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On the Importance of Inelastic Interactions in Direct Dark Matter Searches

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Abstract

The approach proposed earlier for describing the scattering of weakly interacting nonrelativistic massive neutral particles off nuclei is used as the basis to derive explicit expressions for the event counting rate expected in experiments aimed at directly detecting dark matter (DM) particles. These expressions make it possible to estimate the rates in question with allowance for both elastic (coherent) and inelastic (incoherent) channels of DM particle interaction with a target nucleus. Within this approach, the effect of a nonzero excitation energy of the nucleus involved is taken into account for the first time in calculating the contribution of inelastic processes. A correlation between the excitation energy and admissible values of the kinetic recoil energy of the excited nucleus constrains substantially the possibility of detection of the inelastic channel with some nuclei. In addition to the standard model of the DM distribution in the Milky Way Galaxy, the effect of some other models that allow significantly higher velocities of DM particles is considered. A smooth transition from the dominance of the elastic channel of the DM particle–nucleus interaction to the dominance of its inelastic channel occurs as the nuclear recoil energy \(T_{A}\) grows. If the DM detector used is tuned to detecting elastic-scattering events exclusively, then it cannot detect anything in the case where the nuclear recoil energy turns out to be below the the detection threshold. As \(T_{A}\) grows, such a detector loses the ability to see anything, since elastic processes quickly become nonexistent. Radiation associated with the deexcitation of the nucleus becomes the only possible signature of the interaction that occurred. In the case of a spin-independent interaction, the inelastic contribution becomes dominant rather quickly as \(T_{A}\) grows, while the differential event counting rate decreases insignificantly. If a DM particle interacts with nucleons via a spin-dependent coupling exclusively, detectors traditionally set up to detect an elastic spin-dependent DM signal will be unable to to see anything since the signal entirely goes through the inelastic channel. It looks like the sought interactions of DM particles may have a sizable intensity, but the instrument is unable to detect them.

Therefore, experiments aimed at directly detecting DM particles should be planned in such a way that it would be possible to detect simultaneously two signals—that of the recoil energy of the nucleus involved and that of gamma rays having a specific energy and carrying away its excitation. A experiment in this implementation will furnish complete information about the DM interaction that occurred.

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Notes

  1. One needs precision low-background and low-threshold detectors and a protection from a multitude of various background processes. The interaction probability is low, and so is the event counting rate. Therefore, events should be accumulated for years. The uncertainty in the distribution of DM particles is large both in the Milky Way Galaxy and in the immediate vicinity of the Earth. The occurrence of the interaction of DM particles with one target type does not guarantee their interaction with another type if for no other reason than the difference in the nucleon and spin composition.

  2. Indeed, we have \(T_{A^{*}}^{\textrm{max}}=T_{\chi}^{\textrm{max}}\mu_{A}-\dfrac{2r\Delta\varepsilon_{mn}}{1+r}=T_{\chi}^{\textrm{max}}\mu_{A}\Big{(}1-\dfrac{\Delta\varepsilon_{mn}}{T_{\chi}^{\textrm{max}}}\dfrac{(r+1)}{2}\Big{)}\simeq T_{\chi}^{\textrm{max}}\mu_{A}\), since \(\mu_{A}=\dfrac{4r}{(1+r)^{2}}\)

  3. Here, there is no the counting rate for coherent events, \(R_{\text{coh}}\), in the case of rather heavy nuclei.

  4. This is so because \(\dfrac{m_{\chi}c^{2}}{2}\Big{(}\dfrac{v_{0}}{c}\Big{)}^{2}=\dfrac{1}{2}\Big{[}\dfrac{m_{\chi}}{1\text{ GeV}}\Big{]}\Big{[}\dfrac{220\text{ km/s}}{300\times 10^{3}\text{ km/s}}\Big{]}^{2}\times 10^{6}\text{ keV}\simeq 0.269\Big{[}\dfrac{rm_{A}}{1\text{ GeV}}\Big{]}\text{ keV}\).

  5. If \(\omega>1\), then, at the above values of \(m_{A}\), \(m_{\chi}\), \(\eta\), and \(\Delta\varepsilon_{mn}\), an incoherent process is impossible.

  6. As a matter of fact, this distinction stems from a smaller value of the ratio \(\dfrac{m_{A}}{\Delta\varepsilon_{mn}}\) for \({}^{19}\)F and \({}^{69}\)Ga than for \({}^{131}\)Xe and \({}^{73}\)Ge, respectively, despite a relatively small difference in the excitation energy of the first level.

  7. this ‘‘classic’’ inelastic approach should not be confused with ‘‘inelasticity’’ associated with the transition of a \(\chi_{1}\) lepton (dark matter) incident to the nucleus to a more massive \(\chi_{2}\) lepton (also belonging to the dark sector). Concurrently, it is assumed that the nucleus involved undergoes no change—that is, it interacts coherently (see, for example, [23, 24, 35, 38, 40, 43, 44, 108]).

  8. the relativistic version of this description was considered in [98].

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ACKNOWLEDGMENTS

I am grateful to D.V. Naumov, E.A. Yakushev, N.A. Rusakovich, and I.V. Titkova for discussions, enlightening comments, and help in the preparation of the manuscript for publication.

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Bednyakov, V.A. On the Importance of Inelastic Interactions in Direct Dark Matter Searches. Phys. Atom. Nuclei 86, 1196–1231 (2023). https://doi.org/10.1134/S1063778823060078

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