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@ARTICLE{Dao:587976,
      author       = {Dao, Thi Nhung and Gabelmann, Martin and Mühlleitner,
                      Margarete},
      title        = {{T}he ${\mathcal
                      {O}}(\alpha_t+\alpha_\lambda+\alpha_\kappa)^2$ {C}orrection
                      to the $\rho$ {P}arameter and its {E}ffect on the {W}
                      {B}oson {M}ass {C}alculation in the {C}omplex {NMSSM}},
      reportid     = {PUBDB-2023-04637, DESY-23-112. KA-TP-17-2023.
                      arXiv:2308.04059},
      year         = {2023},
      abstract     = {We present the prediction of the electroweak $\rho$
                      parameter and the $W$ boson mass in the CP-violating
                      Next-to-Minimal Supersymmetric extension of the Standard
                      Model (NMSSM) at the two-loop order. The $\rho$ parameter is
                      calculated at the full one-loop and leading and sub-leading
                      two-loop order $\mathcal{O}(\alpha + \alpha_t\alpha_s +
                      \left(\alpha_t+\alpha_\lambda+\alpha_\kappa\right)^2)$. The
                      new $\Delta \rho$ prediction is incorporated into a
                      prediction of $M_W$ via a full supersymmetric (SUSY)
                      one-loop calculation of $\Delta r$. Furthermore, we include
                      all known state-of-the-art SM higher-order corrections to
                      $\Delta r$. By comparing results for $\Delta \rho$ obtained
                      using on-shell (OS) and $\overline{\mathrm{DR}}$
                      renormalization conditions in the top/stop sector, we find
                      that the scheme uncertainty is reduced at one-loop order by
                      55\%, at two-loop $\mathcal{O}(\alpha_s\alpha_t)$ by 22\%,
                      and at two-loop
                      $\mathcal{O}(\alpha_t+\alpha_\kappa+\alpha_\lambda)^2$ by
                      16\%, respectively. The influence of the two-loop results on
                      the $M_W$ mass prediction is found to be sub-leading. The
                      new calculation is made public in the computer program
                      $\mathrm{\tt NMSSMCALC}$. We perform an extensive comparison
                      in the $W$-mass, Higgs boson mass and the muon anomalous
                      magnetic moment prediction between our calculation and three
                      other publicly available tools and find very good agreement
                      provided that the input parameters and renormalization
                      scales are treated in the same way. Finally, we study the
                      impact of the CP-violating phases on the $W$-mass prediction
                      which is found to be smaller than the overall size of the
                      SUSY corrections.},
      keywords     = {boson, mass (INSPIRE) / CP, violation (INSPIRE) /
                      supersymmetry, correction (INSPIRE) / Higgs particle, mass
                      (INSPIRE) / muon, magnetic moment (INSPIRE) / correction,
                      higher-order (INSPIRE) / scale, renormalization (INSPIRE) /
                      minimal supersymmetric standard model (INSPIRE) /
                      electroweak interaction (INSPIRE) / computer (INSPIRE)},
      cin          = {T},
      cid          = {I:(DE-H253)T-20120731},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611) / DFG
                      project G:(GEPRIS)396021762 - TRR 257: Phänomenologische
                      Elementarteilchenphysik nach der Higgs-Entdeckung
                      (396021762) / DFG project G:(GEPRIS)390833306 - EXC 2121:
                      Quantum Universe (390833306)},
      pid          = {G:(DE-HGF)POF4-611 / G:(GEPRIS)396021762 /
                      G:(GEPRIS)390833306},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2308.04059},
      howpublished = {arXiv:2308.04059},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2308.04059;\%\%$},
      doi          = {10.3204/PUBDB-2023-04637},
      url          = {https://bib-pubdb1.desy.de/record/587976},
}