Tetraphenyl-butadiene is the wavelength shifter most widely used in combination with liquid argon. The latter emits scintillation photons with a wavelength of 127 nm that need to be downshifted to be detected by photomultipliers with glass or quartz windows. Tetraphenyl-butadiene has been demonstrated to have an extremely high conversion efficiency, possibly higher than 100% for 127 nm photons, while there is no precise information about the time dependence of its emission. It is usually assumed to be exponentially decaying with a characteristic time of the order of one ns, as an extrapolation from measurements with exciting radiation in the near UV. This work shows that tetraphenyl-butadiene, when excited by 127 nm photons, re-emits photons not only with a very short decay time, but also with slower ones due to triplet states de-excitations. This fact can strongly contribute to clarifying the anomalies in liquid-argon scintillation light reported in the literature since the 1970s, namely, the inconsistency in the measured values of the long decay time constant and the appearance of an intermediate component. Similar effects should be also expected when the TPB is used in combination with helium and neon, which emit scintillation photons with wavelengths shorter than 127 nm.