[Paper Review] Low energy binding of composite dark matter with nuclei as a solution for the puzzles of dark matter searches

Maxim Khlopov, A. G. Mayorov+1 more|ArXiv.org|Nov 30, 2009

Dark Matter and Cosmic Phenomena22 references3 citations

TL;DR

This paper proposes that composite dark matter in the form of O-helium (OHe) — a bound state of a doubly charged particle and helium — can explain the annual modulation signal observed in the DAMA/NaI and DAMA/LIBRA experiments. By solving the Schrödinger equation for OHe interacting with sodium and iodine nuclei via a Yukawa-type nuclear potential and Coulomb repulsion, the authors show that binding energies in the 2–6 keV range are possible under plausible nuclear parameters, leading to ionization signals matching DAMA’s observed modulation, while suppressing signals in other detectors like CDMS due to energy suppression and dipole barriers.

ABSTRACT

Positive results of dark matter searches in experiments DAMA/NaI and DAMA/LIBRA taken together with negative results of other groups can imply nontrivial particle physics solutions for cosmological dark matter. Stable particles with charge -2 bind with primordial helium in O-helium "atoms" (OHe), representing a specific Warmer than Cold nuclear-interacting form of dark matter. Slowed down in the terrestrial matter, OHe is elusive for direct methods of underground Dark matter detection like those used in CDMS experiment, but its low energy binding with nuclei can lead to annual variations of energy release in the interval of energy 2-6 keV in DAMA/NaI and DAMA/LIBRA experiments. Schrodinger equation for system of nucleus and OHe is solved for a spherically symmetrical potential, formed by the Yukawa tail of nuclear scalar isoscalar attraction potential, acting on He beyond the nucleus, and dipole Coulomb repulsion between the nucleus and OHe at distances from the nuclear surface, smaller than the size of OHe. The values of coupling strength and mass of meson, mediating scalar isoscalar, are rather uncertain. Within the uncertainties of parameters of nuclear potential we find a range of these parameters, at which the sodium and/or iodine nuclei have a few keV binding energy with OHe. At nuclear parameters, reproducing DAMA results, the energy release predicted for detectors with chemical content other than NaI differ in the most cases from the one in DAMA detector. In particular, it is shown that in the case of CDMS germanium state has binding energy with OHe beyond the range of 2-6 keV and its formation should not lead to ionization in the energy range of DAMA signal. (abridged)

Motivation & Objective

• To resolve the long-standing discrepancy between positive DAMA/NaI and DAMA/LIBRA results and negative results from other direct detection experiments.
• To explore whether composite dark matter, specifically O-helium (OHe), can account for the observed annual modulation in the energy range 2–6 keV.
• To investigate the conditions under which OHe forms low-energy bound states with sodium and iodine nuclei, consistent with DAMA’s signal.
• To predict the existence of anomalous superheavy isotopes of Na and I, which could serve as a testable signature of the OHe scenario.
• To assess the viability of OHe as a non-thermal, nuclear-interacting dark matter candidate that avoids overproduction of anomalous hydrogen/helium isotopes.

Proposed method

• Modeling the OHe-nucleus system as a spherically symmetric potential with a Yukawa-tail nuclear scalar interaction and a dipole Coulomb repulsion at short distances.
• Reducing the Schrödinger equation to a radial form for relative motion and solving it in four regions: inside OHe, in the nuclear potential well, in the intermediate region, and in the external classically forbidden region.
• Using a rectangular potential well approximation for the nuclear potential to simplify the solution and explore parameter space.
• Applying boundary conditions on logarithmic derivatives of the wavefunction at the interfaces between regions to determine bound state energies.
• Calculating the binding energy of OHe with Na and I nuclei by solving the system of transcendental equations derived from continuity conditions.
• Assessing the suppression of transitions to higher-energy states due to the dipole Coulomb barrier, which explains the absence of signal in other energy ranges.

Experimental results

Research questions

• RQ1 Can O-helium (OHe) form bound states with sodium and iodine nuclei at binding energies of 2–6 keV, consistent with the DAMA signal?
• RQ2 Why do other direct detection experiments like CDMS not observe a signal, despite detecting OHe, if OHe binds to nuclei?
• RQ3 How does the dipole Coulomb barrier suppress transitions to higher-energy states, explaining the absence of high-energy ionization signals?
• RQ4 What are the implications for the abundance of anomalous superheavy isotopes of sodium and iodine in DAMA detectors under the OHe scenario?
• RQ5 Can the annual modulation in the DAMA signal be explained by the Earth’s motion modulating the flux of OHe, leading to time-dependent capture rates?

Key findings

• Within uncertainties in nuclear parameters and under the rectangular well approximation, OHe can form bound states with sodium and/or iodine nuclei at binding energies in the 2–6 keV range, matching the DAMA signal window.
• The dipole Coulomb barrier strongly suppresses transitions to higher-energy states, explaining why no significant ionization signal is observed outside the 2–6 keV range in DAMA.
• In detectors like CDMS, which use germanium, the OHe binding energy with the nucleus lies outside the 2–6 keV range, and its formation does not lead to ionization in that energy window.
• The model predicts the formation of anomalous superheavy isotopes of sodium and iodine, with mass increased by approximately the OHe mass, which could be detectable via mass spectrometry.
• The relaxation time for OHe concentration in underground detectors is on the order of minutes, allowing the annual modulation of the incoming flux to be rapidly reflected in the capture rate.
• The proposed mechanism provides a consistent explanation for the DAMA signal while remaining compatible with the null results from other experiments, due to energy suppression and detector-specific nuclear response.