Testing variants of the Diósi–Penrose collapse model with public XENONnT data, and heating predictions of a parameter-free model with a phonon-scale cutoff

Predictions of the Diósi–Penrose (DP) gravity-related collapse model depend strongly on the mass-density smoothing length R₀ and on the frequency spectrum of the gravitational fluctuations. We reanalyze the public low-energy electronic-recoil data of XENONnT (1–30 keV, 433 events, 1.16 t·yr) with an unbinned likelihood and report four results. First, when R₀ exceeds the atomic size, the equivalence principle makes the nucleus and its electrons accelerate together, and low-energy X-ray emission is strongly cancelled (about 2×10⁻⁴ at 1 keV and 0.16 at 10 keV for xenon). Including this screening, the bound on the white-noise DP model is R₀ > ~0.9 nm, much weaker than the unscreened value (~4.0 nm). Second, the reported bound R₀ > 2.8 nm of an earlier collapse analysis of XENONnT data appears to differ from the Majorana analysis in signal normalization by a factor π^(3/2). With the same normalization it corresponds to 1.56 nm, in agreement with the 1.52 nm we obtain under the same conditions. Third, an 'atomic-unit' variant, with R₀ set to the atomic radius and the fluctuation cutoff set to the electronic time scale, cannot be decided with these data: its verdict ranges from allowed (prediction/limit 0.006) to excluded (11) depending on how strongly the electrons co-move with the nucleus. Fourth, a parameter-free 'phonon-unit' variant, with both R₀ and the cutoff fixed by the lattice vibration of the same nucleus (Debye–Waller rms displacement and Debye frequency), passes the X-ray data independently of the screening treatment and predicts spontaneous heating of about 9.4 pW/kg in copper at cryogenic temperature. This lies just below the currently known unexplained heat-leak limit (~10 pW/kg). X-rays cannot separate the two variants; the (atomic mass × Debye temperature)^(3/2) heating scaling predicted by the phonon-unit variant can be tested by comparing heat leaks in tungsten and aluminium (a factor of about 16).