Detectors based upon the noble elements, especially liquid xenon as well as liquid argon, as both single- and dual-phase types, require reconstruction of the energies of interacting particles, both in the field of direct detection of dark matter (weakly interacting massive particles WIMPs, axions, etc.) and in neutrino physics. Experimentalists, as well as theorists who reanalyze/reinterpret experimental data, have used a few different techniques over the past few decades. In this paper, we review techniques based on solely the primary scintillation channel, the ionization or secondary channel available at non-zero drift electric fields, and combined techniques that include a simple linear combination and weighted averages, with a brief discussion of the application of profile likelihood, maximum likelihood, and machine learning. Comparing results for electron recoils (beta and gamma interactions) and nuclear recoils (primarily from neutrons) from the Noble Element Simulation Technique (NEST) simulation to available data, we confirm that combining all available information generates higher-precision means, lower widths (energy resolution), and more symmetric shapes (approximately Gaussian) especially at keV-scale energies, with the symmetry even greater when thresholding is addressed. Near thresholds, bias from upward fluctuations matters. For MeV-GeV scales, if only one channel is utilized, an ionization-only-based energy scale outperforms scintillation; channel combination remains beneficial. We discuss here what major collaborations use.
Design of Low-energy Calibration Sources for Liquid Xenon Dark Matter Detectors