Atomic ionization by sterile-to-active neutrino conversion and constraints on dark matter sterile neutrinos with germanium detectors

The transition magnetic moment of a sterile neutrino can give rise to its conversion to an active neutrino through radiative decay or nonstandard interaction (NSI) with matter. For sterile neutrinos of keV-mass as dark matter candidates, their decay signals are actively searched for in cosmic x-ray spectra. In this work, we consider the NSI that leads to atomic ionization, which can be detected by direct dark matter experiments. It is found that this inelastic scattering process for a nonrelativistic sterile neutrino has a pronounced enhancement in the differential cross section at energy transfer about half of its mass, manifesting experimentally as peaks in the measurable energy spectra. The enhancement effects gradually smear out as the sterile neutrino becomes relativistic. Using data taken with low-threshold low-background germanium detectors, constraints on sterile neutrino mass and its transition magnetic moment are derived and compared with those from astrophysical observations.

Figure 1

Left: The radiative decay of a sterile neutrino to an active neutrino where the shaded circle represents its transition magnetic moment. Right: The atomic ionization induced by the transition magnetic moment of a sterile neutrino where the intermediate photon is virtual.

Figure 2

The differential scattering cross sections of nonrelativistic sterile neutrinos ($v_s=10^{-3}$) and hydrogen atoms through the transition magnetic moment ${\mu }_{{\nu }_{\mathrm{sa}}}$ with selected $m_s$.

Figure 3

The differential scattering cross sections of relativistic sterile neutrinos ($m_s=7.1\mathrm{keV}$) and hydrogen atoms through the transition magnetic moment ${\mu }_{{\nu }_{\mathrm{sa}}}$ with selected $E_s$.

Figure 4

The differential scattering cross section of nonrelativistic sterile neutrinos ($v_s=10^{-3}$) and germanium atoms through the transition magnetic moment ${\mu }_{{\nu }_{\mathrm{sa}}}$ with selected $m_s$.

Figure 5

The differential scattering cross section of relativistic sterile neutrinos and germanium atoms through the transition magnetic moment ${\mu }_{{\nu }_{\mathrm{sa}}}$ with $m_s=7.1\mathrm{keV}$ and $E_{\nu }=1\mathrm{MeV}$ (solid line). For comparison, the results of free electron approximation (dashed line) and the nonrelativistic case with $v_s=10^{-3}$ (dotted line) are also shown.

Figure 6

Experimental data and analysis: (a) Measured spectrum of germanium detector at KSNL. All peaks can be accounted for by internal and ambient radioactivity. (b) The zoomed energy range relevant to a ${\nu }_s$ with $m_s=7.1\mathrm{keV}$. The spectrum due to ${\mu }_{{\nu }_{\mathrm{sa}}}=2.5\times {10}^{-14}{\mu }_{\mathrm{B}}$ excluded at 90% C.L. is superimposed.

Figure 7

Exclusion curve at 90% C.L. for the absolute value of the transition magnetic moment of sterile neutrinos, based on reactor neutrino data of Fig. 6.