Inelastic charged current interaction of supernova neutrinos in two-phase liquid xenon dark matter detectors

It has been known that neutrinos from supernova (SN) bursts can give rise to nuclear recoil (NR) signals arising from coherent elastic neutrino-nucleus scattering (CE$\nu$NS) interaction, a neutral current (NC) process, of the neutrinos with xenon nuclei in future large (multi-ton scale) liquid xenon (LXe) detectors employed for dark matter search, depending on the SN progenitor mass and distance to the SN. In this paper, we show that the same detectors will also be sensitive to inelastic charged current (CC) interactions of the SN electron neutrinos ($\nu_e$CC) with the xenon nuclei. Such interactions, while creating an electron in the final state, also leave the post-interaction target nucleus in an excited state, the subsequent deexcitation of which produces, among other particles, gamma rays and neutrons. The electron and deexcitation gamma rays will give ``electron recoil" (ER) type signals, while the deexcitation neutrons produce, through their multiple scattering on the xenon nuclei, further xenon nuclear recoils that will also give NR signals (in addition to those produced through the CE$\nu$NS interactions). We discuss the observable scintillation and ionization signals associated with SN neutrino induced CE$\nu$NS and $\nu_e$CC events in a generic LXe detector and argue that upcoming sufficiently large LXe detectors should be able to detect both these types of events due to neutrinos from reasonably close by SN bursts. We also note that since the total CC induced ER and NR signals receive contributions predominantly from $\nu_e$CC interactions while the CE$\nu$NS contribution comes from NC interactions of {\emph all the six species of neutrinos}, identification of the $\nu_e$CC and CE$\nu$NS origin events may offer the possibility of extracting useful information about the distribution of the total SN explosion energy going into different neutrino flavors.Comment: Replaced with revised version; new references; new figures, 13 two-column Latexed pages; 11 captioned figures (total 15 individual figures); matches version accepted for publication in PR