The usual assumption in direct dark matter searches is to only consider the spin-dependent or spin-independent scattering of dark matter particles. However, especially in models with light dark matter particles $\mathcal{O}(\mathrm{GeV/c^2})$, operators which carry additional powers of the momentum transfer $q^2$ can become dominant. One such model based on asymmetric dark matter has been invoked to overcome discrepancies in helioseismology and an indication was found for a particle with preferred mass of 3 $\mathrm{GeV/c^2}$ and cross section of $10^{-37} \mathrm{cm^2}$. Recent data from the CRESST-II experiment, which uses cryogenic detectors based on $\mathrm{CaWO_4}$ to search for nuclear recoils induced by dark matter particles, are used to constrain these momentum-dependent models. The low energy threshold of 307 eV for nuclear recoils of the detector used, allows us to rule out the proposed best fit value above.
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