Two-loop $$ \mathcal{O} $$ ($$ {\alpha}_t^2 $$) corrections to the neutral Higgs boson masses in the CP-violating NMSSM

Abstract

We present our calculation of the two-loop corrections of O(α 2 t ) to the neutral Higgs boson masses of the CP-violating Next-to-Minimal Supersymmetric extension of the Standard Model (NMSSM). The calculation is performed in the Feynman diagrammatic approach in the gaugeless limit at vanishing external momentum. We apply a mixed DR-on-shell (OS) renormalization scheme for the NMSSM input parameters. Furthermore, we exploit a DR as well as an OS renormalization in the top/stop sector. The corrections are implemented in the Fortran code NMSSMCALC for the calculation of the Higgs spectrum both in the CP-conserving and CP-violating NMSSM. The code also provides the Higgs boson decays including the state-of-the-art higher-order corrections. The corrections computed in this work improve the already available corrections in NMSSMCALC which are the full one-loop corrections without any approximation and the two-loop O(α t α s ) corrections in the gaugeless limit and at vanishing external momentum. Depending on the chosen parameter point, we find that the O(α t α s + α 2 t ) corrections add about 4-7% to the one-loop mass of the SM-like Higgs boson for DR renormalization in the top/stop sector and they reduce the mass by about 6-9% if OS renormalization is applied. For an estimate of the theoretical uncertainty we vary the renormalization scale and change the renormalization scheme and show that care has to be taken in the corresponding interpretation. *

Precise prediction for the Higgs-Boson masses in the $${\varvec{\mu }}{\varvec{\nu }}$$SSM with three right-handed neutrino superfields

“…[87]. According to a comparison of the various two-loop contributions, at present the theoretical uncertainties from unknown higher-order corrections in the NMSSM are expected to be still larger than for the MSSM [92][93][94].…”

“…A two-loop calculation of the O(α t α s ) corrections with the top/stop sector renormalized in the OS scheme or in the DR scheme was provided in Ref. [91], while the two-loop corrections of O(α 2 t ) in the CP-violating NMSSM were calculated in a mixed OS-DR scheme [92]. These contributions are implemented in the public code NMSSMCalc.…”

One-loop corrections to the two-body decays of the charged Higgs bosons in the real and complex NMSSM

“…In this section, we briefly introduce the model and set up the notation used throughout the paper. Our notation and conventions follow those already used and explained in detail in our previous works [45][46][47][48][50][51][52]56]. We work in the frame-work of the scale-invariant NMSSM, in which the superpotential is constrained by a Z 3 symmetry.…”

“…Following Refs. [47,[50][51][52], we set the phases of the Yukawa couplings to zero and rephase the left-and right-handed up-quark fields as u L → e −iϕ u u L and u R → e iϕ u u R , so that the quark and lepton mass terms yield real masses. Inserting Eq.…”

“…The one-loop corrections are based on the renormalization schemes that we have introduced and applied in Refs. [45,47,[50][51][52]. In particular, we use a mixed DR-OS scheme in the Higgs sector and have the possibility to choose between OS and DR renormalization in the electroweakino sector and in the squark and slepton sectors.…”