Observing the Migdal effect from nuclear recoils of neutral particles with liquid xenon and argon detectors

In recent years, dark matter direct detection experiments have spurred interest in the Migdal effect, where it is employed to extend their sensitivity to lower dark matter masses. Given the lack of observation of the Migdal effect, the calculation of the signal is subject to large theoretical uncertainties. It is therefore desirable to attempt a first measurement of the Migdal effect, and to test the theoretical predictions of the Migdal effect for the calibration of the experimental response to a potential dark matter signal. In this work, we explore the feasibility of observing the Migdal effect in xenon and argon. We carry out proof-of-concept calculations for low-energy neutrons from a filtered source, and using a reactor, the Spallation Neutron Source, or ${}^{51}\mathrm{Cr}$ as potential neutrino sources. We perform a detector simulation for the xenon target and find that, with available technology, the low-energy neutron source is the most promising, requiring only a modest neutron flux, detector size, and exposure period.

Figure 1

The elastic (solid) and neutron capture (dotted) cross sections in the lab frame for neutrons scattering on xenon (left) and argon (right), as a function of the incoming neutron energy. For xenon, a weighted average was taken over the naturally occurring isotopes. Data obtained from [24] with line widths characteristic of 300 K.

Figure 2

The total elastic (black), Migdal (blue) and neutron capture (red) rates in xenon (left) and argon (right), as a function of the incoming neutron energy with a flux of $100\mathrm{neutrons}/{\mathrm{cm}}^2/\mathrm{s}$ (with the spectrum assumed to be a $\delta$ function at each energy). Line widths are characteristic of 300 K. The rates are integrated above three different benchmark detector thresholds: none, low (Xe: $1{\mathrm{keV}}_{\mathrm{NR}}$, Ar: $10{\mathrm{keV}}_{\mathrm{NR}}$) and high (Xe: $5{\mathrm{keV}}_{\mathrm{NR}}$, Ar: $20{\mathrm{keV}}_{\mathrm{NR}}$), shown in solid, dotted and dashed respectively. The gray vertical lines correspond to potential neutron beam energies of (17, 24, 47, 59, 82) keV, from left to right.

Figure 3

The spectra of neutrino energies for the three neutrino sources considered in this work.

Figure 4

The integrated rate of neutrino induced nuclear recoils (dashed) and Migdal events (solid) in xenon (left) and argon (right) from three neutrino sources: nuclear reactors, the SNS and chromium-51.

Figure 5

Cross sectional geometry of a liquid xenon TPC (not to scale), where cylindrical symmetry is assumed. Dimensions for the detector modeled in this work are given in Table 2.

Figure 6

The 1 and $2\sigma$ confidence regions for NR and Migdal events in the S1-S2 plane for the four sources considered in this work. The overlayed dots show events from a representative exposure: $1\mathrm{kg}\text{−}\mathrm{day}$ for neutrons, and ${10}^{-1}\mathrm{tonne}\text{−}\mathrm{years}$ for reactor neutrinos, ${10}^{-2}\mathrm{tonne}\text{−}\mathrm{years}$ for SNS neutrinos and $10\mathrm{tonne}\text{−}\mathrm{years}$ for chromium neutrinos.

Figure 7

The differential nuclear recoil and Migdal scattering rates for 17 keV neutrons as a function of detected energy. The Migdal rate is given separately for each atomic shell, $n$.

Figure 8

The differential nuclear recoil and Migdal scattering rates for reactor neutrinos as a function of detected energy. The Migdal rate is given separately for each atomic shell, $n$.

Figure 9

The differential nuclear recoil and Migdal scattering rates for SNS neutrinos as a function of detected energy. The Migdal rate is given separately for each atomic shell, $n$.

Figure 10

The differential nuclear recoil and Migdal scattering rates for chromium neutrinos as a function of detected energy. The Migdal rate is given separately for each atomic shell, $n$.

Figure 11

Top: the rate of prompt (blue) and delayed (red) gamma-ray emission following neutron capture in xenon, data from [42]. Bottom: the rate of electron capture and $\beta$ decays of unstable xenon isotopes that accumulate over time due to neutron capture.

Figure 12

Top: the $\beta$ decay spectra from the three relevant xenon isotopes, data from [43]. Bottom: the simulated S1-log(S2) distribution of ${}^{133}\mathrm{Xe}$ $\beta$ decay events based on $1\mathrm{kg}\text{−}\mathrm{day}$ of exposure at the steady state background rate (after $\sim 20\mathrm{days}$ of continuous beam).

Figure 13

Comparison of $\gamma$ (red) and $\beta$ (blue) charge yield at $V=180\mathrm{V}/\mathrm{cm}$ in NESTv2.3 with data from LUX’s electron capture calibration (green) [44]. Errors correspond to statistical and systematic errors summed in quadrature.