  Recent experiments have reported the emergence of high temperature
superconductivity with critical temperature $T_c$ between 43K and 123K in a
potassium doped aromatic hydrocarbon para-Terphenyl or p-Terphenyl. This
achievement provides the record for the highest Tc in an organic superconductor
overcoming the previous record of Tc=38 K in Cs3C60 fulleride. Here we propose
that the driving mechanism is the quantum resonance between superconducting
gaps near a Lifshitz transition which belongs to the class of Fano resonances
called shape resonances. For the case of p-Terphenyl our numerical solutions of
the multi gap equation shows that high Tc is driven by tuning the chemical
potential by K doping and it appears only in a narrow energy range near a
Lifshitz transition. At the maximum critical temperature, Tc=123K, the
condensate in the appearing new small Fermi surface pocket is in the BCS-BEC
crossover while the Tc drops below 0.3 K where it is in the BEC regime. Finally
we predict the experimental results which can support or falsify our proposed
mechanism: a) the variation of the isotope coefficient as a function of the
critical temperature and b) the variation of the gaps and their ratios
2Delta/Tc as a function of Tc.
