Higher Order Corrections to the Trilinear Higgs Self-Couplings in the Real NMSSM

Abstract

After the discovery of a Higgs-like boson by the LHC experiments ATLAS and CMS, it is of crucial importance to determine its properties in order to not only identify it as the boson responsible for electroweak symmetry breaking but also to clarify the question if it is a Standard Model (SM) Higgs boson or the Higgs particle of some extension beyond the SM as {\it e.g.} supersymmetry. In this context, the precise prediction of the Higgs parameters as masses and couplings play a crucial role for the proper distinction between different models. In extension of previous works on the loop-corrected Higgs boson masses of the Next-to-Minimal Supersymmetric Extension of the SM (NMSSM), we present here the calculation of the loop-corrected trilinear NMSSM Higgs self-couplings. The loop corrections turn out to have a substantial impact on the decay widths of Higgs-to-Higgs decays and on the production cross section of Higgs pairs via gluon fusion. They are therefore indispensable for the correct interpretation of the experimental Higgs results.

Figures (9)

• Figure 1: Generic Feynman diagrams contributing to the 1-point irreducible vertex functions. They are grouped by loops over scalars ($S$), vector bosons ($V$), fermions ($f$) and ghost particles ($\eta$).
• Figure 2: Generic one-loop Feynman diagrams involving $A_l Z$ and $A_l G$ transitions contributing to $\delta M^{G,Z \, \text{mix}}$.
• Figure 3: Normalised deviation of the trilinear Higgs self-coupling of the SM-like NMSSM Higgs boson, here $H_1=h$, from the corresponding SM coupling, $\Delta \lambda^\text{eff}/\lambda^\text{eff}_{\text{SM}}$, with $\Delta \lambda^\text{eff}= \lambda^\text{eff}_{hhh} -\lambda^\text{eff}_{\text{SM}}$, as a function of the singlet admixture squared of $H_1$, $(R_{13}^{S})^2$, both for tree-level and one-loop corrected self-couplings. In this figure $A_t$ is varied such that $H_1$ is kept SM-like according to our definitions in subsection \ref{['sect-constraints']}. The remaining parameters have been chosen as given in Eqs. (\ref{['eq:param1']})-(\ref{['eq:param4']}). The $\overline{\text{DR}}$ renormalised parameters are taken at the renormalisation scale, $\mu_{R}=M_{\text{SUSY}}=700\,~\text{GeV}$.
• Figure 4: Absolute value of $\Delta \lambda^\text{eff}/\lambda^\text{eff}_{\text{SM}}$ for tree-level couplings (dashed) and one-loop corrected couplings (full) as a function of the tree-level lightest CP-odd Higgs mass $m_{a_1}$ for a 125 GeV $H_1$ (left) and as a function of the tree-level lightest CP-even Higgs mass $m_{h_1}$ for a 125 GeV $H_2$ (right). The scales on top of each figure refer to the loop-corrected mass $M_{A_1}$ (left) and $M_{H_1}$ (right). The parameters have been chosen as specified in Eqs. (\ref{['eq:param1']})-(\ref{['eq:param4']}), and the renormalisation scale has been set $\mu_{R}=M_{\text{SUSY}}=700\,~\text{GeV}$.
• Figure 5: The branching ratio of heavier CP-even Higgs bosons, $H_2$ or $H_3$, decaying into two SM-like Higgs bosons at loop level versus the tree-level branching ratio, for scenarios with $h\equiv H_1$ (case 1), $h\equiv H_2$ (case 2, scen1, scen2) as well as $H_1$ and $H_2$ close in mass near 125 GeV (case 3). The difference between the one-loop and the tree-level branching ratio is quantified by $\delta \equiv (\text{BR}^{\text{loop}}-\text{BR}^{\text{tree}})/\text{BR}^{\text{tree}}$. The colored areas refer to different ranges of $\delta$.