Abstract
We present our computation of the mathcal{O} ((αt + αλ + ακ)2) two-loop corrections to the Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric Standard Model (NMSSM) using the Feynman-diagrammatic approach in the gaugeless limit at vanishing external momentum. We choose a mixed overline{mathrm{DR}} -on-shell (OS) renormalisation scheme for the Higgs sector and apply both overline{mathrm{DR}} and OS renormalisation in the top/stop sector. For the treatment of the infrared divergences we apply and compare three different regularisation methods: the introduction of a regulator mass, the application of a small momentum expansion, and the inclusion of the full momentum dependence. Our new corrections have been implemented in the Fortran code NMSSMCALC that computes the Higgs mass spectrum of the CP-conserving and CP-violating NMSSM as well as the Higgs boson decays including the state-of-the-art higher-order corrections. Our numerical analysis shows that the newly computed corrections increase with rising λ and κ, remaining overall below about 3% compared to our previously computed mathcal{O} (αt(αt + αs)) corrections, in the region compatible with perturbativity below the GUT scale. The renormalisation scheme and scale dependence is of typical two-loop order. The impact of the CP-violating phases in the new corrections is small. We furthermore show that the Goldstone Boson Catastrophe due to the infrared divergences can be treated in a numerically efficient way by introducing a regulator mass that approximates the momentum-dependent results best for squared mass values in the permille range of the squared renormalisation scale. Our results mark another step forward in the program of increasing the precision in the NMSSM Higgs boson observables.
Highlights
The Standard Model (SM) of particle physics belongs to the most successful theories ever tested
We present our computation of the O((αt + αλ + ακ)2) two-loop corrections to the Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric Standard Model (NMSSM) using the Feynman-diagrammatic approach in the gaugeless limit at vanishing external momentum
We address the issue of IR divergences in the CP-conserving and CP-violating NMSSM in the Feynman-diagrammatic approach going beyond the limit of vanishing/small external momentum expansion while using an OS scheme for the electroweak vacuum expectation value (VEV), the charged Higgs boson as well as an OS or DR scheme in the top/stop sector and discuss our practical treatment in the code NMSSMCALC
Summary
The Standard Model (SM) of particle physics belongs to the most successful theories ever tested. We provide the two-loop corrections controlled by the NMSSM superpotential parameters λ and κ using the diagrammatic approach in the mixed DR-OS scheme of NMSSMCALC, that was missing in our previous calculations of O(αt2) [59] These corrections can be important for light singlet-like Higgs boson states as well as for the doublet-like states in case of large singlet-doublet mixings. We address the issue of IR divergences in the CP-conserving and CP-violating NMSSM in the Feynman-diagrammatic approach going beyond the limit of vanishing/small external momentum expansion while using an OS scheme for the electroweak VEV, the charged Higgs boson as well as an OS or DR scheme in the top/stop sector and discuss our practical treatment in the code NMSSMCALC.
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