Decays of a NMSSM CP-odd Higgs in the low-mass region

A popular regime in the NMSSM parameter space involves a light CP-odd Higgs $A_1$. This scenario has consequences for e.g. light singlino Dark Matter annihilating in the $A_1$-funnel. In order to confront the pseudoscalar to experimental limits such as flavour observables, Upsilon decays or Beam-Dump experiments, it is necessary to control the interactions of this particle with hadronic matter and derive the corresponding decays. The partonic description cannot be relied upon for masses close to $m_{A_1}\sim1$GeV and we employ a chiral lagrangian, then extended to a spectator model for somewhat larger masses, to describe the interplay of the CP-odd Higgs with hadrons. Interestingly, a mixing can develop between $A_1$ and neutral pseudoscalar mesons, leading to substantial hadronic decays and a coupling of $A_1$ to the chiral anomaly. Additionally, quartic $A_1$-meson couplings induce tri-meson decays of the Higgs pseudoscalar. We investigate these effects and propose an estimate of the Higgs widths for masses below $m_{A_1}\leq3$GeV. While we focus on the case of the NMSSM, our results are applicable to a large class of models.