It has been recently argued that the HCN J=1--0 line emission may not be an unbiased tracer of dense molecular gas ($rm nga 10^4 cm^{-3}$) in Luminous Infrared Galaxies (LIRGs: $rm L_{FIR}> 10^{11} L_{odot}$) and HCO$^+$ J=1--0 may constitute a better tracer instead (Gracia-Carpio et al. 2006), casting doubt into earlier claims supporting the former as a good tracer of such gas (Gao & Solomon 2004; Wu et al. 2006). In this paper new sensitive HCN J=4--3 observations of four such galaxies are presented, revealing a surprisingly wide excitation range for their dense gas phase that may render the J=1--0 transition from either species a poor proxy of its mass. Moreover the well-known sensitivity of the HCO$^+$ abundance on the ionization degree of the molecular gas (an important issue omitted from the ongoing discussion about the relative merits of HCN and HCO$^+$ as dense gas tracers) may severely reduce the HCO$^+$ abundance in the star-forming and highly turbulent molecular gas found in LIRGs, while HCN remains abundant. This may result to the decreasing HCO$^+$/HCN J=1--0 line ratio with increasing IR luminosity found in LIRGs, and casts doubts on the HCO$^+$ rather than the HCN as a good dense molecular gas tracer. Multi-transition observations of both molecules are needed to identify the best such tracer, its relation to ongoing star formation, and constrain what may be a considerable range of dense gas properties in such galaxies.
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