LUX likelihood and limits on spin-independent and spin-dependent WIMP couplings with LUXCalc

We present LUXCalc, a new utility for calculating likelihoods and deriving weakly interacting massive particle (WIMP)-nucleon coupling limits from the recent results of the LUX direct search dark matter experiment. After a brief review of WIMP-nucleon scattering, we derive LUX limits on the spin-dependent WIMP-nucleon couplings over a broad range of WIMP masses, under standard assumptions on the relevant astrophysical parameters. We find that, under these and other common assumptions, LUX excludes the entire spin-dependent parameter space consistent with a dark matter interpretation of DAMA’s anomalous signal, the first time a single experiment has been able to do so. We also revisit the case of spin-independent couplings, and demonstrate good agreement between our results and the published LUX results. Finally, we derive constraints on the parameters of an effective dark matter theory in which a spin-1 mediator interacts with a fermionic WIMP and Standard Model fermions via axial-vector couplings. A detailed appendix describes the use of LUXCalc with standard codes to place constraints on generic dark matter theories.

Figure 1

Spin-independent cross-section constraints for the LUX experiment. Constraints are generated with and without background subtraction: a Poisson-based analysis with one observed event and 0.64 expected background events is used in the former case (dashed black), while the maximum gap method is used in the latter case (solid black); see the text for details. For comparison, the official LUX Collaboration constraints are also shown (red), based upon an event-likelihood analysis. All constraints are at the 90% C.L.; cross sections above the curves are excluded at greater than this level.

Figure 2

Spin-independent cross-section constraints from various direct searches. Parameters that can reproduce the CoGeNT (90% C.L.), CRESST ($2\sigma$), and DAMA ($3\sigma$) anomalous signals are shown in the filled regions. SuperCDMS and LUX exclusion constraints are shown at the 90% C.L. The LUX maximum gap constraints (solid black) are shown with nuclear recoil spectra limited to $E>0$, 1, 2, 3 keV (strongest to weakest). The official LUX limit used a conservative 3 keV minimum.

Figure 3

Spin-dependent WIMP-neutron cross-section constraints for the neutron-only coupling case.

Figure 4

Spin-dependent WIMP-proton cross-section constraints for the proton-only coupling case, including indirect search limits from the IceCube/DeepCore experiment. Note the IceCube/DeepCore $W^{+}{W}^{-}$ constraint uses the tau channel for masses smaller than that of the $W$ boson.

Figure 5

Constraints on the parameters of the effective Lagrangian given in Eq. (24) for a 25 GeV Dirac WIMP. The LUX SDn limit obtained by LUXCalc is shown in black, with coupling values above the black line excluded for a given mediator mass. Also shown are the results of a previous analysis utilizing the XENON100 SDn limit (green line) [79], The red line shows the parameter values required to obtain the correct DM relic density (${\mathrm{\Omega }}_{\mathrm{DM}}=0.268_{-0.010}^{+0.013}$) as measured by WMAP and Planck [79, 81].

Figure 6

Similar to Fig. 5 but for a Majorana WIMP.