Absence of permanent dipole transitions in HD$^{+}$ strong-field dissociation

One of the important questions in strong-field molecular physics is: \textit{what is the role of the permanent electric dipole moment of heteronuclear molecules in dissociation?} Recently Kiess \textit{et al}. [Phys. Rev. A \textbf{77}, 053401 (2008)] reported the first exciting evidence for direct two-photon dissociation of an HD$^{+}$ beam involving its permanent dipole moment, using 790 nm, 100 fs laser pulses. However, the measurement was hampered by the fact that the H$^{+ }$(H) and D$^{+ }$(D) fragments could not be well resolved. Using coincidence 3D-momentum imaging we clearly separate and distinguish all fragments in our measurement. Thus, it allows us to determine that the small peak observed and assigned to two-photon dissociation by Kiess \textit{et al}. is instead due to strong bond-softening in the one-photon dissociation. We find no evidence to support the elusive direct two-photon dissociation at 790 nm in the intensity range 5$\times $10$^{12}$ -- 2$\times $10$^{15}$ W/cm$^{2}$.