  It has been recently argued that the HCN J=1--0 line emission may not be an
unbiased tracer of dense molecular gas ($\rm n\ga 10^4 cm^{-3}$) in Luminous
Infrared Galaxies (LIRGs: $\rm L_{FIR}> 10^{11} L_{\odot}$) and HCO$^+$ J=1--0
may constitute a better tracer instead (Graci\'a-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.
