will be included in the public code $\texttt{FeynHiggs}$.Comment: 15 pages, 9 figure

Implementation of the O(αt2)\mathcal{O}{\left(\alpha_t^2\right)} MSSM Higgs-mass corrections in FeynHiggs\tt{FeynHiggs}

We describe the implementation of the two-loop Higgs-mass corrections of $\mathcal{O}{\left(\alpha_t^2\right)}$ in the complex MSSM in $\tt{FeynHiggs}$. The program for the calculation is included in $\tt{FeynHiggs}$ and documented here in some detail such that it can be re-used as a template for similar calculations.Comment: 12 pages, 1 figur

Towards Higgs masses and decay widths satisfying the symmetries in the (N)MSSM

In models with an extended Higgs sector, such as the (N)MSSM, scalar states mix with one another. Yet, the concept of Higgs mixing is problematic at the radiative level, since it introduces both a scheme and a gauge dependence. In particular, the definition of Higgs masses and decay amplitudes can be impaired by the presence of gauge-violating pieces of higher order. We discuss in depth the origin and magnitude of such effects and suggest two strategies preserving or restoring gauge invariance. In addition, the intuitive concept of mixing and the simplicity of its definition in terms of two-point diagrams can make it tempting to include higher-order corrections on this side of the calculation, irrespectively of the order achieved in vertex diagrams. Using the global $SU(2)_{\mathrm{L}}$-symmetry in the decoupling limit, we show that no improvement can be expected from such an approach at the level of the Higgs decays, but that, on the contrary, the higher-order terms may lead to numerically large spurious effects.Comment: 49 pages, 12 figures, version accepted by EPJ

Two-loop top-Yukawa-coupling corrections to the charged Higgs-boson mass in the MSSM

The top-Yukawa-coupling enhanced two-loop corrections to the charged Higgs-boson mass in the real MSSM are presented. The contributing two-loop self-energies are calculated in the Feynman- diagrammatic approach in the gaugeless limit with vanishing external momentum and bottom mass, within a renormalization scheme comprising on-shell and $\overline{\text{DR}}$ conditions. Numerical results illustrate the effect of the $\mathcal{O}{(\alpha_t^2)}$ contributions and the importance of the two-loop corrections to the mass of the charged Higgs bosons.Comment: 12 pages, 5 figure

All two-loop scalar self-energies and tadpoles in general renormalisable field theories

We calculate the complete tadpoles and self-energies at the two-loop order for scalars in general renormalisable theories, a crucial component for calculating two-loop electroweak corrections to Higgs-boson masses or for any scalar beyond the Standard Model. We renormalise the amplitudes using mass-independent renormalisation schemes, based on both dimensional regularisation and dimensional reduction. The results are presented here in Feynman gauge, with expressions for all 121 self-energy and 25 tadpole diagrams given in terms of scalar and tensor integrals with the complete set of rules to reduce them to a minimal basis of scalar integrals for any physical kinematic configuration. In addition, we simplify the results to a set of only 16 tadpole and 58 self-energy topologies using relations in order to substitute the ghost and Goldstone-boson couplings that we derive. To facilitate their application, we also provide our results in electronic form as a new code TLDR. We test our results by applying them to the Standard Model and compare with analytic expressions in the literature.Comment: 76 pages, 5 figure