Dark matter effective field theory scattering in direct detection experiments

We examine the consequences of the effective field theory (EFT) of dark matter–nucleon scattering for current and proposed direct detection experiments. Exclusion limits on EFT coupling constants computed using the optimum interval method are presented for SuperCDMS Soudan, CDMS II, and LUX, and the necessity of combining results from multiple experiments in order to determine dark matter parameters is discussed. We demonstrate that spectral differences between the standard dark matter model and a general EFT interaction can produce a bias when calculating exclusion limits and when developing signal models for likelihood and machine learning techniques. We also discuss the implications of the EFT for the next-generation (G2) direct detection experiments and point out regions of complementarity in the EFT parameter space.

Figure 1

Upper limits on the dimensionless isoscalar coefficients $c_3^0$ (left) and $c_8^0$ (right) as a function of WIMP mass for SuperCDMS Soudan (light blue) [10], CDMS II Ge reanalysis (dark blue) [29], and CDMS II Si (red) [30], and estimated limits for LUX (black) [11], for the Maxwellian halo (solid) and an alternate halo model (dashed).

Figure 2

Polar limits on ${\mathcal{O}}_1$ isospin for SuperCDMS Soudan (blue) [10], LUX [11] (black), and CDMS II Si (red) [30] at a WIMP mass of $6\mathrm{GeV}/c^2$.

Figure 3

Coadded energy spectrum from 100 simulated experiments (blue histogram) assuming the dark matter interaction proceeds according to the isoscalar ${\mathcal{O}}_3$ operator for a $10\mathrm{GeV}/c^2$ (left) and a $300\mathrm{GeV}/c^2$ WIMP (right). The detection efficiency is assumed to be independent of energy. The smooth cyan, magenta, and black curves show the expected spectrum for the standard spin-independent rate for several WIMP masses, while the dashed dark blue curve shows the ${\mathcal{O}}_3$ spectrum from which the simulated experiments were sampled.

Figure 4

Distribution of 90% confidence level upper limits calculated using the optimum interval method for the simulated experiments discussed in Sec. 3 and shown in Fig. 3, sampled from the event rate for isoscalar ${\mathcal{O}}_3$. Shaded blue bands show the 68% and 95% confidence level uncertainty on the distribution. The zero-background Poisson limit is shown in magenta.

Figure 5

Constructive interference eigenvectors for 2D ${\mathcal{O}}_4$ isospin interference. Proton-dominated interactions occur along the $x=y$ diagonal, while neutron-dominated interactions occur along the $x=-y$ diagonal.

Figure 6

Constructive interference eigenvectors for 4D ${\mathcal{O}}_8/{\mathcal{O}}_9$ interference.

Figure 7

Differential event rate evaluated at the ${\mathcal{O}}_8/{\mathcal{O}}_9$ constructive interference vector from Fig. 6 for fluorine (top) and germanium (bottom).

Figure 8

Relative event rates for LZ (black), SuperCDMS SNOLAB Ge iZIP (blue), and SuperCDMS SNOLAB Si (red), normalized to 1 observed event in SuperCDMS Ge ($3\mathrm{GeV}/c^2$) or LZ (10, $300\mathrm{GeV}/c^2$). From left to right are shown the rates for a 3, 10, and $300\mathrm{GeV}/c^2$ WIMP, assuming isoscalar interactions and the standard Maxwellian halo model. The $3\mathrm{GeV}/c^2$ case also shows the rates from SuperCDMS SNOLAB Ge high voltage (light blue), which has similar parameters to SuperCDMS Si high voltage, but a target mass of 6 kg. The top row shows cumulative event rates, while the bottom row shows events per time per target mass. True interaction strengths may differ from this calculation since the interaction may proceed via a linear combination of operators.

Figure 9

Event rate suppression relative to ${\mathcal{O}}_1$ scattering in LZ (black), SuperCDMS SNOLAB Ge iZIP (blue), and SuperCDMS SNOLAB Si (red) for interference in germanium, with interference ranging from constructive (left) to maximally destructive (right), as determined by the magnitude of the corresponding eigenvalue. The rate for SuperCDMS SNOLAB Ge high voltage (light blue) is shown for the $3\mathrm{GeV}/c^2$ case where LZ sees no events above threshold. The seven operator-operator interference cases are shown, as well as pure isoscalar ${\mathcal{O}}_1$, which is used as a reference point.