TSpectrum and something else

oh and I recommend in general to compile the code, it will quickly reveal
possible C++ issues:

 root [0] .L Multiphoton_spectrum_analysis_asym.C+
 root [1] Multiphoton_spectrum_analysis()

The possible left-side tail could be coming from the experimental setup.
Smaller/lower signals might start your trigger a bit later thereby opening the
integration “gate” to your ADC a bit later, but that is nearly half a century ago for me.