  A low energy theory of suspended carbon nanotube quantum dots in weak
tunnelling coupling with metallic leads is presented. The focus is put on the
dependence of the spectrum and the Franck-Condon factors on the geometry of the
junction including several vibronic modes. The relative size and the relative
position of the dot and its associated vibrons strongly influence the
electromechanical properties of the system. A detailed analysis of the complete
parameters space reveals different regimes: in the short vibron regime the
tunnelling of an electron into the nanotube generates a plasmon-vibron
excitation while in the long vibron regime polaron excitations dominate the
scenario. The small, position dependent Franck-Condon couplings of the small
vibron regime convert into uniform, large couplings in the long vibron regime.
Selection rules for the excitations of the different plasmon-vibron modes via
electronic tunnelling events are also derived.
